From 65ad771827e2af51be02a33a0762bca09552c89e Mon Sep 17 00:00:00 2001 From: Artur Torun Date: Fri, 15 Jul 2022 19:04:22 +0100 Subject: [PATCH] Initial commit --- .gitignore | 10 + .vscode/launch.json | 166 +++ .vscode/settings.json | 1 + CHANGELOG.md | 5 + Doc/LinearRGB Approximations.ipynb | 327 +++++ Doc/approx-quality.png | Bin 0 -> 116068 bytes LICENSE | 21 + Package.swift | 95 ++ README.md | 494 ++++++++ Sources/Colorful/colorgens.swift | 56 + Sources/Colorful/colors.swift | 1087 +++++++++++++++++ Sources/Colorful/happy_palettegen.swift | 22 + Sources/Colorful/hsluv.swift | 209 ++++ Sources/Colorful/soft_palettegen.swift | 221 ++++ Sources/Colorful/sort.swift | 194 +++ Sources/Colorful/warm_palettegen.swift | 21 + Sources/Demos/Benchmark/main.swift | 77 ++ Sources/Demos/ColorBlend/clamped.png | Bin 0 -> 6305 bytes Sources/Demos/ColorBlend/clamped.xcf | Bin 0 -> 22625 bytes Sources/Demos/ColorBlend/colorblend.png | Bin 0 -> 2268 bytes Sources/Demos/ColorBlend/invalid.png | Bin 0 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mode 100644 .gitignore create mode 100644 .vscode/launch.json create mode 100644 .vscode/settings.json create mode 100644 CHANGELOG.md create mode 100644 Doc/LinearRGB Approximations.ipynb create mode 100644 Doc/approx-quality.png create mode 100644 LICENSE create mode 100644 Package.swift create mode 100644 README.md create mode 100644 Sources/Colorful/colorgens.swift create mode 100644 Sources/Colorful/colors.swift create mode 100644 Sources/Colorful/happy_palettegen.swift create mode 100644 Sources/Colorful/hsluv.swift create mode 100644 Sources/Colorful/soft_palettegen.swift create mode 100644 Sources/Colorful/sort.swift create mode 100644 Sources/Colorful/warm_palettegen.swift create mode 100644 Sources/Demos/Benchmark/main.swift create mode 100644 Sources/Demos/ColorBlend/clamped.png create mode 100644 Sources/Demos/ColorBlend/clamped.xcf create mode 100644 Sources/Demos/ColorBlend/colorblend.png create mode 100644 Sources/Demos/ColorBlend/invalid.png create mode 100644 Sources/Demos/ColorBlend/invalid.xcf create mode 100644 Sources/Demos/ColorBlend/main.swift create mode 100644 Sources/Demos/ColorDist/colordist.png create mode 100644 Sources/Demos/ColorDist/colordist.xcf create mode 100644 Sources/Demos/ColorDist/main.swift create mode 100644 Sources/Demos/ColorGens/colorgens.png create mode 100644 Sources/Demos/ColorGens/main.swift create mode 100644 Sources/Demos/ColorSort/colorsort.png create mode 100644 Sources/Demos/ColorSort/main.swift create mode 100644 Sources/Demos/GradientGen/gradientgen.png create mode 100644 Sources/Demos/GradientGen/main.swift create mode 100644 Sources/Demos/PaletteGens/main.swift create mode 100644 Sources/Demos/PaletteGens/palettegens.png create mode 100644 Sources/Demos/Shared/shared.swift create mode 100644 Tests/ColorfulTests/Resources/hsluv-snapshot-rev4.json create mode 100644 Tests/ColorfulTests/swift_colorfulTests.swift create mode 100644 Tests/ColorfulTests/swift_hsluvTests.swift create mode 100644 Tests/ColorfulTests/swift_sortTests.swift diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..deba8bf --- /dev/null +++ b/.gitignore @@ -0,0 +1,10 @@ +.DS_Store +/.build +/Packages +/*.xcodeproj +xcuserdata/ +DerivedData/ +.swiftpm/config/registries.json +.swiftpm/xcode/package.xcworkspace/contents.xcworkspacedata +.netrc +**/zzzTrash \ No newline at end of file diff --git a/.vscode/launch.json b/.vscode/launch.json new file mode 100644 index 0000000..7b57d4c --- /dev/null +++ b/.vscode/launch.json @@ -0,0 +1,166 @@ +{ + "configurations": [ + { + "type": "lldb", + "request": "launch", + "name": "Debug swift-colorful", + "program": ".build/debug/swift-colorful", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Debug swift-colorful" + }, + { + "type": "lldb", + "request": "launch", + "name": "Release swift-colorful", + "program": ".build/release/swift-colorful", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Release swift-colorful" + }, + { + "type": "lldb", + "request": "launch", + "name": "Debug DemoColorBlend-macOS", + "program": ".build/debug/DemoColorBlend-macOS", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Debug DemoColorBlend-macOS" + }, + { + "type": "lldb", + "request": "launch", + "name": "Release DemoColorBlend-macOS", + "program": ".build/release/DemoColorBlend-macOS", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Release DemoColorBlend-macOS" + }, + { + "type": "lldb", + "request": "launch", + "name": "Debug DemoColorDist-macOS", + "program": ".build/debug/DemoColorDist-macOS", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Debug DemoColorDist-macOS" + }, + { + "type": "lldb", + "request": "launch", + "name": "Release DemoColorDist-macOS", + "program": ".build/release/DemoColorDist-macOS", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Release DemoColorDist-macOS" + }, + { + "type": "lldb", + "request": "launch", + "name": "Debug DemoShared", + "program": ".build/debug/DemoShared", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Debug DemoShared" + }, + { + "type": "lldb", + "request": "launch", + "name": "Release DemoShared", + "program": ".build/release/DemoShared", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Release DemoShared" + }, + { + "type": "lldb", + "request": "launch", + "name": "Debug DemoColorGens-macOS", + "program": ".build/debug/DemoColorGens-macOS", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Debug DemoColorGens-macOS" + }, + { + "type": "lldb", + "request": "launch", + "name": "Release DemoColorGens-macOS", + "program": ".build/release/DemoColorGens-macOS", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Release DemoColorGens-macOS" + }, + { + "type": "lldb", + "request": "launch", + "name": "Debug DemoGradientGen-macOS", + "program": ".build/debug/DemoGradientGen-macOS", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Debug DemoGradientGen-macOS" + }, + { + "type": "lldb", + "request": "launch", + "name": "Release DemoGradientGen-macOS", + "program": ".build/release/DemoGradientGen-macOS", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Release DemoGradientGen-macOS" + }, + { + "type": "lldb", + "request": "launch", + "name": "Debug DemoPaletteGens-macOS", + "program": ".build/debug/DemoPaletteGens-macOS", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Debug DemoPaletteGens-macOS" + }, + { + "type": "lldb", + "request": "launch", + "name": "Release DemoPaletteGens-macOS", + "program": ".build/release/DemoPaletteGens-macOS", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Release DemoPaletteGens-macOS" + }, + { + "type": "lldb", + "request": "launch", + "name": "Debug DemoColorSort-macOS", + "program": ".build/debug/DemoColorSort-macOS", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Debug DemoColorSort-macOS" + }, + { + "type": "lldb", + "request": "launch", + "name": "Release DemoColorSort-macOS", + "program": ".build/release/DemoColorSort-macOS", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Release DemoColorSort-macOS" + }, + { + "type": "lldb", + "request": "launch", + "name": "Debug Benchmark-macOS", + "program": ".build/debug/Benchmark-macOS", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Debug Benchmark-macOS" + }, + { + "type": "lldb", + "request": "launch", + "name": "Release Benchmark-macOS", + "program": ".build/release/Benchmark-macOS", + "args": [], + "cwd": "${workspaceFolder:swift-colorful}", + "preLaunchTask": "swift: Build Release Benchmark-macOS" + } + ] +} \ No newline at end of file diff --git a/.vscode/settings.json b/.vscode/settings.json new file mode 100644 index 0000000..9e26dfe --- /dev/null +++ b/.vscode/settings.json @@ -0,0 +1 @@ +{} \ No newline at end of file diff --git a/CHANGELOG.md b/CHANGELOG.md new file mode 100644 index 0000000..c57d6a9 --- /dev/null +++ b/CHANGELOG.md @@ -0,0 +1,5 @@ +Please check original project CHANGELOG first: +https://github.com/lucasb-eyer/go-colorful/blob/master/CHANGELOG.md + +# Changelog +All notable changes to this project will be documented in this file. diff --git a/Doc/LinearRGB Approximations.ipynb b/Doc/LinearRGB Approximations.ipynb new file mode 100644 index 0000000..9c3c7ad --- /dev/null +++ b/Doc/LinearRGB Approximations.ipynb @@ -0,0 +1,327 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Taylor approximations to color conversion" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This notebook shows how to come up with all these magic constants that appear in the approximations to `LinearRgb` in my [go-colorful](https://github.com/lucasb-eyer/go-colorful) library in order to speed them up at almost no loss in accuracy.\n", + "\n", + "The gist is to compute a Taylor expansion up to a degree that gives enough accuracy.\n", + "Taylor expansions work well for relatively linear-ish functions, as `LinearRgb` is.\n", + "\n", + "Doing this is especially easy thanks to the SymPy library which has symbolic Taylor expansion built-in!" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2017-08-26T21:02:11.366875Z", + "start_time": "2017-08-26T21:02:11.352525Z" + }, + "collapsed": true + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "import matplotlib as mpl\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('ggplot')\n", + "\n", + "import numpy as np\n", + "\n", + "from sympy import *\n", + "init_printing()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following is the conversion from RGB to linear RGB (aka. gamma-correction), where I'm dropping the conditional part for very small values of `x` as a first approximation." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "ExecuteTime": { + "end_time": "2017-08-26T21:02:11.703826Z", + "start_time": "2017-08-26T21:02:11.698713Z" + }, + "collapsed": true + }, + "outputs": [], + "source": [ + "def linear_rgb(x):\n", + " return ((x+0.055)/1.055)**2.4" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, we can use SymPy to create a symbolic version of that equation, and compute a symbolic Taylor expansion around $0.5$ (the middle of our target range) up to the fourth degree:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2017-08-26T21:04:49.413810Z", + "start_time": "2017-08-26T21:04:48.874572Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/latex": [ + "$$-0.248750514614486 + 1.16740237321695 \\left(x - 0.5\\right)^{2} + 0.280457026598666 \\left(x - 0.5\\right)^{3} + 0.925583310193438 x + \\mathcal{O}\\left(\\left(x - 0.5\\right)^{4}; x\\rightarrow 0.5\\right)$$" + ], + "text/plain": [ + " 2 \n", + "-0.248750514614486 + 1.16740237321695⋅(x - 0.5) + 0.280457026598666⋅(x - 0.5)\n", + "\n", + "3 ⎛ 4 ⎞\n", + " + 0.925583310193438⋅x + O⎝(x - 0.5) ; x → 0.5⎠" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = Symbol('x', real=True)\n", + "series(linear_rgb(x), x, x0=0.5, n=4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to use it numerically, we will \"drop the O\", which means do the actual approximation, and \"lambdify\" the function, which turns a symbolic function into a NumPy function:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2017-08-26T21:08:28.502517Z", + "start_time": "2017-08-26T21:08:28.183433Z" + }, + "collapsed": true + }, + "outputs": [], + "source": [ + "fast_linear_rgb = lambdify([x], series(linear_rgb(x), x, x0=0.5, n=4).removeO())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As additional heuristic approximations, we'll include simply squaring the values, which should also be very fast, but quite wrong. Then, plot all these functions in order to see their behaviour, and compute errors:" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": { + "ExecuteTime": { + "end_time": "2017-08-26T21:36:50.404073Z", + "start_time": "2017-08-26T21:36:49.535984Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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z4/cUak3R1Jh5amZN0qy+oWrRjgQjAACAy9UvJzJ04HReFSNPN0PD\n2uRVMTJNU3E7z+e7RCT8qDp+uTK6XOeSOCuqxnxzi42NlSR17NhRlj9kafn4+Kh169bKzs5WfHy8\nK8IDAOCyk5PrkC3bVF3DXTZbrhz5tRsBAAAAACinLKtDP/7vnJKT7M62xld4qtv1fnJ3r/jNq4Ar\nmI5cmQvnyPxqkbOtWbCfXh/VQQ2bRrowMgAAALiSaZpafEEVo0FX1lVd77wNxo4dzlHamVxJkiU3\nWy0PfC5j6GgZltq1m0iVbJdWFU6cOCFJCg8PL/J4WFiYoqOjlZCQoA4dOpQ41jPPPFNk+6xZsyRJ\nISEhFY7z9OnTcncv+rIV134pcnPL+w/dYrE43/fUqVP12GOPKTIystquxeV0jV2B61u9uL7Vi+tb\n9U5lZMnXcJObpLqGu9yzbHL3CSjTay0WS6X+3gIAAAAALh3pZ3O15btzsmaev3mlVXtvtWjrVanq\n+IArZFmtmrtog0Zs36wG+Y1tO8vy0DMyvH1dGRoAAABcbFdSpvYm51UrcrcYurVtXhUju93Unhir\ns98VR1bLp463jG69XBJnZdSYSkaZmZmSJF/foifh+e0ZGRkXLSaUT2hoqFq0aCEPDw9XhwIAqKSc\nXIdsWbly5k6bDnkFsFAGAAAAACif06fs+mHd+QQjw5A6dvNRy3beJBih1jl7Jk3TFm3VWq9meumq\nCUp395XRvY8sk58nwQgAAABaHHO+itGNzeso2Dcvd+Lg3mxlWfO+E3lmp+qKIyvzqhi51a4qRlIN\nqmRUGtPM/xJa+hfP/IpFxUlOTi7xeEkcDofsdnuBtvzqGX9sv5Tl5uaV8brwejz++OP6/PPPtXnz\nZjVq1EiS9Ntvv6lHjx4aNWqUpkyZopkzZ2rTpk3KzMxUq1at9OSTT2rAgAFFnmP58uVauHCh4uLi\nlJWVpcaNG2v48OF66KGH5OXlVaDv6tWrtXLlSu3YsUOJiYkyDEPNmzfXqFGjNG7cuEJb8OXH+uOP\nP2rdunX65JNPdOjQIXXu3FlLliyp6stV412O/w1fTFzf6sX1rR7J52zyNc5PbHzdc+SQpxxlvM4O\nh6PUv7cNGzasVIwAAAAAgJot4ZhN23/KlMOR99zNXepynZ9Cw7lJEbWPmXJKRz/4l/ZHDpckHfcL\n1Y9979WQUYNlWGrM/dwAAABwkbiTmYo9mVetyM2QRrQNlpS3dfT+PVnOfq0OLJV7vboyrunjkjgr\nq8YkGeVXKsqvaPRHVqu1QD/ULseOHdPQoUPVuHFjjRgxQqmpqfrqq680fvx4ffrpp+rZs2eB/lOm\nTNGnn36q8PBwDRkyRHXr1tUvv/yi1157Td9//70+/fTTAlsjzZw5UxaLRZ07d1Z4eLjOnj2rH374\nQS+88IJ27typt99+u8i4XnjhBW3dulU33HCD+vfvXygZCQAuR/Zch3KzJY/f83oNh10+wf7KNc2S\nXwgAAAAAwO8O7ctW7I7z2wF4ehnq3ttPdevVmCVpoMzMY4fleGuG2qSm6LH0LL3R9k6NCUjWTcNu\ncnVoAAAAqCE+i01xPu53RR018M+7uWJvbJZyf7+HPyD9qCJPbJRx78My3Gvnd6MaE3V+NYOEhIQi\njycmJkqSwsPDL1pMqDo//fSTpkyZoieffNLZduutt+quu+7S+++/XyDJ6LPPPtOnn36qIUOG6O23\n35aPj48zoWjWrFl6/fXXFRUVpfvuu8/5mo8++khNmzYtcE6Hw6EnnnhCS5Ys0bhx43T11VcXiis2\nNlZr1qxR48aNq/gdA0DtlZqZK2/jfNKln4c9r1wj1aIAAAAAAKUwTVO/7srSgT3ZzjY/f4u69/GT\nn3/t2woAMPfGyvHuK5I1Q5LU83Scrmh6RpHX93ZxZAAAAKgp9iVbtTMhb75ouaCK0dnUXB09ZHP2\nax3/qYzg+jKu7eeSOKtCjUkyateunSQpOjpaDoejQEUZq9WqPXv2yNPTUy1atHBViKXKnfgnV4dQ\nZm7/XnFRzxcZGanHHnusQFvfvn0VERGhHTt2FGifN2+e3N3dNXv2bPn4+BQ49vjjj2v+/PlatmxZ\ngSSjPyYYSZLFYtF9992nJUuW6Lvvvisyyeihhx4iwQgALmB3mHLknH9u5NrkFRLguoAAAAAAALVG\nbq6p6K2ZOn70/BfLoGA3devlJy8vKoij9tn+3c9qtXi2vG2/78Dg7SPLpGcV2aajawMDAABAjbI4\nNtn5uFeTQDUM9JRpmoqLtkq/bxRSPzla9U/Hyrh7kgz32ruF9EVPMrLb7UpKSpKbm5vCwsKc7WFh\nYerYsaOio6O1Zs0aDRkyxHls8eLFys7O1o033ihvb++LHTKqQLt27eTmVvhOpYYNG+qXX35xPrda\nrYqLi1O9evU0d+5cZ3t+0pnD4ZCXl5fi4+MLjHP69Gm9//77+t///qcjR44U2navuApZnTp1qvB7\nAoBLUVqGXZ4ynM/9PHJkWLjTFAAAAABQshybQz//kKmUk+er4IZGuOvqHn5ydzdKeCVQM321YpPm\nnQ1Wl5aj9czuj+QWWEeWR6fJaHyFq0MDAABADXLwdJZ+Pp5XxciQNLJ9XhWjk4l2nUr8/fuR6VDr\n+E+loBAZ193gokirRpUkGW3dulU///yzJCk1NVWSFB8fr3fffVeSFBAQoHvvvVdSXjLIE088ofr1\n6zuP55swYYKmTp2q+fPnKyYmRpGRkYqPj9fu3bsVHh6uO+64oyrChQsEBgYW2e7u7i6Hw+F8npqa\nKtM0lZKSotdff71MY6elpWno0KE6evSoOnfurJEjR6pu3bpyd3dXWlqa5s2bJ5vNVuRrGzRoUP43\nAwCXKHuuQ7qgipHFbpVbiL/rAgIAAAAA1ArWTIe2bDyn9LTz63xNr/RU+84+MiwkGKF2MU1Te5Z8\nobm2dpIhbQtpq8Vtb9Vddw+WERLq6vAAAABQw1xYxejaxgFqXMdLDoepuJ1WZ3uj4xsUkHFcxrAH\nZHjU3ipGUhUlGR0+fFjfffddgbakpCQlJSVJkurXr+9MMipJWFiYXn31VS1evFg7d+7Ujh07FBQU\npCFDhmjUqFHy96/ZP3Re7C3ILkX5yUjt27fXmjVrnO3u7nn/qdrt9kKvWbRokY4ePaonn3xSU6ZM\nKXBs27ZtmjdvXrHnMwwWOQAg39mMXLn9XsXIlOTnaaeKEQAAAACgRGdTc7Vl4zllWU1nW5urvNW8\ntRdrb6h1THuOzAXvqOXm9bqt2WB90aS/Wmaf1C13/0lGSJCrwwMAAEANcyQ1Wz/9ds75fPTvVYyO\nHrTp3Nm8mzDc7Fa1PPiFVKeejOsHuCTOqlQlSUajR4/W6NGjy9S3QYMGWrx4cbHHQ0JCNGnSpKoI\nC7WQn5+fWrVqpX379unMmTMKCir9i9uhQ4ckSTfddFOhY5s3b67yGAHgUmTPdUj284u/bjkZsoQU\nXYUOAAAAAABJSk7K0c8/ZMj+e1VcwyJ16uaryKaerg0MqAAzK1OOObOkuB2SpLsOrVZQ/SANvHO4\nvP18XBwdAAAAaqIlsSnOx9dE+qtZkLdyckztjc1ytjc//LW8bGdl3HqfDI/a/13J4uoAgD+6//77\nZbPZNGXKFKWlpRU6npqaqpiYGOfzRo0aSZJ++umnAv1iY2P1zjvvVG+wAHCJOHsu1zkpcJim/L1y\nZbhRxQgAAAAAULRjh23avPF8gpG7u9S9tx8JRqiV0k+lKPe155wJRpJk6TVQt4wfTYIRAAAAinT8\nrE3fHz3rfJ5fxWj/r1myZedVevXOSlGzo6ulwLoyeg1ySZxVrUoqGQFV6c9//rN27dqlBQsW6Lrr\nrlPfvn0VGRmp1NRUHTlyRFu2bNHo0aM1a9YsSdLIkSM1Z84cTZs2TT/++KOaNWumQ4cO6dtvv9WQ\nIUO0YgXb2AFASXJyHDJyz1cxcs85K6NuXRdGBAAAAACoqUzT1P492dqz6/ydud4+hq7p5a86Qdys\ngtrn2MHfNOO7E7rerYXu1gFJknHLHTJu+TNb/gEAAKBYS3Yny/H7rtGdw/3UIthHmRkOHdyb7ezT\nav/ncnPkyBh0qwwvLxdFWrVIMkKNNHPmTPXr108ff/yxNm3apLNnz6pu3bqKiIjQgw8+qBEjRjj7\nhoWFadmyZZo5c6a2bt2qDRs26Morr9TMmTPVq1cvkowAoBTnMhzKXzKzmw7V8zaoYgQAAAAAKMR0\nmIrZbtWRAzZnW0CgRd37+MvHl6L5qH2O796j//s5U+medfRFk/4Ktp3VTTdcLUuvga4ODQAAADVY\nYrpNGw6dr2J0++9VjPbsssrhyGurk3ZQDRN/kvwDZfQZ4oowqwVJRqiQRo0a6fjx4wXa3nzzTb35\n5pul9rvQkiVLij02YMAADRgwQJLk7p73n6rdbi+yb8uWLRUVFVXksaLOX1SsAHA5ys52yHCcf+5p\nS5XRINh1AQEAAAAAaiS73dT2nzKUdOL8+lxwA3d16+krD08SjFD7mNE/q/4Hr6llqzv0S3Abeeba\n1OCGgbL0utrVoQEAAKCGWxqX4qxi1CHUV20a+OpMil3Hj+Y4+7SJ/0SGTBkDb5Xh5e2iSKse3/4A\nALhMmaapzMzzGUY2h10BPm5UMQIAAAAAFJCd5dBP688VSDBq2NhD3Xv7kWCEWsmxcY0c774iN1uW\npuxeqK6p+/RyR09dQ4IRAAAASnEqI0f/O5jmfD66fbBM09TunVZnW+jJbaqXuk/yC5DR79KpYiRR\nyQgAgMtWVpYp4/csa1OSjy1VCqrv0pgAAAAAADVLRnquNm/MUOa58zepNG/tpTZXecswjBJeCdQ8\npmnKXLFI5tefOtu869XT8yO6yAiLcGFkAAAAqC2+iEuR/fevR23q+6hDqK8SjuXoTHKuJMlw2NU6\n/rO8xwOGyfD2dVWo1YIkIwAALkMOh6ls6/kF4mxHjur6elDFCAAAAADgdCbFrq2bMmTLNp1t7a/2\nUbMWXi6MCqiYnBy73v90g67a86uuz29s3FyWR1+QUSfIlaEBAACgljhttWvt/oJVjBwO6dddWc62\nJse+lZ81SfL1k9H/ZleEWa1IMgIA4DJkvSDBKFem/GypUlADF0YEAACA2iAlJUWfffaZoqOjlZ6e\nrqCgIHXr1k0jR46Uv79/qa/PysrSzz//rO3bt+vQoUNKSUmRYRhq2LChevbsqSFDhsjdvfTlqiVL\nlmjx4sWSpOeff15XXXVVpd8bgIISj+fol58y5Mi7GVcWN+nqHr4Kj/R0bWBABWRmZOq1xVu03TNS\nG1rfrjq2c+oQESjLg89ccneWAwAAoPosi0tRjiPvJowr63mrc7ifDu7LdlZ+9bBn6sqDX0qSjBuH\nyfC59OaaJBkBAHCZyc01lXPBXajZjhzV8/WiihEAAABKlJiYqKlTpyotLU1du3ZVRESE9u/fr1Wr\nVmnnzp166aWXFBAQUOIYe/bs0dtvvy1/f3+1a9dO3bp107lz5/TLL7/o448/1tatWzV16lR5ehaf\nxHDw4EEtXbpU3t7eysrKKrYfgIo7FJ+t2B3WvL21JXl6Gbrmej8FhbCcjNrHPJsq27t/18ngQZKn\nZLe4a0uHwep45w0yypDYCgAAAEhSapZdq+NTnc9HdwhWjs1U/O5sZ9uVB5bJ054h+fjKuOHSq2Ik\nkWQEAMBlx5p5vopRjkwF2FKleqEujAgAAAC1wbx585SWlqZx48ZpyJAhzvYFCxZo5cqVWrRoke6/\n//4Sx6hbt64mT56sa6+9tkDFIqvVqunTp2vv3r1as2aNbrnlliJfb7PZ9M4776h58+YKCwvTxo0b\nq+bNAZAkmaapX3dl6cCe84vkvv4Wde/tJ/8AbkxB7WOePCHHm9MVcCpRzx8/pr9e/Yhu8Dunu+4Y\nIMNicXV4AAAAqEW+/PW0bLl5d2I0C/LSNRH+2r3DqpycvDbf7GQ1OfatJMnof7MM39IrPtdGzKIB\nALiM5NgcsudcUMUoN1v+fj4yLCwWAwAAoHhJSUmKjo5W/fr1NWjQoALHRo8eLS8vL23atKnUykJN\nmzZVr169Cm2J5uPj40ws2r17d7Gv/+STT3Ty5ElNmjRJhmFU8N0AKEpurqntP2UWSDCqW89N19/g\nT4IRaiXz0D45Xn1aOpUoSWpgO6u3mp7WPbf3l4UEIwAAAJTD2excrdp3vorRqPbByjjn0OH9Nmdb\n6z3/kcXMlbx9ZAwY5oowLwpm0gAAXCZM0yxQxSjLdKhOTroUUMeFUQEAAKA2iI2NlSR17Nix0A+z\nPj4+at26tbKzsxUfH1/hc7j9vn2vWzHb+MbGxuq///2v7rzzTjVs2LDC5wFQmM3m0ObvzunEbznO\nttAId13bz19e3iwho/bZumm74ue8LZ07m9fg6SnLpP9Tnf6DXRsYAAAAaqWv955Wlj3vN7ZGdTx1\nbaMA/RqdJfP3+/rrZRxS6KlfJP1exciv5O3kazO2SwMA4DJhyzbl+D3HyJSU48iWv78P5cEBAABQ\nqhMnTkiSwsPDizweFham6OhoJSQkqEOHDhU6x/r16yVJnTp1KnQsMzNT7733nlq3bl1gq7byeuaZ\nZ4psnzVrliQpJCSkwmO7Un5lqNoa/6WgNn8G6WdztPGbE0o7k+tsa92hjrpfHyKLpXZVDKvNn8Ol\noiZ8Bp9/9l/9M8FPga3v0d92vKtQD4fqPvt3ebau2N+n2qYmfAYAAACXkgxbrr7ec8b5fFS7YJ0+\nlavE4+dv0mgdGyVDkry8Zdx46VYxkqhkBADAZcHhMJVlPV/FKNPMVd2cc5J/oAujAgAAQG2RmZkp\nSfL19S3yeH57RkZGhcZfvXq1du7cqaZNm6pfv36Fjn/44YdKT09nmzSgiiWfzNLKpceUdub84njX\na4PVo1ftSzACTNPU8YXzNPc3NzkMi1K9AvVB+ztU79V/XTYJRgAAAKh6K/edUUZO3m9sDQM81LNx\ngOJ2Wp3HG6ZFq276IUmS0fcmGQGX9m9vVDICAOAykGV1OEs25spUrsNGFSMAAABUGfP3yWZFEoC2\nbNmiqKgo1a1bV1OmTHFWYLjw+MaNGzVhwgSFhoZWKs78ikXFSU5OrtT4rpJfraK2xn8pqI2fQdKJ\nHP3yU4Zy7XnPLRapU3dfhTfOVUpKimuDq6Da+Dlcalz1GZh2u8yP3pH7T//T/9Vpqukd71fj/2fv\nvsObKtsHjn+T7gVdVKAUaMsGKfAWygZR9t7DFxmC4sDF+rkY4iuIIi5EllUEsQVBkNJC2atCUdmi\nlE2hUCjdTdok5/dHTdqQlA4qpXB/rotL85znnOfOk7TNObnP/eTcZmK/YJIdnOERek+U958DWRJV\nCI2kW8MAACAASURBVCGEEA+SzBw9G/9MMj0e1NCLa5d0pkqwapWBusdCczfaO6Dq0q8swryvJMlI\nCCGEeMjpdQrZWsX0OEMx4KFLB697+4JGCCGEEEI8OoyViowVje6UlZVl1q+oDh06xKeffkrFihWZ\nMWOGRRJReno6S5YsoVGjRnTp0qUEkQshrLl4Vsvx37JMN6PY2alo3tYFLx+5XCzKH0WTiWHRh3Dq\nDwAapFxgetoeaj8zCmdXlzKOTgghhBBClGdRfyeTlp1bxcjHxY62fhXYE5Vm2h5wcx9O2twkJFXH\n7qgquJdJnPeTnDUKIYQQDzFFUcjKt0xatqKAQYurq7NUMRJCCCGEEEVmrCpw7do1q9sTEhIAqFKl\nSpGPGRMTw+eff467uzvTp0+3uu/NmzdJS0vjxIkTDB061Opx3n//fQBGjRpFz549izy+EI8iRVE4\nfVxD3J9aU5uTs4qQDq64VbApw8iEKJmkhESUbz7B/fxJU5uqzZM0/u9zqGzl6w8hhBBCCFFyWp2B\nn0/nVTEa3MiLi2ey0WTl3q3hYKMj4Nj3uRvt7FF16V8WYd538u2iKLHly5fTsWNHAgMD8fX1ZenS\npWUdUqE++ugjAgICiI+PL+tQhBCiSN555x0aNGhAUlJS4Z2t0OUo6HLyVTFCj6cuA1wf7vVghRBC\nCCFE6WrYsCEAR48exWAwmG3Lysri9OnT2NvbU7t27SIdb9++fXz22Wd4eHgwc+bMApOTXF1d6dSp\nk9V/xn2aNm1Kp06d8PPzu4dnKMTDz6BX+ONgplmCUUUPG9o+5SYJRqJcuhR3kamR5/ifRyeybOwB\nUPUehmrUK5JgJIQQQggh7tmWuGRSNLnLonk729KqshtxpzWm7XWuRWKrzz2/UnXohqqiR5nEeb9J\nkpEokQ0bNjB9+nQcHBwYN24cb7zxBs2aNftXx9y/fz++vr7Mnz+/RPvHx8fz9ddf8/TTT+Pr61vK\n0ZWNI0eO4Ovry+LFi8s6lIdeVlYWH3/8Me3atSMgIIDGjRvz/PPPc+bMmWIfS6/Xs3TpUp566ikC\nAwNp2LAhI0eOJDY2tlTGP3DgAL6+voX+y59sd+3aNb755hv++9//EhISgr+/Pw0bNmTYsGFs3ry5\n2M/RKDExET8/P959990i9b99+zbTp083xdCsWTPeeOMNrl69WuyxS/KaFXf8TZs28c4779C/f3/q\n1q2Lr68vEydOLDS22NhYRo4cScOGDQkMDOSpp55i6dKl6PV6i76vvPIKWq22RL/7FEUhKzMvwUij\nGLDVZ+Pi6oJKpSr28YQQQgghxKOrcuXKBAUFkZiYyJYtW8y2hYeHo9Vqad++PY6Ojqb2+Ph4qzf5\n7Nq1iy+++AJvb29mzZplsURaft7e3kyYMMHqvzp16gDQs2dPJkyYQOPGjUvp2Qrx8MnJNvDrngzi\nL+aY2nyq2NL6CVccneQSsSh/Mk6f4u19N0m0r8jZCn58Wn8EjHwZdZ8Rcs1DCCGEEELcs2y9gXWn\n8goADGjgxblTWvS63MduDlqqHVub+8DWDlXXR6OKEchyaaKEtm3bBsB3331H5cqVyziaovnss8/I\nzs5mwoQJZR1KqYmMjASgW7duZRzJw02r1TJ8+HBiY2MJCgri2Wef5erVq2zatInt27cTHh5e5CQ7\nRVF44YUXiIiIIDAwkNGjR5OcnMzGjRvZvXs3S5cupWvXrvc0vp+fH2+88YbV8U+fPs3mzZtNCTFG\noaGhLFy4kOrVq9O6dWt8fHy4cuUKkZGR7N27l/HjxzNz5sxiz92WLVswGAxFeo8mJSXRt29fzp07\nR5s2bejbty9xcXGEhYWxfft2Nm7cSI0aNYo0bkles5KM/9lnn3Hq1ClcXFyoUqUKcXFxRZqT8ePH\n4+DgQJ8+fXB3dyc6OpqZM2cSGxvLkiVLzPr7+PgwZMgQVq5cyYsvvlisJEmtRsFgyE0yMgAZGKis\nzwDX8vF7WwghhBBCPFieffZZ3n33XUJDQzl+/DjVqlXjzJkznDx5kipVqjB8+HCz/q+//jqQm4Rk\ndOLECRYtWoSiKDRs2JCdO3dajOPi4iLLnglRijIzDBzck056al4VsuoB9jz+HyfUaknGEOWP8tsB\nHJfNZ3ilZiyuOxAHfTZdg/2xadO0rEMTQgghhBAPiW1nU7idlZtR5OFkS4i3KzFHMkzb619Yi4rc\n7+BU7bqgcvcqkzjLgiQZiRJJSEgAKDcJRqmpqaxbt462bds+NFWMAKKiomjQoEGREy9EySxZsoTY\n2Fh69uzJ119/jVqde4dfnz59GDt2LJMmTWL79u2m9rvZsGEDERERBAcHExYWZrrLd+TIkfTv358p\nU6bQpk0bXF1dSzy+n58fkyZNsjr+iy++CMDTTz9t1t6kSRPWrl1Lq1atzNrPnDlD7969Wbp0KQMG\nDCj2ncFRUVF4eHjQsmXLQvvOnTuXc+fOWSQ0LV++nOnTp/PWW2+xatWqIo1bktesJOMbl3Xw9/cn\nJiaGwYMH3zWutLQ0pkyZgo2NDWvXriUoKAiAKVOmMGTIECIiItiwYQN9+/Y122/w4MGsWLGClStX\nMm3atCLNgUGvoNXkXUDOVPQ46LU4u7nKHX1CCCGEEKJEKleuzJw5cwgPD+fIkSP88ccfeHh40L17\ndwYPHmx2HlOQmzdvoii5F+GsJRgBVKpUSZKMhCglKbd1HNyTgVaTV+W23uOO1KrvIOeGolwybNuI\nEr4cFIWu1w6S6eJOUI/O1H68TlmHJoQQQgghHhI5eoWfTt4yPR5Q35Mzx/OWnfZxy8R72z9Vnm1t\nUXUbeL9DLFNSC1cUy/z58/H19eXAgQMAZksvGUVFRTFx4kTatm1LrVq1qF27Nt26dWP58uUYDAaL\nYyYmJvLee+/Rrl07atWqRf369WnXrh2vvfYaFy9eBHKXCxowYAAAn3zyidm4xlju5ueffyYrK4s+\nffpYbLt8+TK+vr689tprXLhwgfHjx9OwYUPq1KnD8OHDOX36NAC3bt1i6tSpNG3alICAAHr06MH+\n/fstjpeQkMCCBQvo27cvTZo0oWbNmjRr1oyXXnrJ6jJNY8eOxdfXl2+++cZi27x58/D19WXy5MkW\n2+Li4oiLi6N79+4lGvvw4cP4+voybty4AuetQ4cO+Pv7c/v2bVObcdmmVq1a4e/vT8uWLfnwww/R\narX4+voyaNCgAo9nze+//8748eNN8QYHBzN16lRTIlt+gwYNwtfXl+zsbBYsWEC7du3w9/fntdde\nAyAsLAxfX1/CwsLYuXMngwYNol69eveUWKYoCt9//z0A77zzjllSSteuXQkJCeHvv/8mJiamSMdb\nsWIFAFOnTjVbRqBJkyb07t2bW7duERER8a+Mn5SURFRUFI6OjgwcaP7HrkePHhYJRgC1a9c2/dwU\n5Wctv9TUVPbv30/nzp2xsbG5a9/MzEx++uknnJ2dLd7vY8aMwc/Pj127dpl+J9xNSeaspOO3adOG\ngICAIl+YjYiI4NatW/Tp08eUYATg6OjI1KlTgbz3SH7NmjXDz8+PsLAw0xcyhcnKMmDsqkNBgwFP\nfSa4FP7FjxBCCCGEEAXx9vbmxRdfZMmSJaxevZqvvvqKMWPGWE0wCg8PN6tiBNCxY0dTe0H/Fi5c\nWKRYXnrpJcLDw2WZNCEKcP1aDvt3pJsSjFRqaBriTO0GjpJgJModvV6PNuwblLBlmC54+FRl4NiB\nkmAkhBBCCCFK1c7zKdzMzK1iVNHRhmauLty8nvtYpYK6p1ea+qradkbl6V0mcZYVSTISxdKqVSve\neOMNqlWrBsAbb7xh+mf0wQcfcPz4cZo2bcrYsWMZOHAgGRkZTJ8+nVdffdXseFlZWfTr14/FixdT\nrVo1nnnmGYYNG0a9evXYunUrf//9N5C7HNjQoUPNYjD+8/PzKzTuvXv3AtC8efMC+1y5coVevXpx\n8+ZNhgwZQocOHdi7dy+DBg3i3Llz9O7dmyNHjtC7d2969erFqVOnGDlyJPHx8WbHOXjwIF9++SUV\nKlSgR48ejB8/nmbNmhEREUGPHj04efKkWX9j4tb777/PiRMnzGL+4osvqFOnDrNnz7aId/PmzQBm\nSUbFGTs4OJjAwEC2bdtGUlKSxfH/+OMP4uLieOqpp/Dw8ABykzfGjx/PJ598go2NDaNHj6Zz586E\nh4ebKuQUR1hYGP369WPnzp20bt2acePGERQUxOrVq+nRo4fF3BqNHz+e7777juDgYMaNG0e9evXM\ntkdERDBq1ChcXFwYOXIkvXv3Nm0zzvf8+fOLFOOFCxeIj48nICCA6tWrW2x/4oknAKwmnN1Jq9Vy\n+PBhnJycCAkJsdjeqVMnAPbt2/evjB8eHo5Wq6VXr164u7sX2t/I1tbW7L9FtX37drKzs83eowU5\nfPgwGo2G5s2bW3w5oVarad++PVC0RKeSzFlpjn83xjGNMeTXsmVLnJycOHz4MFqt1mJ78+bNuX79\nOn/99Veh4+hyFHKy85KRMhQDTnotThWkipEQQgghhBBCPAountUSuzcDfe51cGztoGV7F6rVtC/b\nwIQoAa1Gw8ff7+KLeCcM/HNdI7Ae6v+bh6pS+ai0L4QQQgghygedQWFtvipG/eqaVzGq7pmG25//\nfJdrY4uqW/EKcDwMZLk0USytW7emdevWxMTEcOXKFatLMq1YsYKaNWuatRkMBl5//XXWrl3LmDFj\naNasGZCbSHPhwgXGjRvHrFmzzPbJzs4mOzsbyK2yUrFiRcLCwmjVqlWBS0EVJDY2FldXVwIDAwvs\nExMTw9SpU80SoRYsWMDHH39sSiyaM2eOqSpK+/btefXVV1myZIlZ7G3atOHo0aMWiQonT56kX79+\nzJkzh5Ur87IbPTw8WLhwIYMGDWLChAls2bKFrKwsXnnlFezt7fn6669xcnKyiDcqKoqaNWtSv379\nEo89ePBg5s6dy/r163n22WfN9lmzZo2pj9FPP/3E9u3bCQkJ4ccff8TePvfC1OTJk80SeYri7Nmz\nTJs2DT8/P9auXUuVKlVM2/bt28fw4cOZPn06y5cvt9g3Pj6eHTt24OnpafXYO3bs4Pvvv7eayFFc\nZ8+eBSAgIMDqdn9/fwDOnTtX6LEuXLiAXq+nRo0aVhN2jMc6f/78vzL+6tWrAfjvf/9baF+jtLQ0\nNm/ejEqlokOHDkXeDyAyMhJnZ2dTgs7dGOMv6Hka24vyPEsyZ6U5fkljs7W1pXr16vz1119cunSJ\n2rVrm20PCgpi3bp1/PrrrxaJdfkpikJWZl7VOK1iIAcDPvoscJYLb0IIIYQQQgjxMFMUhdPHNcT9\nmXcR3MlZRUh7V9wq3r3KsBAPIk1KCjN/OsKfDr7wmC/e2mRGVriNevwkVPYOZR2eEEIIIYR4yOy5\nkMr19BwA3OzVNLR15u+03PMrWzuodfRbU19VmydReVUqizDLlCQZlaK+q06XdQhFtuHpgr+gvld3\nJhhBbiWQcePGsXbtWnbv3m1KMjLKv2yUkb29vSmJ5V5kZ2eTmJiIv7//XSt4+Pn58fLLL5u1DRky\nhI8//hitVsu7775rtuxS//79mTRpkkVlIm9v6+XQGjZsSJs2bdizZw85OTnY2dmZtjVv3pwpU6Yw\nZ84cpk2bxq1bt7hx4wYfffQRdevWtThWfHw8R48eZcKECfc09sCBA5k3bx7h4eFmSUbZ2dls2LAB\nb29vU3UdyEs8mjp1qtlrU7FiRV577TUmTpxodXxrVqxYQU5ODrNmzTJLMAJo27YtXbp0ITo6mvT0\ndIukqSlTphSYYAS5S2IVlGA0ZswY+vbte9f980tLSwOgQoUKVrcb21NTUws9lrGPm5ub1e3G9pSU\nlFIfPyYmhri4OOrWrXvXil75KYrC5MmTSUxMZNSoURZJL3ej0WjYtWsXTzzxhNWf7zuVZG4KUpI5\nK83x7+ZexqlUKfdDytWrV+86RrZWQa/PrWKkABkYcNZpcKzoJlWMhBBCCCGEEOIhptcrHI3NJP5i\njqmtoocNLdq54OgkBe1F+aPcvI7tZ7Oo7tacP30fAyC7eh1UwzqgspGvNoQQQgghROnSGxTWnLhp\netynticXTmebHtfyTsYhMjb3gY0Nqu6PXhUjkCQj8S9ISkri66+/ZseOHVy8eJHMzEyz7deuXTP9\nf6tWrahcuTILFy7kxIkTdOrUiebNm9OwYUNsbErn7qrbt28DFLo8lLUxH3ss9+Q1ICDAItHFxsYG\nb29vs+djtG3bNr7//nuOHTtGUlISOp3ObHtSUpLp2EYvvfQSMTExrF+/HoB+/foxYsQIq7FGRUUB\nucvI3cvYVatWpW3btuzZs4e//vrLVOkpOjqa5ORkxo8fb1Zx58SJE6jVaoKDgy3GbdGihdVYC/Lb\nb78B8Ouvv3L06FGL7Tdv3kSv13Pu3DkaN25stq1JkyZ3Pfbdtnt6ehY5wagolH/WgC+N5I2SHKuo\n+6xatQooXhWjWbNmsWnTJkJCQpgxY0aR9wPYs2cPGRkZRVoqrSjKyzzfq7uNY1y20NryhkYGg4Im\nK6+KUaZiwICCh6IBp6IvkSeEEEIIIYQQonzJzjZweH8mt27kXQfyqWLLf1q5YGsnN5yI8ke5eBbD\nF++hSrnNuOtXue3gRoMalejb5wmzG0GFEEIIIYQoLfsupnI1LfemDRc7NXUNTlzS5j52clFTIzbU\n1FfVqhMq78esHudhJ0lGolSlpKTQs2dPLl26RNOmTRk0aBDu7u7Y2tqSkpLC8uXLTUugQW7Vjl9+\n+YX58+ezdetWdu3aBeQmgowaNYpXX33VrOJPSRirqGg0mrv2s1ZZxJhgU1BFFFtbW4sknuXLlzN9\n+nTc3d1p164dvr6+ODk5oVKpiIqK4tSpU2ZzYKRSqejWrZtpDsaNG1dgrJGRkfj4+Fgk+5Rk7CFD\nhrBnzx7Cw8N58803AetLpUFuhRjj63mngqooFcSY/LVo0aK79svIyLBo8/Hxues+hW0vDuP7oqBK\nQcaqOQVVpsnP+D4y7nOn9PR0s36lNf7t27fZvHkzjo6ODBw4sNA4AWbPns3SpUtp2bIlK1aswMGh\neOWnIyMjsbe358knnyxS/5LMTUFKMmelOf7d3Ms4xt9hd6sMpcky8E+eEnoUstDjosvCsWJFqWIk\nhBBCCCGEEA+pzAw9B/dkkJ6ad9NJjUB7GjVzQq2Wc0FR/ijHf8Ow+EPQ5l4LsbFRM63VY9i2aFfG\nkQkhhBBCiIeVQVFYc/KW6XHvAA+unM2rElvf5yY2G/7IfaBWP7JVjECSjErVv7kEWXmxevVqLl26\nxBtvvMGkSZPMth0+fJjly5db7FO1alXmz5+Poij8/fff7N+/n2+//ZYFCxZgMBiYOnXqPcVUsWJF\n7O3tTUkt/yadTsf8+fPx8fEhKirKolqRsXqPNefOnWP27Nm4u7uTmprKlClT2LRpk0VCQVJSEocO\nHWLEiBFmSQMlHbtbt264ubmxdu1apk6dSnJyMjt37qRBgwY0bNjQrK+bmxvJycnodDqLRKObN29S\nHMYkitOnTxcpQSe/+5ksYazudO7cOavbz58/D+RWuypMzZo1sbGx4eLFi1bn0Hgsf3//Uh1/zZo1\naLVaBg8eTMWKFQuNc8aMGSxbtozWrVuzYsUKnJycCt0nP71eT3R0NG3atClyUo4x/oKep7G9KPNc\nkjkrzfELi+3o0aNWK3TpdDouXbqEra0t1atXt9jX+DvMy8vL6rF1OoVsrWJ6nKHkXlz2IBuVU+lV\n7xJCCCGEEEII8eBITtJxaG8GWk3e+WD9xo4E1nOQm01EubQlcj/ph3+l3z8JRji7oH7pbVR1GpVt\nYEIIIYQQ4qEWczmNyym5xTocbdX4ZzmRaMgtNuLhZcNj+7819VWFdETlU6UMonwwSF1RUaqMX973\n6NHDYtuvv/56131VKhV169Zl7NixrF69GoAtW7aYthuXMtPr9cWOq169ety4caPA6iGlJSkpiZSU\nFIKDgy2SfDIyMjh+/LjV/bRaLS+88AKZmZl89dVXvPzyy/z5559Wl6iKjo5Gr9dbLENV0rGdnJzo\n06cPCQkJ7N27l3Xr1qHT6SyqGEHuknIGg4HDhw9bbDt06JDV4xekWbNmABw8eLBY+91vNWvWxNfX\nl3PnznHp0iWL7Tt37gSgTZs2hR7LwcGB4OBgsrKyrD7vHTt2ANC2bdtSHf+HH34A4Omnn75rfIqi\n8NZbb7Fs2TLat29fogQjyP1Zv337ttXl/Aryn//8B0dHR2JjY03VfIwMBgN79uwBoHXr1oUeqyRz\nVprj341xTGMM+f36669kZWURHBxstXJUXFwcgEXyH+S+dprMvDtWsxWFbAy46LJwKGSpSCGEEEII\nIYQQ5dP1qzkc2JFuSjBSq6FZK2dq1XeUBCNR7hgMBlaG7+CrJC9WBPRkr08T8KyEetqHkmAkhBBC\nCCH+VQZFIfx4XhWjvtU9Sbyat5pRg0o3UJ06kvtApUbVc8j9DvGBIklGolT5+fkBEBMTY9Z+4sQJ\nvvzyS4v+p0+f5vLlyxbtxqo4+RMcPDw8AIiPjy92XK1atcJgMPDHH38Ue9/i8Pb2xsnJiWPHjpkt\n85WTk8P06dNJSkqyut/s2bM5ceIEL774Ih06dGDy5Mk0b96clStXsnHjRrO+mzdvpmLFihbJDiUd\nG2DYsGEArF27lrVr12Jra8uAAQMs+g0alFv2bd68eWbLrqWmpvLpp58WeHxrxowZg52dHTNnzuTs\n2bMW27Ozs/+VBKSkpCTi4uLuOh/5qVQqRo4cCcD777+PwZCXyLFlyxYOHjxInTp1aNWqldl+8fHx\nxMXFkZWVZdb+zDPPALlzmH8JvyNHjvDLL7/g5eVllqRX0vGNDh48yJkzZ6hXrx7Nmzcv8HkqisLU\nqVP57rvv6NSpE6GhoSVKMILcpdLUajVdu3Yt8j4uLi4MHDiQzMxM5s+fb7YtNDSUy5cv07FjR2rU\nqGG27cKFC5w5c4acnLxyhSWZs5KOX1w9e/bE09OTjRs3cvToUVO7RqNh3rx5QN575E6///47NjY2\ntGzZ0mJbTraCTpevihG5yZieqhxUDgUvryaEEEIIIYQQony6cEbLoX0ZGO/Fs7NX0bKDK77V7cs2\nMCFKQNHlkPPtF5xKzLuOFhHQCf5vHqqqltWehRBCCCGEKE2xV9K5kKwFwMFGRdW0vPOqqtXtqLjr\ne9NjVUh7VI9Vve8xPkhkuTRRqgYNGsSiRYuYMWMGBw4cwN/fn/Pnz7Nt2za6d+9ukTCzd+9eZs2a\nRXBwMLVq1cLLy4tr166xdetW1Go1EyZMMPWtVasWlStXZuPGjdjb21O1alVUKhWDBg2iWrVqd42r\nR48eLF68mN27d9O+fft/5bkDqNVqnn32Wb788kuefPJJunTpQk5ODgcOHCA5OZnWrVtz4MABs32i\noqIIDQ2ladOmpqXhbGxsWLhwIV26dGHq1KkEBQVRo0YNMjIy2LdvHz169MDOzu6exzZq0aIF/v7+\nbNq0iZycHDp37oy3t7dFv8GDB7Nx40Z27txJp06d6NKlCzqdjoiICIKCgjh79myR75SrVasW8+fP\nZ9KkSXTq1ImOHTsSEBCATqcjPj6egwcP4uXlZaogU1pCQ0P55JNPrC7pV5DnnnuObdu2ERERQa9e\nvWjbti3x8fFs2rQJJycn5s+fj1ptnrP56quvEhMTw5o1a8zec3379mXz5s1ERETQtWtXOnfuzO3b\nt9m4cSN6vZ6PPvrIYvm4koxvtHLlSqDwKkYLFizghx9+wNHRkQYNGrBw4UKLPg0bNixSdaKoqCiC\ng4OpVKlSoX3z+7//+z9iYmJYsmQJJ0+epGnTppw5c4YtW7bg7e3N//73P4t9hg4dypUrV4iNjaVq\n1bw/6CWZs5KMHxUVRVRUFACJiYlA7tKEr732GgCenp5Mnz7d1N/NzY2PPvqI5557jkGDBtG3b1/c\n3d3ZunUrZ8+epWfPnvTp08dinNTUVI4cOULbtm0tlqBTDAqarLxEqizFgB4Ft5xM7D2lipEQQggh\nhBBCPEwUReHPoxrO/qU1tTm5qAlp74JbBZsyjEyIklEyMzB8PRfbP48yzfYAbzd9AW87A1OHtMDG\nzbWswxNCCCGEEA85RVEIO5GvilEVL9IScr93U6uhnsc1OPF77kapYgRIkpEoZZUrV2b9+vV88MEH\nHDp0iF27dlGrVi0++OAD2rVrZ5Fk1LFjR1NCyZYtW0hPT8fHx4d27drx3HPPmVVesbGxYfny5Xzw\nwQf88ssvpKenoygKLVq0KDTJKDg4mEaNGrF+/Xreeust09Jr/4YpU6bg6enJ6tWrWbVqFW5ubrRr\n145p06bx8ccfm/WNj49n0qRJVKhQga+++gpb27wfSV9fXz755BPGjh3Liy++yPr169mxYwcajcZi\nqbSSjH2nIUOG8OGHHwJYXSoNcivELFu2jC+++IKffvqJ0NBQfHx8GDx4MKNGjWLLli0WCTJ3M3Dg\nQBo0aMDixYs5cOAAe/bswdnZmccee6zAZIuy4ODgwI8//sjChQtZv349S5cuxdXVla5duzJ58mTq\n1KlT5GOpVCq++uorvvnmG8LCwggNDcXBwYGWLVvyyiuvWK02VNLxk5OT2bx5M46OjgwcOPCucRmX\nFdNoNFarjkHu+6KwJKMjR45w7do1xo8ff9d+1hgr/CxYsICoqCgOHTqEh4cHQ4cOZfLkyWZJRIUp\nyZyVZPyTJ0+yZs0as7aLFy9y8eJFAKpVq2aWZATQrVs3fvrpJz7//HM2b96MVqulZs2azJgxg2ef\nfdZqot7GjRvRaDRWqxxpNArGYk0GIJPcBx62BlT2lsuuCSGEEEIIIYQon/Q6hT8OZnLtSl41X3dP\nG1q0c8HBUQrWi/JHSbqJ4fNZEJ97HcVVl8V79qdxG/EsdvZ2hewthBBCCCHEvfv9agZnk3JXCjeG\n4QAAIABJREFUn3GyUVEpxQ4tuauHBNRxwHHrD6a+qubtUFW+e17Co0ClKIpSeLeHy9WrV0u8782b\nNy0qvBgTQ3Q6nbVdRCkojTn++eefeemll1i2bFmBSToPupdeeomoqChOnDhR4qWsrCmN+d2zZw/D\nhw/n5Zdf5s033yyt0B4Kj9LviDlz5vDll18SExND9er3p5z1ozC/3bt3JyMjg507d5olSer1Cmkp\netPjNEWPFgMVcjKo5FURlV3pXJAryRxb+3t5p+Ikjol/1718NhL3xvhzYlwqVtx/8hqUPXkNyp68\nBmVPPhc9OMrr5yL5OS57//ZroNUaiN2bwe1beeeAj/na0qylC7a2Rasq/SiQn4WyV9TX4PzpsySF\nr6TJ5d9Mbaq+I1D1HFrkSunCuvL+cyCfix4c5fVz0cOgvP8cPwzkNSh78hqUvUfhNVAUhWlbL/LX\nzdwko6E+3rgl5X4nZu+g4olGidh8+EZuZ5UK9awvUVXxu2/xPaifi+QWF/HI6Nu3L02bNmX+/PmU\nx9y67Oxstm/fTocOHUo1wai4EhISLNqSkpL44IMPAIq0nJZ4eEVFRdGgQYP7lmD0KIiKiuLYsWO8\n++67FlXYNJl5y6TloKA1VjGyo9QSjIQQQgghhBBClK30ND37t6WbJRj517aneWtJMBLl05Ffj/HW\nwTTm1ezHWVdfsLFBNeZV1L2GSYKREEIIIYS4b44mZJoSjFzVNlRMyVt1qG4jR2yifjQ9VgW3va8J\nRg8yWS5NPDJUKhXz5s0jMjKShIQEqlSpUtYhFYu9vT2nT58u6zCYNWsWp06dIjg4GC8vL65du8aO\nHTtITk7mv//9L02bNi3rEEUZ2r17d1mH8NDRaDTMnDmTzp07m7XnZBvIyclLmMxQci82V8zJwNbb\n/b7GKIQQQgghhBDi35GUqOPQvgxysvPO/xo2dSKgjiyPLcqn7P3b+fqUA5nOuXfGL2j4NF+0csWm\nYZMyjkwIIYQQQjxqwo7nVWnqVdEDQ1ru/7tWUONnewWOHsptUKlQ9RxaBhE+mCTJSDxSGjRoQIMG\nDco6jHKte/fuJCYmEh0dTWpqKg4ODtSpU4dhw4YxYsSIsg5PiIdOv379LNoURSErM+8Cs0YxoENB\npSh42KtQ2cqfdyGEEEIIIYQo765eyuaPg5kY/iliq7aBZi2dqVLNvmwDE6IEFEVB2RSGzcYfeNPZ\nhzebvoiDomdq2yrY1gss6/CEEEIIIcQj5sT1TE4lZgHgrbLFNS3vu7WGTZxgXZjpsapZa1S+soqL\nkXwLKYQolj59+tCnT5+yDkOIR5pWo2Aw5CYZKUDGP8ukuedkYOPjWYaRCSGEEEIIIYS4V4qicPa0\nlj+PaUxt9g4qWrRzwcNLLueK8kfR6VBWLkTZvx2Aapk3eOd6JJX+O45Kvo+VcXRCCCGEEOJRlL+K\nUVcXD/jn9KtSZVsq6a5gOPKrabuql1Qxyk/OSoUQQohyRK9X0GQZTI8zFD0KCmrFgLuTDSobmzKM\nTgghhBBCCCHEvTAYFE78nsXFs9mmNhc3NSHtXXBxlfM9Uf5kpKaT/O1XVD6+L6+xQRPqT3gdlZNz\n2QUmhBBCCCEeWX/eyOTY9UwAqqvscdL8c66lggZBThhW51UxolkrVNVq3v8gH2CSZCSEEEKUI5rM\nvAQjHQqaf6oYeeRkoPb0LquwhBBCCCGEEELcI12Owm8xGdy4pjO1eVayoXkbF+wd1GUYmRAlc/Pq\ndWZHnSHTuS1z7Y7gnpOOqvWTqEa+JEu9CyGEEEKIMhN24hYAKqCjgzv8cwpW3d8et/TLGH4/YOqr\n7ilVjO4kn+SFEEKIciIn20BOjmJ6nK7oAbBR9FR0sUellovOQgghhBBCCFEeZWUaOLQ3g9RkvanN\nt7odQS2csbFRlWFkQpSM7vI5pm+9Rrxj7g1R/3t8DB9WvYltn2GoVPKeFkIIIYQQZePvm1n8cS0D\ngPpqJ+x1ud+t2dhCvccdUb7NV8WoSQiq6gFlEeYDTb6NFEIIIcoBRVHIysxLMNIqBnTkPvbMyUDl\nWqGsQhNCCCGEEEIIcQ9Sk/Xs25ZmlmBUu4EDTVtKgpEon7RHDqGa9yaj/96AWjFgY9DTw98Fu77D\nJcFICCGEEEKUqfATNwGwQ0UL27zv1mrXd8T+1hWU/FWMeg277/GVB1LJSAghhCgHtBoFgyFfFaN/\nlkmzM+hwc3WSKkZCCCGEEEIIUQ7duJbDbwcy0P1Tnl+lgsbBTlQPcCjbwIQooaztm0hd9CHo9fxH\nc5oXzv+CT+fuNGnZuqxDE0IIIYQQj7hzSRpi43OrGDVRu2BryE2Ad3JWEVDHAeWbMFD++S4uqAWq\nGoFlFeoDTZKMhBBCiAecXq+gyTKYHmcoehRjFSN9JipXn7IKTQghhBBCCCFECV08q+X4b1mma9i2\ndhDc2oVKle3KNjAhSsBgMKDZGI4+4oe8Rg9vOo8ZiqpazTKLSwghhBBCCCNjFSNXbHhc7WJqr9/Y\nCfWNyxgO7zO1qXtLFaOCSJKREEII8YDTZOYlGCkqhSwl97GDPgfXCq5SalwIIYQQQgghyhFFUTh9\nTEPcaa2pzdFZRUg7Vyq425RhZEKUTLY2m4Vhe0hMc2O6ygY7RQ/V/FG/Mh2Vh1dZhyeEEEIIIQQX\nbmuIuZwOQAu1K2pyv1tz97ShanU7lGVr8qoYPR6Mqkatsgr1gSdJRkIIIcQDLCfbQE5O3jJpKQa9\n6f89lSxwkipGQgghhBBCCFFe6PUKRw5mcvVyjqmtoocNLdq54Ogky2CL8keXkcbssMMcc6gG7rCw\n3mCmOJ5HP/Z1VI7OZR2eEEIIIYQQAISfuAWAD3YEqJ1M7Q2bOsH1eJTYvaY2qWJ0d3LmKoQQQjyg\nFEUhKzMvwUivMqD7Z5k0J70W54oVpIqREEIIIYQQQpQTWo2BmJ3pZglGj1W1pfUTrpJgJMol5dYN\nVPPepPGVP0xtzpWr4PZ/8yTBSAghhBBCPDAup2g5cCkNgJY2bqb2qn52eHrbokSEwz+riNCoGSr/\nOmURZrkhZ69C3Cf79+/H19eXX375paxDEUKUE1qNgsGQm1SkUkGyIW/ZNE9VNipHp4J2vWeKotC5\nc2f69+//r40hhBBCCCGEEI+K9DQ9+7anc/tWXnVa/9r2NG/jgq2d3Dwiyh/l4lkMc6bA1Uv0v7yL\nrvExPO14jbdfHoidvV1ZhyeEEEIIIYTJmhO3UIAAlSM+KnsA1Gqo39gRJSEe5eAeU191L6liVBhZ\nLk2I+8BgMDBz5kwaNGhAr169yjqcUpGTk0NQUBAtWrTg22+/LetwHnrh4eF89913/P3339jY2NCo\nUSOef/55OnfuXOxjRUdHs3jxYk6cOIFer6du3bo888wzDBkypNB9tVot3bt356+//qJy5cr89ttv\nZtszMzOJiopi+/btHD9+nKtXr6JWqwkMDKRv376MHTsWe3t7i+P6+voWOGbTpk3ZtGlTsZ9nYmIi\nzZo1Y/To0cyePbvQ/rdv32bBggVs2bKFGzdu4OHhQceOHZk8eTJVq1Yt1thZWVksXLiQDRs2EB8f\nj6urK61atWLy5MnUrl3brG9BcxYQEEi3rr0ZMWI09nb2aNGj/FPFSEm+yZzQxRw/eZKLFy+SnJyM\nq6srfn5+9OvXj6effhpnZ/M7Bv/880+WL1/OsWPHuHbtGunp6Xh5eREYGMioUaPo3r27WVUklUrF\n5MmTGTt2LL/88gu9e/cu1hwIIYQQQgghhMh1K1FH7L4McrLzKtU2bOJIQF3HMoxKiJJTjsZiWPoR\naDUAqGxteb59ADYtO6BWy33NQgghhBDiwXE1NZu9F1OxAVqo86oY+ddxwNnVBkN4vipGDZqiCqxX\nNoGWI5JkJMR9sGHDBk6dOsWXX3750CxtdODAAVJSUujevXtZh/LQe++991i8eDFVqlRhxIgR5OTk\nsGHDBkaPHs3777/PmDFjinys0NBQ3nnnHTw8PBgwYAB2dnZERETw+uuvc/r0aaZPn37X/efOncuV\nK1cK3H7w4EEmTpyIu7s7rVu3plu3biQnJxMdHc3s2bOJjIwkLCwMR0fLC6nVqlWzmuhUpUqVIj+/\n/LZs2YLBYKBbt26F9k1KSqJv376cO3eONm3a0LdvX+Li4ggLC2P79u1s3LiRGjVqFGlcrVbL8OHD\niY2NJSgoiGeffZarV6+yadMmtm/fTnh4OM2aNTP1tzZnt2/fJjo6mo8+/h/R26IIDf2BVBsb0z7q\njCRWrV5NkyZNePLJJ/H09CQtLY39+/czc+ZMfvjhBzZu3IibW96HpWPHjhEVFUWzZs0IDg7Gzc2N\nxMREoqOjGT9+PAMGDOCLL74wey5du3aldu3azJkz56FJkBRCCCGEEEKI++nKxWyOHsrEWJhWbQPN\nWjpTpZrlDThClAcRm/Zx+dTfjNNqUAE4u6B+8W1UdRuVdWhCCCGEEEJYWHPyFgYFglQuuKpyv2uz\nd1BRu74jyo2rKAd3m/qqe0sVo6KQJCMh7oNvv/0WNze3IiU7lBeRkZHY2NiUqJKOKLrY2FgWL15M\nzZo1iYiIwN3dHYAXXniBbt26MXv2bJ566in8/PwKPdbly5eZPXs27u7uREZGmvZ5/fXX6dmzJ4sX\nL6ZHjx4EBwdb3f/AgQMsXbqUDz74gDfffNNqn0qVKvHFF1/Qq1cvs4pF6enpDBo0iMOHD/Ptt98y\nYcIEi339/PyYNGlSoc+jqKKiovDw8KBly5aF9p07dy7nzp1j/PjxzJw509S+fPlypk+fzltvvcWq\nVauKNO6SJUuIjY2lZ8+efP3116Y7+Pr06cPYsWOZNGkS27dvN7Vbm7PsbAOvvfI2o8cM5ciR3/h2\nVSgDnhkHgJsuE6+69Th9+jR2dpblxydOnMi6dev4/vvvefHFF03tffv2ZejQoRb909LS6N27N+vW\nrWPs2LE0bdrUbPvgwYP54IMP2LNnD23atCnSHAghhBBCCCHEo05RFM6c0vLXCY2pzd5BRUg7F9y9\n5JKsKH/0ej3fhe9mg6Eq+HpTSXObfpl/on51BqoqhV+XEkIIIYQQ4n5LSMtm1/kUnFATpHYxtddt\n5IidvQpDxBpMd4TUD0JVq34ZRVq+SO1SUSJbt25lyJAhNG3aFH9/f5o1a8bAgQOtLpt17Ngxnn76\naerUqUPdunUZOnQohw8fZv78+fj6+nLgwAFT38uXL+Pr68trr71mddxBgwZZLKuUnZ1NaGgoI0eO\npEWLFvj7+9OwYUOGDh3Kjh07rB4nJCSEkJAQ0tLSmDlzJiEhIdSoUYP58+eb+uh0Or799lt69epF\n3bp1CQwMpEuXLoSGhmIw/rIpgri4OA4fPkznzp1xcnIqMJaMjAxmzJhBcHAwgYGBdO7cmaioKFMs\nn3/+OW3atCEgIIDWrVsTGhpqcazizsXixYvx9fVl7NixFtv27NmDn58fTz75JFlZWWbbFEVh69at\ntGjRAk9Pz2KPrdFoqF+/Po0bN0an01mdt2nTpuHr68u2bdvM2tetW0fXrl0JDAykcePGTJw4kYSE\nBKvvjcJcvXqVt99+m1atWpniHT16NEeOHLHom//9un79enr16kXt2rUJCQkBzN+7Z8+eZcKECTRu\n3Jhq1aqxf//+YsWV3/fffw/AK6+8YkowgtyEnNGjR6PVagkLCyvSsX788Ue0Wi1jxowxS0pyd3dn\n4sSJZuPdKS0tjddff522bdvyzDPPFDhGo0aNGDBggMWSaK6urjz//PMAxMTEFCnee5Gamsr+/fvp\n3LkzNvkqAFmTmZnJTz/9hLOzM5MnTzbbZpyrXbt2cfHixULHVRTFNIfvvPOOWYnwrl27EhISwt9/\n/202B3fOmaIoaDINuLi4MmrUeAAOHTpo6u9hr8LWwcFqghFgqjh0/vx5s3Zr1aMA3Nzc6NChg9V9\nIDc5CeCHH364yzMXQgghhBBCCGFk0CscPZRllmDkWkFNu86ukmAkyiUlW4thyUckXbtuaoup1hzD\n/82TBCMhhBBCCPHA+ulUbhWj/6hdsVflfmfnWkFN9QB7lBvXUH7daeqr7j28rMIsd+SsVhTbypUr\nmTZtGj4+PnTu3BkPDw9u3brFn3/+SXh4OKNHjzb1jY2NZdiwYeTk5NC9e3dq1qzJqVOnGDx4cKlV\nxEhOTmb69OkEBwfTvn17vLy8uH79OtHR0YwcOZKPPvqIESNGWOyXk5PDkCFDSE5OpkOHDri6upoS\nL3Jychg9ejS7du0iMDCQfv364eDgwIEDB3jnnXf4/fffLZYVKsjevXsBaNGiRYF9dDodw4YNIzk5\nma5du5KTk8PPP//M+PHj+eGHH1ixYgW///47nTp1wt7enk2bNvHOO+/g6elpSgAoyVw8//zzxMTE\nEBERYUoQArhx4wavvPIKDg4OLFq0yCI56vDhw1y/fp2XX365RGM7OjrSu3dvVq1axY4dO+jSpYvZ\n8bVaLZs2baJSpUp07NjR1L5o0SLef/993N3dGTRoEBUqVGDPnj3069fPbFmoojh+/DjDhw8nOTmZ\njh070r17d5KSktiyZQv9+/dn2bJlPPnkkxb7LV68mL179/LUU0/RunVrUlNTzbZfvHiR3r17ExAQ\nQP/+/dFoNKbYDhw4wODBg2nVqhVr164tUpzGBKX882D0xBNP8Omnn7J//36L5JiSHCt/nzu9++67\npKSkmCXiFZetra3Zf++UkpLCjz/+yI0bN6hQoQKPP/44//nPf0o01vbt28nOzi7Scn6HDx9Go9GY\nfg/kp1arad++PatWreLAgQOFLpl24cIF4uPjCQgIoHr16hbbn3jiCQ4ePMj+/fsL/B2oyVJMSdPG\nRCKbf+asYk4GdpU87hpDdHQ0APXrFy3bOisry/S616tnuc5stWrVqFKlCnv37kVRlIdmycfiuHXr\nFmFhYRw9epS0tDQ8PDxo3rw5gwYNsnjP3E16ejpr164lNjaW27dv4+bmRlBQEEOHDsXLy8vqPr//\n/jubN2/mypUrprEDAgLo1asXderUKa2nKIQQQgghhCgl2dkGDu/P5NaNvJuqvH1sCW7jjJ293O8p\nyh8lLQXDl++jPvcXL6sOcsuhIq4ujkwa2go7F8sbKoV4lJTWNaNDhw4RGRnJ+fPnycnJwcfHhzZt\n2tCnTx+LmzkBDAYD+/fvJzo6mmvXrpGVlYWXlxd169ald+/eRap6L4QQQjzsbqTnsONcCp7YUkeV\n97m1YRMn1GoVhs35qhjVfRxV7QZlFGn5I0lGothWrlyJvb090dHReHt7m21LSkoy/b+iKEyaNAmN\nRsM333xD165dTduWLVvGjBkzSiWeihUrcvDgQapWrWrWnpqaSr9+/fjf//5H//79LRJlrl+/Tu3a\ntU0VTPL7/PPP2bVrF2PGjGHWrFmmSih6vZ6pU6fy448/0qtXL7PnVJBDhw4BEBQUVGCfhIQEGjVq\nxNq1a3FwcABg4MCBDBgwgAkTJlCjRg127NhBxYoVAXjuuefo0KEDCxcuNEsyKslcfPLJJ3Tt2pWZ\nM2fSrFkz6tevz8SJE0lMTOSTTz6x+iW2scJS/udf3LGHDBnCqlWrWLNmjUWS0datW0lOTua5554z\nJaRcvHiRuXPn4unpSVRUlKlq0VtvvcVLL73Ehg0bCpzfO+l0OiZMmEBmZiZr1qyhVatWpm0JCQn0\n7NmTyZMn8+uvv5peD6P9+/ezceNGGjWyvs78oUOHePnll82WEysoqaYwmZmZJCQk4OLiwmOPPWax\nPSAgAIBz584V6Xhnz5412y+/xx57DGdnZ9NJaf73SGRkJGvWrOHjjz8udrWo/IwVl6wlOQGcOnXK\nYrm0Bg0a8Pnnnxc5YcYoMjISZ2dn2rdvX2hf4/xZm5f87UWZ57vNMYC/v/9dj6XXK2g1eZXS1v2c\nO2chbdqjVhQ8nGxR5avMpNPp+Oyzz4DcRL9ff/2VU6dO0bp1a6vJlZBbrWjdunXo9Xpu3rzJ9u3b\nSUhI4OWXX6ZBA+sfoJo0aUJkZCRnzpx55BJbEhISTEl2wcHB+Pr6EhcXx+bNmzly5AizZ88uUpJj\nWloa77zzDteuXaNRo0a0bt2a+Ph4du3axR9//MH7779v8XO+cuVKNm7ciJubG82bN8fNzY2EhARi\nY2M5ePAgL730UpHe40IIIYQQQoj7Iy01h/3b0klPyzuv86tpT+NgJ9Q2j94NG6L8UxKuYPj8PUhM\nAMBO0fO213UcB40s8fUuIR4WpXXN6Mcff2TdunU4OjoSEhKCm5sbp0+fJjw8nKNHj/Luu+9aJBp9\n9tlnxMTE4OXlRUhICI6Ojly+fJndu3ezb98+3nrrrQKvXwshhBCPinWnbqEzQIjaDfU/N9BXqmyL\nTxU7lMQEqWJ0D+RMoBT9EpZc1iEUWe+h7oV3ugsbGxurJ5LGpbMgtzrI2bNnadmypUUyzpgxYwgN\nDeXChQv3FAeAg4ODRWILQIUKFRg6dCjvvfceR48epWXLlhZ9pk+fbpFgZDAYCA0NxcfHh5kzZ5ot\ntWRjY8P06dMJCwszLdtVmPj4eAB8fHzu2m/WrFlmCS0hISFUr16dS5cusXjxYlOCEUCNGjUIDg7m\n0KFD6PV6U4wlmQtPT0++/vpr+vfvzwsvvED37t3Zt28fAwYMYOjQoVZjjYqKIigoyCzhpLhjBwcH\nExAQwLZt27h9+zYeHnnVWdasWQPA4MGDTW3r169Hp9MxduxYs3FVKhVvvfUWmzZtQq/XFzC75rZv\n386FCxeYMGGCWYIRQOXKlXnhhReYMWMG+/bts6hm9PTTT9/1BK1SpUq88cYbVrc1bdqU3bt3W102\nzxpjlaSCTkaN7XdWUypIWloakPuaWFOhQgUyMzNJTU01xZiYmMi0adPo1KkTw4eX/A9saGgoO3fu\npGHDhgwbNsxi+3PPPUePHj0IDAzEwcGBuLg4Fi5cSEREBEOGDGHr1q1UqVKlSGNpNBp27drFE088\nUeASYfkVdZ5TUlIKPVZR5jj/mPkpikJWRt6F6NVh37Fv725q1atPj36DcNdlYONpXu1Gp9PxySef\nmLUNHDiQOXPmFPjcL1y4YLaPvb097777rmk5O2uMv7/i4+MfuSSj5cuXk5KSwpgxY8wqY3333XdE\nRESwevVqnnvuuUKPs3r1aq5du0bPnj0ZNWqUqX3z5s18++23LFu2jLffftvUnpyczC+//ELFihX5\n+OOPzf4GnDhxgvfee4/w8HBJMhJCCCGEEOIBkZigYdvma2iy8s7r6j3uSK36Do9kRVhR/p347QTX\nNkfQ6Z8EI1QqVEPH4fpk77INTIgHRGlcMzp//jzr16/HxcWFuXPnmm5AUxSF0NBQoqKi+Pnnnxky\nZIhpn7i4OGJiYvDz8+ODDz4w+05h586dLFq0iJ9++kmSjIQQQjzSbmXmEH02BT+VA77qf/5WqnKr\nGAEokWvB+L1ynUao6srfzeKQJCNRbP379+e9996jU6dO9O7dm1atWtG8eXOLpV6OHz8OYDW5x8bG\nhubNm5dKkhHAX3/9xaJFizh48CA3btxAo9GYbU9ISLDYx9HR0WrVjnPnznH79m38/f1NFUKs7RsX\nF1ek2G7fvg1g9gXxnSpWrEjNmjUt2h977DEuXbpE48aNLbZVqVIFvV7PjRs3zJIvSjIXISEhTJky\nhblz5/Lll1/i7+/P3LlzrcZ66tQpLly4wLRp0yy2FXfswYMH8+GHH7JhwwbTMnuJiYns3r2bRo0a\nmb0+J0+eBKB58+YW41arVo2qVaty+fJlqzHf6bfffgPgypUrVpf/On/+PABnzpyxSDJq2rTpXY/d\noEEDi+pHRk5OTtSqVatIMRZHaV2sVBTF4nhTpkxBp9Mxb968Eh938+bNzJgxAx8fH5YuXWpaAiy/\nOyubBQUFsWTJEsaPH8/mzZv5+uuvmTVrVpHG27NnDxkZGUVaKq0orM3Lv3GsnGwFnS53e/S2SObM\nmYWndyVmf7IQRxs17k4OqNTmpfUdHR2Jj49HURQSEhLYu3cvc+fOpXv37qxatcpqaeQnnniC+Ph4\ncnJyiI+PZ/369cydO5eYmBiWLl1qtQSzu3tuYmr+anWPguvXr3P06FEqVapkkVQ6ZMgQtm3bxt69\ne3nmmWfumtCm0WjYs2cPDg4OZheFALp160ZERARHjx7l+vXrpotJiYmJKIpC7dq1Lf5+NGrUCCcn\npyInGAohhBBCCCH+XVcvZ3PkYDx6fe45nVoNTVo441vD8vxKiPJg17aDfHHNBYN/L9zTb9Is/Tzq\n8ZNRNbG8zivEo6i0rhkdOnQIRVHo1KmTWYVrlUrF8OHD2bJlC9HR0QwaNAj1P9cFb9y4AeReH7rz\nOnTz5s1ZtGiRXDMSQgjxyFt3Kgm9QSHEJq/AQI0Ae9wq2qDcvI5yYLupXd3bsjiCuDtJMhLF9vzz\nz+Pp6cl3333HN998w7Jly1CpVLRs2ZJ3333XtCyY8YNspUqVrB6nsMo+RfXbb78xZMgQ9Ho9bdu2\npXPnzri5uaFWqzl58iRbtmxBq9Va7Ofl5WX1i35jUtD58+ctKoTkl5GRUaT4jCcRWq22wAo2BVVQ\nMVaLslYVxVi9SKfTmdpKOhcAPXv2ZN68eRgMBkaMGIGLi4vVfsal0nr06GHWXpKxBw0axEcffcTa\ntWtNSUbr1q1Dp9OZVTGCwt9P3t7eRU4yMr7GmzZtumu/zMxMi7aCxi/q9uIwvu7G6jh3MrYXpeyu\nsV9SUhKpqalmVccKOt6aNWuIjo7m008/LXIVoTtFRUXx4osv4u3tTXh4ODVq1CjW/iNHjmTz5s0c\nPHiwyPtERkZib29vkSBWkMLmOT093azf3RRWXaqg18xgUMjKzL3bdfv2LUyZOhF3Ty8+XbaSqtWq\n45mThsql4PeWSqWiSpUqDBkyhMDAQPr06cPbb7/NihUrCtzHzs6OmjVr8vrrr2NnZ8doLFk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l2K48ePX1GSkVarxYIFC/D9999jyZIlWLduHQwGA9q2bYvo6Gi89NJLuP322xt0Lr1ej8mTJ+PT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\n2rKyMuzbtw/9+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+ "text/plain": [ + "" + ] + }, + "metadata": { + "image/png": { + "height": 265, + "width": 1164 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "X = np.linspace(0,1,1001)\n", + "\n", + "ref = linear_rgb(X) # The (almost) correct implementation.\n", + "fast = fast_linear_rgb(X) # The Taylor approximation\n", + "square = X*X # The approximation by squaring.\n", + "\n", + "fig, (ax1, ax2, ax3, ax4) = plt.subplots(1, 4, figsize=(20,4))\n", + "ax1.plot(X, ref, label='linear')\n", + "ax1.plot(X, fast, label='fast (max/avg err: {:.4f} / {:.4f})'.format(np.max(np.abs(ref - fast)),\n", + " np.mean(np.abs(ref - fast))))\n", + "ax1.plot(X, square, label='square (max/avg err: {:.4f} / {:.4f})'.format(np.max(np.abs(ref - square)),\n", + " np.mean(np.abs(ref - square))))\n", + "ax2.plot(X, ref)\n", + "ax2.plot(X, fast)\n", + "ax2.plot(X, square)\n", + "ax2.set_xlim(0, 0.1)\n", + "ax2.set_ylim(0, 0.1)\n", + "ax2.set_title(\"Left end\")\n", + "ax3.plot(X, ref)\n", + "ax3.plot(X, fast, ls=':')\n", + "ax3.plot(X, square)\n", + "ax3.set_xlim(0.45, 0.55)\n", + "ax3.set_ylim(0.15, 0.25)\n", + "ax3.set_title(\"Middle\")\n", + "ax4.plot(X, ref)\n", + "ax4.plot(X, fast)\n", + "ax4.plot(X, square)\n", + "ax4.set_xlim(0.9, 1)\n", + "ax4.set_ylim(0.9, 1)\n", + "ax4.set_title(\"Right end\")\n", + "\n", + "ax1.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# The inverse function (for Lab->RGB)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The inverse function is significantly more difficult, because its left part is highly non-linear and changes much faster than the rest of the function.\n", + "\n", + "So what we do here, in order to keep reasonable accuracy, is split it into three parts with three different approximations. You will notice that the leftmost part has quite large coefficients, which hints to the approximation being worse/\"harder\"." + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "ExecuteTime": { + "end_time": "2017-08-26T21:22:50.729724Z", + "start_time": "2017-08-26T21:22:49.727604Z" + } + }, + "outputs": [], + "source": [ + "def delinear_rgb(x):\n", + " return 1.055*(x**(1.0/2.4)) - 0.055\n", + "\n", + "fast_delinear_rgb_part1 = lambdify([x], series(delinear_rgb(x), x, x0=0.015, n=6).removeO())\n", + "fast_delinear_rgb_part2 = lambdify([x], series(delinear_rgb(x), x, x0=0.03, n=6).removeO())\n", + "fast_delinear_rgb_part3 = lambdify([x], series(delinear_rgb(x), x, x0=0.6, n=6).removeO())" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": { + "ExecuteTime": { + "end_time": "2017-08-26T21:37:16.798913Z", + "start_time": "2017-08-26T21:37:16.158896Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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vT4cqItIiWiTJaNu2bRw+fJjU1FTS0tIoKSnhpptu4pFHHmn0WLm5ufznP/9h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BQlF3yEmGChHOOMZc+ePZw9e5asrCzuuuuuj/SxhRBiJni/tov1WXEBK+tMisK2goSg2xoejYHf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zF4DLFW+fG2zloRumMHXO+hG8O5HUcTYofmhfgHAoERR3Og3mLfYwZYZLm/VEROS8YjGLprow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+ "text/plain": [ + "" + ] + }, + "metadata": { + "image/png": { + "height": 265, + "width": 1164 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "ref = delinear_rgb(X)\n", + "fast1 = fast_delinear_rgb_part1(X)\n", + "fast2 = fast_delinear_rgb_part2(X)\n", + "fast3 = fast_delinear_rgb_part3(X)\n", + "sqrt = np.sqrt(X)\n", + "\n", + "def plot(ax):\n", + " ax.plot(X, ref, label='linear')\n", + " l, = ax.plot(X, fast1, label='fast, part1', ls=':')\n", + " ax.plot(X, fast2, label='fast, part2', c=l.get_color(), ls='--')\n", + " ax.plot(X, fast3, label='fast, part3', c=l.get_color(), ls='-')\n", + " ax.plot(X, sqrt, label='sqrt')\n", + "\n", + "fig, (ax1, ax2, ax3, ax4) = plt.subplots(1, 4, figsize=(20,4))\n", + "plot(ax1)\n", + "ax1.set_ylim(0, 1)\n", + "plot(ax2)\n", + "ax2.set_xlim(0, 0.05)\n", + "ax2.set_ylim(0, 0.25)\n", + "ax2.set_title(\"Left end\")\n", + "plot(ax3)\n", + "ax3.set_xlim(0.45, 0.55)\n", + "ax3.set_ylim(0.65, 0.75)\n", + "ax3.set_title(\"Middle\")\n", + "plot(ax4)\n", + "ax4.set_xlim(0.95, 1)\n", + "ax4.set_ylim(0.95, 1)\n", + "ax4.set_title(\"Right end\")\n", + "\n", + "ax1.legend()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Doc/approx-quality.png b/Doc/approx-quality.png new file mode 100644 index 0000000000000000000000000000000000000000..6f2c3ae4f8da7640edbb038b6508123d2586dc08 GIT binary patch literal 116068 zcmd43gAJ=t`N6wD5?t9*Ijxpw#>x-0x&^4UfI4BhA8d~_J3<`Cb7==2E_s>Q6 z&5J|jtMJEps~2dwf8fXYAMMZZ_sizON>(ToAtmz98MF+=9~9~?3jOlAoPFfdu${e} z{BiACYt$yry>}E8tO2-Z&%VDeZxDY)#3GY5C$`UgtBCe2p=wV}E}`lz3TisfyPto) 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z2!Lh40p%As=#cAbC>c{AobD9B`p1pCUO_|-s(xM&dJRPbh8k;W_#GITu;ykJe#5G@ zETc-dS^Kj~=>x&AI?pgU+# z$AHd1f`aRO?;guVLNg%RwulLYcwZ(crkj4UJfZ>2NK2tq&KRwV9!lU>*=tz8XwHsR zZS|djqQ(W|ZQ+H(7!01Vy2_cWUSGxS$IFSoFZ8T#Dnz(5*!iUIugCbQK)6F_FgO?w z{F3GXB80$3gr#lpY5~!J*Zu;kUaW4x1>h*4QjfA-IJ#i#kwDZwi|#0Z7Af$)z)gqv z5`KOMGcobC6(-GbwwV}47BRPKYHIaxFae*62Q380AA8_H_e%7(NN;i??3-bC(fBCA z+5csaz_5cL)XvOyzRg2*KnBQs)3Pz)J0I0xnzLJ)lXUy~=2%{-4I5x7wPte^80Q-+Qhj9|5CKJ@$=x|9w36IU-W4#*HV?qTK0K}kPG8q#kU zF#@nBZH8cDKj(ez(6W1wK$4Aloo0R=*ah#|x)r^ Add Packages...` +- paste URL: `https://github.com/mojzesh/swift-colorful.git` in the right top corner: `Search or Enter Package URL` + +The package can then be used through this: +```swift +import Colorful +``` + +To run demo projects from CLI: +- `swift run DemoColorBlend-macOS` +- `swift run DemoColorDist-macOS` +- `swift run DemoColorGens-macOS` +- `swift run DemoColorSort-macOS` +- `swift run DemoGradientGen-macOS` +- `swift run DemoPaletteGens-macOS` + +To run tests: +- `swift test` + +To run benchmark: +- `swift run Benchmark-macOS` + +### Basic usage + +Create a beautiful blue color using different source space: + +```swift +import Colorful + +// Any of the following should be the same +var c = Color(R: 0.313725, G: 0.478431, B: 0.721569) +do { + c = try Color.Hex("#517AB8") +} catch let error { + print("\(error)") +} + +c = Color.Hsv(H: 216.0, S: 0.56, V: 0.722) +c = Color.Xyz(x: 0.189165, y: 0.190837, z: 0.480248) +c = Color.Xyy(x: 0.219895, y: 0.221839, Y: 0.190837) +c = Color.Lab(l: 0.507850, a: 0.040585, b: -0.370945) +c = Color.Luv(l: 0.507849, u: -0.194172, v: -0.567924) +c = Color.Hcl(h: 276.2440, c: 0.373160, l: 0.507849) + +let (r, g, b) = c.Values() +print(String(format: "RGB values: %f, %f, %f", r, g, b)) + +let (r255, g255, b255) = c.RGB255() +print(String(format: "RGB values: %i, %i, %i", r255, g255, b255)) +``` + +And then converting this color back into various color spaces: + +```swift +let hex := c.Hex() +let (h, s, v) = c.Hsv() +let (x, y, z) = c.Xyz() +let (x, y, Y) = c.Xyy() +let (l, a, b) = c.Lab() +let (l, u, v) = c.Luv() +let (h, c, l) = c.Hcl() +``` + +### *This library is trying to keep function naming conventions as close to original `go-colorful` implementation as possible.* + +### Comparing colors +In the RGB color space, the Euclidian distance between colors *doesn't* correspond +to visual/perceptual distance. This means that two pairs of colors that have the +same distance in RGB space can look much further apart. This is fixed by the +CIE-L\*a\*b\*, CIE-L\*u\*v\* and CIE-L\*C\*h° color spaces. +Thus you should only compare colors in any of these spaces. +(Note that the distances in CIE-L\*a\*b\* and CIE-L\*C\*h° are the same, since it's the same space but in cylindrical coordinates) + +![Color distance comparison](Sources/Demos/ColorDist/colordist.png) + +The two colors shown at the top look much more different than the two shown at +the bottom. Still, in RGB space, their distance is the same. +Here is a little example program that shows the distances between the top two +and the bottom two colors in RGB, CIE-L\*a\*b\* and CIE-L\*u\*v\* space. You can find it in `Sources/Demos/ColorDist/main.swift`. + +```swift +import Foundation + +import Colorful + +let c1a = Color(R: 150.0 / 255.0, G: 10.0 / 255.0, B: 150.0 / 255.0) +let c1b = Color(R: 53.0 / 255.0, G: 10.0 / 255.0, B: 150.0 / 255.0) +let c2a = Color(R: 10.0 / 255.0, G: 150.0 / 255.0, B: 50.0 / 255.0) +let c2b = Color(R: 99.9 / 255.0, G: 150.0 / 255.0, B: 10.0 / 255.0) + +print(String(format: "DistanceRgb: c1: %.17f\tand c2: %.17f", c1a.DistanceRgb(c1b), c2a.DistanceRgb(c2b))) +print(String(format: "DistanceLab: c1: %.17f\tand c2: %.17f", c1a.DistanceLab(c1b), c2a.DistanceLab(c2b))) +print(String(format: "DistanceLuv: c1: %.17f\tand c2: %.17f", c1a.DistanceLuv(c1b), c2a.DistanceLuv(c2b))) +print(String(format: "DistanceCIE76: c1: %.17f\tand c2: %.17f", c1a.DistanceCIE76(c1b), c2a.DistanceCIE76(c2b))) +print(String(format: "DistanceCIE94: c1: %.17f\tand c2: %.17f", c1a.DistanceCIE94(c1b), c2a.DistanceCIE94(c2b))) +print(String(format: "DistanceCIEDE2000: c1: %.17f\tand c2: %.17f", c1a.DistanceCIEDE2000(c1b), c2a.DistanceCIEDE2000(c2b))) +``` + +Running the above program shows that you should always prefer any of the CIE distances: + +```bash +$ swift run DemoColorDist-macOS +Building for debugging... +[3/3] Linking DemoColorDist-macOS +Build complete! (0.38s) +DistanceRgb: c1: 0.38039215686274508 and c2: 0.38587139311711588 +DistanceLab: c1: 0.32042638877384100 and c2: 0.24395387956805947 +DistanceLuv: c1: 0.51331140446133072 and c2: 0.25683706276058060 +DistanceCIE76: c1: 0.32042638877384100 and c2: 0.24395387956805947 +DistanceCIE94: c1: 0.19795102869625045 and c2: 0.12206359588444481 +DistanceCIEDE2000: c1: 0.17271531164545623 and c2: 0.10664280425514172 +``` + +It also shows that `DistanceLab` is more formally known as `DistanceCIE76` and +has been superseded by a slightly more accurate, but much more expensive +`DistanceCIE94` and `DistanceCIEDE2000`. + +Note that `AlmostEqualRgb` is provided mainly for (unit-)testing purposes. Use +it only if you really know what you're doing. It will eat your cat. + +### Blending colors +Blending is highly connected to distance since it basically "walks through" the +colorspace, thus if the colorspace maps distances well, the walk is "smooth". + +Colorful comes with blending functions in RGB, HSV and any of the LAB spaces. +Of course, you'd rather want to use the blending functions of the LAB spaces since +these spaces map distances well but, just in case, here is an example showing +you how the blendings (`#fdffcc` to `#242a42`) are done in the various spaces: + +![Blending colors in different spaces.](Sources/Demos/ColorBlend/colorblend.png) + +What you see is that HSV is really bad: it adds some green, which is not present +in the original colors at all! RGB is much better, but it stays light a little +too long. LUV and LAB both hit the right lightness but LAB has a little more +color. HCL works in the same vein as HSV (both cylindrical interpolations) but +it does it right in that there is no green appearing and the lighthness changes +in a linear manner. + +While this seems all good, you need to know one thing: when interpolating in any +of the CIE color spaces, you might get invalid RGB colors! This is important if +the starting and ending colors are user-inputted or random. An example of where this +happens is when blending between `#eeef61` and `#1e3140`: + +![Invalid RGB colors may crop up when blending in CIE spaces.](Sources/Demos/ColorBlend/invalid.png) + +You can test whether a color is a valid RGB color by calling the `IsValid` method +and indeed, calling IsValid will return false for the redish colors on the bottom. +One way to "fix" this is to get a valid color close to the invalid one by calling +`Clamped`, which always returns a nearby valid color. Doing this, we get the +following result, which is satisfactory: + +![Fixing invalid RGB colors by clamping them to the valid range.](Sources/Demos/ColorBlend/clamped.png) + +The following is the code creating the above three images; it can be found in `Sources/Demos/ColorBlend/main.swift` + +```swift +import Foundation +import AppKit + +import Colorful +import DemoShared + +let blocks = 10 +let blockw = 40 + +let (image, imageRep) = createImageRep(NSSize(width: blocks*blockw, height: 200)) + +let c1 = try! Color.Hex("#fdffcc") +let c2 = try! Color.Hex("#242a42") + +// Use these colors to get invalid RGB in the gradient. +// let c1 = try! Color.Hex("#EEEF61") +// let c2 = try! Color.Hex("#1E3140") + +var col = Color() +for i in 0.. Bool { + let (h, c, L) = Color.LabToHcl(L: l, a: a, b: b) + return 10.0 < h && h < 50.0 && 0.1 < c && c < 0.5 && L < 0.5 +} +// Since the above function is pretty restrictive, we set ManySamples to true. +do { + brownies = try SoftPaletteEx(colorsCount: colors, settings: SoftPaletteSettings(checkColorFn: isbrowny, iterations: 50, manySamples: true)) +} catch {} +``` + +The following picture shows the palettes generated by all of these methods +(sourcecode in `Sources/Demos/PaletteGens/main.swift`), in order they were presented, i.e. +from top to bottom: `Warm`, `FastWarm`, `Happy`, `FastHappy`, `Soft`, +`SoftEx(isbrowny)`. All of them contain some randomness, so YMMV. + +![All example palettes](Sources/Demos/PaletteGens/palettegens.png) + +Again, the code used for generating the above image is available as [Sources/Demos/PaletteGens/main.swift](https://github.com/mojzesh/swift-colorful/blob/master/Sources/Demos/PaletteGens/main.swift). + +### Sorting colors + +Sorting colors is not a well-defined operation. For example, {dark blue, dark red, light blue, light red} is already sorted if darker colors should precede lighter colors but would need to be re-sorted as {dark red, light red, dark blue, light blue} if longer-wavelength colors should precede shorter-wavelength colors. + +Go-Colorful's `Sorted` function orders a list of colors to minimize the average distance between adjacent colors, including between the last and the first. (`Sorted` does not necessarily find the true minimum, only a reasonably close approximation.) The following picture, drawn by [Sources/Demos/ColorSort/main.swift](https://github.com/mojzesh/swift-colorful/blob/master/Sources/Demos/ColorSort/main.swift), illustrates `Sorted`'s behavior: + +![Sorting colors](Sources/Demos/ColorSort/colorsort.png) + +The first row represents the input: a slice of 512 randomly chosen colors. The second row shows the colors sorted in CIE-L\*C\*h° space, ordered first by lightness (L), then by hue angle (h), and finally by chroma (C). Note that distracting pinstripes permeate the colors. Sorting using *any* color space and *any* ordering of the channels yields a similar pinstriped pattern. The third row of the image was sorted using Go-Colorful's `Sorted` function. Although the colors do not appear to be in any particular order, the sequence at least appears smoother than the one sorted by channel. + + +### Using linear RGB for computations +There are two methods for transforming RGB⟷Linear RGB: a fast and almost precise one, +and a slow and precise one. + +```swift +let (r, g, b) = try Color.Hex("#FF0000").FastLinearRgb() +``` + +TODO: describe some more. + +### Want to use some other reference point? + +```swift +let c = Color.LabWhiteRef(l: 0.507850, a: 0.040585, b: -0.370945, wref: D50) +let (l, a, b) = c.LabWhiteRef(wref: D50) +``` + +### Reading and writing colors from databases + +- Not implemented + +FAQ +=== + +### Q: I get all f!@#ed up values! Your library sucks! +A: You probably provided values in the wrong range. For example, RGB values are +expected to reside between 0 and 1, *not* between 0 and 255. Normalize your colors. + +### Q: Lab/Luv/HCl seems broken! Your library sucks! +They look like this: + + + +A: You're likely trying to generate and display colors that can't be represented by RGB, +and thus monitors. When you're trying to convert, say, `Color.Hcl(h: 190.0, c: 1.0, l: 1.0).RGB255()`, +you're asking for RGB values of `(-2105.254 300.680 286.185)`, which clearly don't exist, +and the `RGB255` function just casts these numbers to `uint8`, creating wrap-around and +what looks like a completely broken gradient. What you want to do is either use more +reasonable values of colors which actually exist in RGB, or just `Clamp()` the resulting +color to its nearest existing one, living with the consequences: +`Hcl(h: 190.0, c: 1.0, l: 1.0).Clamp().RGB255()`. It will look something like this: + + + +[Here's an issue going in-depth about this](https://github.com/lucasb-eyer/go-colorful/issues/14), +as well as [my answer](https://github.com/lucasb-eyer/go-colorful/issues/14#issuecomment-324205385), +both with code and pretty pictures. Also note that this was somewhat covered above in the +["Blending colors" section](https://github.com/lucasb-eyer/go-colorful#blending-colors). + +### Q: In a tight loop, conversion to Lab/Luv/HCl/... are slooooow! +A: Yes, they are. +This library aims for correctness, readability, and modularity; it wasn't written with speed in mind. +A large part of the slowness comes from these conversions going through `LinearRgb` which uses powers. +I implemented a fast approximation to `LinearRgb` called `FastLinearRgb` by using Taylor approximations. +The approximation is roughly 5x faster and precise up to roughly 0.5%, +the major caveat being that if the input values are outside the range 0-1, accuracy drops dramatically. +You can use these in your conversions as follows: + +```swift +let (R, G, B) = c1.LinearRgb() +let (x, y, z) = Color.LinearRgbToXyz(r: R, g: G, b: B) +let (l, a, b) = Color.XyzToLab(x: x, y: y, z: z) +``` + +If you need faster versions of `Distance*` and `Blend*` that make use of this fast approximation, +feel free to implement them and open a pull-request, I'll happily accept. + +The derivation of these functions can be followed in [this Jupyter notebook](doc/LinearRGB Approximations.ipynb). +Here's the main figure showing the approximation quality: + +![approximation quality](Doc/approx-quality.png) + +More speed could be gained by using SIMD instructions in many places. +You can also get more speed for specific conversions by approximating the full conversion function, but that is outside the scope of this library. +Thanks to [@ZirconiumX](https://github.com/ZirconiumX) for starting this investigation, +see [issue #18](https://github.com/lucasb-eyer/go-colorful/issues/18) for details. + +Who? +==== + +This library has been ported from Golang to Swift by Artur Torun (a.k.a. Mojzesh) + +Original `go-colorful` library was developed by Lucas Beyer with contributions from +Bastien Dejean (@baskerville), Phil Kulak (@pkulak), Christian Muehlhaeuser (@muesli), and Scott Pakin (@spakin). + +## Known Issues: +- For some strange reasons the following functions are an 2 orders of magnitude slower than the original Golang implementation. If you have an idea of how to speed it up please let me know or open PR. + - WarmPalette + - HappyPalette + - SoftPalette + - SoftPaletteEx + +## License + +This repo is under the MIT license, see [LICENSE](LICENSE) for details. diff --git a/Sources/Colorful/colorgens.swift b/Sources/Colorful/colorgens.swift new file mode 100644 index 0000000..99e7d0e --- /dev/null +++ b/Sources/Colorful/colorgens.swift @@ -0,0 +1,56 @@ +// Various ways to generate single random colors + +public func randomFloat64() -> Float64 { + return Float64.random(in: 0.0...1.0) +} + +// // Creates a random dark, "warm" color through a restricted HSV space. +public func FastWarmColor() -> Color { + return Color.Hsv( + H: randomFloat64()*360.0, + S: 0.5+randomFloat64()*0.3, + V: 0.3+randomFloat64()*0.3) +} + +// Creates a random dark, "warm" color through restricted HCL space. +// This is slower than FastWarmColor but will likely give you colors which have +// the same "warmness" if you run it many times. +public func WarmColor() -> Color { + var c = randomWarm() + while !c.IsValid() { + c = randomWarm() + } + + return c +} + +func randomWarm() -> Color { + return Color.Hcl(h: randomFloat64()*360.0, + c: 0.1+randomFloat64()*0.3, + l: 0.2+randomFloat64()*0.3) +} + +// Creates a random bright, "pimpy" color through a restricted HSV space. +public func FastHappyColor() -> Color { + return Color.Hsv(H: randomFloat64()*360.0, + S: 0.7+randomFloat64()*0.3, + V: 0.6+randomFloat64()*0.3) +} + +// Creates a random bright, "pimpy" color through restricted HCL space. +// This is slower than FastHappyColor but will likely give you colors which +// have the same "brightness" if you run it many times. +public func HappyColor() -> Color { + var c: Color = randomPimp() + while !c.IsValid() { + c = randomPimp() + } + + return c +} + +func randomPimp() -> Color { + return Color.Hcl(h: randomFloat64()*360.0, + c: 0.5+randomFloat64()*0.3, + l: 0.5+randomFloat64()*0.3) +} diff --git a/Sources/Colorful/colors.swift b/Sources/Colorful/colors.swift new file mode 100644 index 0000000..1f669c3 --- /dev/null +++ b/Sources/Colorful/colors.swift @@ -0,0 +1,1087 @@ +import Foundation + +public struct WhiteReference { + var wref: [Float64] = [0, 0, 0] + init(X: Float64, Y: Float64, Z: Float64) { + self.wref = [X, Y, Z] + } +} + +func sq(_ v: Float64) -> Float64 { + return v * v +} + +func cub(_ v: Float64) -> Float64 { + return v * v * v +} + +// clamp01 clamps from 0 to 1. +func clamp01(_ v: Float64) -> Float64 { + return max(0.0, min(v, 1.0)) +} + +// This is the tolerance used when comparing colors using AlmostEqualRgb. +let Delta: Float64 = 1.0 / 255.0 + +// This is the default reference white point. +public var D65: WhiteReference = WhiteReference(X: 0.95047, Y: 1.00000, Z: 1.08883) + +// And another one. +public var D50: WhiteReference = WhiteReference(X: 0.96422, Y: 1.00000, Z: 0.82521) + +public struct Color: CustomStringConvertible, Equatable, Comparable { + var R: Float64 + var G: Float64 + var B: Float64 + + public init(R: Float64 = 0.0, G: Float64 = 0.0, B: Float64 = 0.0) { + self.R = R + self.G = G + self.B = B + } + + public func RGBA() -> (UInt32, UInt32, UInt32, UInt32) { + let r = UInt32(self.R * 65535.0 + 0.5) + let g = UInt32(self.G * 65535.0 + 0.5) + let b = UInt32(self.B * 65535.0 + 0.5) + let a: UInt32 = 0xFFFF + return (r, g, b, a) + } + + // Might come in handy sometimes to reduce boilerplate code. + public func RGB255() -> (r: UInt8, g: UInt8, b: UInt8) { + let r = UInt8((self.R * 255.0) + 0.5) + let g = UInt8((self.G * 255.0) + 0.5) + let b = UInt8((self.B * 255.0) + 0.5) + return (r, g, b) + } + + // Used to simplify HSLuv testing. + public func Values() -> (R: Float64, G: Float64, B: Float64) { + return (self.R, self.G, self.B) + } + + // Checks whether the color exists in RGB space, i.e. all values are in [0..1] + func IsValid() -> Bool { + return self.R >= 0.0 && self.R <= 1.0 && + self.G >= 0.0 && self.G <= 1.0 && + self.B >= 0.0 && self.B <= 1.0 + } + + // Returns Clamps the color into valid range, clamping each value to [0..1] + // If the color is valid already, this is a no-op. + public func Clamped() -> Color { + return Color(R: clamp01(self.R), G: clamp01(self.G), B: clamp01(self.B)) + } + + // DistanceRgb computes the distance between two colors in RGB space. + // This is not a good measure! Rather do it in Lab space. + public func DistanceRgb(_ c2: Color) -> Float64 { + return (sq(self.R - c2.R) + sq(self.G - c2.G) + sq(self.B - c2.B)).squareRoot() + } + + // DistanceLinearRgb computes the distance between two colors in linear RGB + // space. This is not useful for measuring how humans perceive color, but + // might be useful for other things, like dithering. + public func DistanceLinearRgb(_ c2: Color) -> Float64 { + let (r1, g1, b1) = self.LinearRgb() + let (r2, g2, b2) = c2.LinearRgb() + return (sq(r1 - r2) + sq(g1 - g2) + sq(b1 - b2)).squareRoot() + } + + // DistanceLinearRGB is deprecated in favour of DistanceLinearRgb. + // They do the exact same thing. + public func DistanceLinearRGB(_ c2: Color) -> Float64 { + return DistanceLinearRgb(c2) + } + + // DistanceRiemersma is a color distance algorithm developed by Thiadmer Riemersma. + // It uses RGB coordinates, but he claims it has similar results to CIELUV. + // This makes it both fast and accurate. + // + // Sources: + // + // https://www.compuphase.com/cmetric.htm + // https://github.com/lucasb-eyer/go-colorful/issues/52 + public func DistanceRiemersma(c2: Color) -> Float64 { + let rAvg: Float64 = (self.R + c2.R) / 2.0 + // Deltas + let dR: Float64 = self.R - c2.R + let dG: Float64 = self.G - c2.G + let dB: Float64 = self.B - c2.B + + return ((2 + rAvg) * dR * dR + 4 * dG * dG + (2 + (1 - rAvg)) * dB * dB).squareRoot() + } + + // Check for equality between colors within the tolerance Delta (1/255). + public func AlmostEqualRgb(_ c2: Color) -> Bool { + return abs(self.R - c2.R) + + abs(self.G - c2.G) + + abs(self.B - c2.B) < (3.0 * Delta) + } + + // You don't really want to use this, do you? Go for BlendLab, BlendLuv or BlendHcl. + public func BlendRgb(c2: Color, t: Float64) -> Color { + return Color(R: self.R + t * (c2.R - self.R), + G: self.G + t * (c2.G - self.G), + B: self.B + t * (c2.B - self.B)) + } + + // Utility used by Hxx color-spaces for interpolating between two angles in [0,360]. + static func interp_angle(a0: Float64, a1: Float64, t: Float64) -> Float64 { + // Based on the answer here: http://stackoverflow.com/a/14498790/2366315 + // With potential proof that it works here: http://math.stackexchange.com/a/2144499 + let delta = ((a1 - a0).truncatingRemainder(dividingBy: 360.0) + 540).truncatingRemainder(dividingBy: 360.0) - 180.0 + return (a0 + t * delta + 360.0).truncatingRemainder(dividingBy: 360.0) + } + + /// HSV /// + /////////// + // From http://en.wikipedia.org/wiki/HSL_and_HSV + // Note that h is in [0..360] and s,v in [0..1] + + // Hsv returns the Hue [0..360], Saturation and Value [0..1] of the color. + public func Hsv() -> (h: Float64, s: Float64, v: Float64) { + let min = min(min(self.R, self.G), self.B) + let v = max(max(self.R, self.G), self.B) + let C = v - min + + var s = 0.0 + if v != 0.0 { + s = C / v + } + + var h = 0.0 // We use 0 instead of undefined as in wp. + if min != v { + if v == self.R { + h = ((self.G - self.B) / C).truncatingRemainder(dividingBy: 6.0) + } + if v == self.G { + h = (self.B - self.R) / C + 2.0 + } + if v == self.B { + h = (self.R - self.G) / C + 4.0 + } + h *= 60.0 + if h < 0.0 { + h += 360.0 + } + } + return (h, s, v) + } + + // Hsv creates a new Color given a Hue in [0..360], a Saturation and a Value in [0..1] + public static func Hsv(H: Float64, S: Float64, V: Float64) -> Color { + let Hp = H / 60.0 + let C = V * S + let X = C * (1.0 - abs(Hp.truncatingRemainder(dividingBy: 2.0) - 1.0)) + + let m = V - C + var (r, g, b) = (0.0, 0.0, 0.0) + + if Hp >= 0.0, Hp < 1.0 { + r = C + g = X + } else if Hp >= 1.0, Hp < 2.0 { + r = X + g = C + } else if Hp >= 2.0, Hp < 3.0 { + g = C + b = X + } else if Hp >= 3.0, Hp < 4.0 { + g = X + b = C + } else if Hp >= 4.0, Hp < 5.0 { + r = X + b = C + } else if Hp >= 5.0, Hp < 6.0 { + r = C + b = X + } + + return Color(R: m + r, G: m + g, B: m + b) + } + + // You don't really want to use this, do you? Go for BlendLab, BlendLuv or BlendHcl. + public func BlendHsv(c2: Color, t: Float64) -> Color { + var (h1, s1, v1) = self.Hsv() + var (h2, s2, v2) = c2.Hsv() + + // https://github.com/lucasb-eyer/go-colorful/pull/60 + if s1 == 0, s2 != 0 { + h1 = h2 + } else if s2 == 0, s1 != 0 { + h2 = h1 + } + + // We know that h are both in [0..360] + return Color.Hsv(H: Color.interp_angle(a0: h1, a1: h2, t: t), S: s1 + t * (s2 - s1), V: v1 + t * (v2 - v1)) + } + + /// HSL /// + /////////// + + // Hsl returns the Hue [0..360], Saturation [0..1], and Luminance (lightness) [0..1] of the color. + public func Hsl() -> (h: Float64, s: Float64, l: Float64) { + let min: Float64 = min(min(self.R, self.G), self.B) + let max: Float64 = max(max(self.R, self.G), self.B) + + let l: Float64 = (max + min) / 2 + + let s: Float64 + var h: Float64 + + if min == max { + s = 0 + h = 0 + } else { + if l < 0.5 { + s = (max - min) / (max + min) + } else { + s = (max - min) / (2.0 - max - min) + } + + if max == self.R { + h = (self.G - self.B) / (max - min) + } else if max == self.G { + h = 2.0 + (self.B - self.R) / (max - min) + } else { + h = 4.0 + (self.R - self.G) / (max - min) + } + + h *= 60 + + if h < 0 { + h += 360 + } + } + + return (h, s, l) + } + + // Hsl creates a new Color given a Hue in [0..360], a Saturation [0..1], and a Luminance (lightness) in [0..1] + public static func Hsl(h: Float64, s: Float64, l: Float64) -> Color { + if s == 0 { + return Color(R: l, G: l, B: l) + } + + var r, g, b: Float64 + var t1: Float64 + var t2: Float64 + var tr: Float64 + var tg: Float64 + var tb: Float64 + + if l < 0.5 { + t1 = l * (1.0 + s) + } else { + t1 = l + s - l * s + } + + t2 = 2 * l - t1 + let h = h / 360 + tr = h + 1.0 / 3.0 + tg = h + tb = h - 1.0 / 3.0 + + if tr < 0 { + tr += 1 + } + if tr > 1 { + tr -= 1 + } + if tg < 0 { + tg += 1 + } + if tg > 1 { + tg -= 1 + } + if tb < 0 { + tb += 1 + } + if tb > 1 { + tb -= 1 + } + + // Red + if 6 * tr < 1 { + r = t2 + (t1 - t2) * 6 * tr + } else if 2 * tr < 1 { + r = t1 + } else if 3 * tr < 2 { + r = t2 + (t1 - t2) * (2.0 / 3.0 - tr) * 6 + } else { + r = t2 + } + + // Green + if 6 * tg < 1 { + g = t2 + (t1 - t2) * 6 * tg + } else if 2 * tg < 1 { + g = t1 + } else if 3 * tg < 2 { + g = t2 + (t1 - t2) * (2.0 / 3.0 - tg) * 6 + } else { + g = t2 + } + + // Blue + if 6 * tb < 1 { + b = t2 + (t1 - t2) * 6 * tb + } else if 2 * tb < 1 { + b = t1 + } else if 3 * tb < 2 { + b = t2 + (t1 - t2) * (2.0 / 3.0 - tb) * 6 + } else { + b = t2 + } + + return Color(R: r, G: g, B: b) + } + + /// Hex /// + /////////// + + // Hex returns the hex "html" representation of the color, as in #ff0080. + public func Hex() -> String { + // Add 0.5 for rounding + return String(format: "#%02x%02x%02x", UInt8(self.R * 255.0 + 0.5), UInt8(self.G * 255.0 + 0.5), UInt8(self.B * 255.0 + 0.5)) + } + + // An example error we can throw + public enum HexColorError: Error { + case isNotHexColor + case incorrectFormat + case unknownError + } + + // Hex parses a "html" hex color-string, either in the 3 "#f0c" or 6 "#ff1034" digits form. + public static func Hex(_ scol: String) throws -> Color { + let r, g, b: Float64 + + if scol.hasPrefix("#") { + let start = scol.index(scol.startIndex, offsetBy: 1) + let hexColor = String(scol[start...]) + let scanner = Scanner(string: hexColor) + var hexNumber: UInt64 = 0 + + if hexColor.count == 6 { + if scanner.scanHexInt64(&hexNumber) { + r = Float64((hexNumber & 0xFF0000) >> 16) / 255 + g = Float64((hexNumber & 0x00FF00) >> 8) / 255 + b = Float64((hexNumber & 0x0000FF) >> 0) / 255 + return Color(R: r, G: g, B: b) + } + } else if hexColor.count == 3 { + if scanner.scanHexInt64(&hexNumber) { + r = Float64((hexNumber & 0x000F00) >> 8) / 15 + g = Float64((hexNumber & 0x0000F0) >> 4) / 15 + b = Float64((hexNumber & 0x00000F) >> 0) / 15 + return Color(R: r, G: g, B: b) + } + } else { + throw HexColorError.incorrectFormat + } + } else { + throw HexColorError.isNotHexColor + } + + throw HexColorError.unknownError + } + + /// Linear /// + ////////////// + // http://www.sjbrown.co.uk/2004/05/14/gamma-correct-rendering/ + // http://www.brucelindbloom.com/Eqn_RGB_to_XYZ.html + + public static func linearize(_ v: Float64) -> Float64 { + if v <= 0.04045 { + return v / 12.92 + } + return pow((v + 0.055) / 1.055, 2.4) + } + + // LinearRgb converts the color into the linear RGB space (see http://www.sjbrown.co.uk/2004/05/14/gamma-correct-rendering/). + public func LinearRgb() -> (r: Float64, g: Float64, b: Float64) { + let r = Color.linearize(self.R) + let g = Color.linearize(self.G) + let b = Color.linearize(self.B) + return (r, g, b) + } + + // A much faster and still quite precise linearization using a 6th-order Taylor approximation. + // See the accompanying Jupyter notebook for derivation of the constants. + public static func linearize_fast(_ v: Float64) -> Float64 { + let v1 = v - 0.5 + let v2 = v1 * v1 + let v3 = v2 * v1 + let v4 = v2 * v2 + // v5 := v3*v2 + return -0.248750514614486 + 0.925583310193438 * v + 1.16740237321695 * v2 + 0.280457026598666 * v3 - 0.0757991963780179 * v4 // + 0.0437040411548932*v5 + } + + // FastLinearRgb is much faster than and almost as accurate as LinearRgb. + // BUT it is important to NOTE that they only produce good results for valid colors r,g,b in [0,1]. + public func FastLinearRgb() -> (r: Float64, g: Float64, b: Float64) { + let r = Color.linearize_fast(self.R) + let g = Color.linearize_fast(self.G) + let b = Color.linearize_fast(self.B) + return (r, g, b) + } + + public static func delinearize(_ v: Float64) -> Float64 { + if v <= 0.0031308 { + return 12.92 * v + } + return 1.055 * pow(v, 1.0 / 2.4) - 0.055 + } + + // LinearRgb creates an sRGB color out of the given linear RGB color (see http://www.sjbrown.co.uk/2004/05/14/gamma-correct-rendering/). + public static func LinearRgb(r: Float64, g: Float64, b: Float64) -> Color { + return Color(R: Color.delinearize(r), G: Color.delinearize(g), B: Color.delinearize(b)) + } + + public static func delinearize_fast(_ v: Float64) -> Float64 { + var v1, v2, v3, v4, v5: Float64 + // This function (fractional root) is much harder to linearize, so we need to split. + if v > 0.2 { + v1 = v - 0.6 + v2 = v1 * v1 + v3 = v2 * v1 + v4 = v2 * v2 + v5 = v3 * v2 + return 0.442430344268235 + 0.592178981271708 * v - 0.287864782562636 * v2 + 0.253214392068985 * v3 - 0.272557158129811 * v4 + 0.325554383321718 * v5 + } else if v > 0.03 { + v1 = v - 0.115 + v2 = v1 * v1 + v3 = v2 * v1 + v4 = v2 * v2 + v5 = v3 * v2 + return 0.194915592891669 + 1.55227076330229 * v - 3.93691860257828 * v2 + 18.0679839248761 * v3 - 101.468750302746 * v4 + 632.341487393927 * v5 + } else { + v1 = v - 0.015 + v2 = v1 * v1 + v3 = v2 * v1 + v4 = v2 * v2 + v5 = v3 * v2 + // You can clearly see from the involved constants that the low-end is highly nonlinear. + return 0.0519565234928877 + 5.09316778537561 * v - 99.0338180489702 * v2 + 3484.52322764895 * v3 - 150_028.083412663 * v4 + 7_168_008.42971613 * v5 + } + } + + // FastLinearRgb is much faster than and almost as accurate as LinearRgb. + // BUT it is important to NOTE that they only produce good results for valid inputs r,g,b in [0,1]. + public static func FastLinearRgb(r: Float64, g: Float64, b: Float64) -> Color { + return Color(R: Color.delinearize_fast(r), G: Color.delinearize_fast(g), B: Color.delinearize_fast(b)) + } + + // XyzToLinearRgb converts from CIE XYZ-space to Linear RGB space. + public static func XyzToLinearRgb(x: Float64, y: Float64, z: Float64) -> (r: Float64, g: Float64, b: Float64) { + let r = 3.2409699419045214 * x - 1.5373831775700935 * y - 0.49861076029300328 * z + let g = -0.96924363628087983 * x + 1.8759675015077207 * y + 0.041555057407175613 * z + let b = 0.055630079696993609 * x - 0.20397695888897657 * y + 1.0569715142428786 * z + return (r, g, b) + } + + public static func LinearRgbToXyz(r: Float64, g: Float64, b: Float64) -> (x: Float64, y: Float64, z: Float64) { + let x = 0.41239079926595948 * r + 0.35758433938387796 * g + 0.18048078840183429 * b + let y = 0.21263900587151036 * r + 0.71516867876775593 * g + 0.072192315360733715 * b + let z = 0.019330818715591851 * r + 0.11919477979462599 * g + 0.95053215224966058 * b + return (x, y, z) + } + + // BlendLinearRgb blends two colors in the Linear RGB color-space. + // Unlike BlendRgb, this will not produce dark color around the center. + // t == 0 results in c1, t == 1 results in c2 + public func BlendLinearRgb(c2: Color, t: Float64) -> Color { + let (r1, g1, b1) = self.LinearRgb() + let (r2, g2, b2) = c2.LinearRgb() + return Color.LinearRgb( + r: r1 + t * (r2 - r1), + g: g1 + t * (g2 - g1), + b: b1 + t * (b2 - b1) + ) + } + + /// XYZ /// + /////////// + // http://www.sjbrown.co.uk/2004/05/14/gamma-correct-rendering/ + + public func Xyz() -> (x: Float64, y: Float64, z: Float64) { + let (r, g, b) = self.LinearRgb() + return Color.LinearRgbToXyz(r: r, g: g, b: b) + } + + public static func Xyz(x: Float64, y: Float64, z: Float64) -> Color { + let (r, g, b) = Color.XyzToLinearRgb(x: x, y: y, z: z) + return Color.LinearRgb(r: r, g: g, b: b) + } + + /// xyY /// + /////////// + // http://www.brucelindbloom.com/Eqn_XYZ_to_xyY.html + + // Well, the name is bad, since it's xyY but Golang needs me to start with a + // capital letter to make the method public. + public static func XyzToXyy(X: Float64, Y: Float64, Z: Float64) -> (x: Float64, y: Float64, Yout: Float64) { + return Color.XyzToXyyWhiteRef(X: X, Y: Y, Z: Z, wref: D65) + } + + public static func XyzToXyyWhiteRef(X: Float64, Y: Float64, Z: Float64, wref: WhiteReference) -> (x: Float64, y: Float64, Yout: Float64) { + var x, y: Float64 + let Yout = Y + let N = X + Y + Z + if abs(N) < 1e-14 { + // When we have black, Bruce Lindbloom recommends to use + // the reference white's chromacity for x and y. + x = wref.wref[0] / (wref.wref[0] + wref.wref[1] + wref.wref[2]) + y = wref.wref[1] / (wref.wref[0] + wref.wref[1] + wref.wref[2]) + } else { + x = X / N + y = Y / N + } + return (x, y, Yout) + } + + public static func XyyToXyz(x: Float64, y: Float64, Y: Float64) -> (X: Float64, Yout: Float64, Z: Float64) { + let X, Z: Float64 + let Yout = Y + + if y > -1e-14 && y < 1e-14 { + X = 0.0 + Z = 0.0 + } else { + X = Y / y * x + Z = Y / y * (1.0 - x - y) + } + + return (X, Yout, Z) + } + + // Converts the given color to CIE xyY space using D65 as reference white. + // (Note that the reference white is only used for black input.) + // x, y and Y are in [0..1] + public func Xyy() -> (x: Float64, y: Float64, Y: Float64) { + let (x, y, z) = self.Xyz() + let (X, Y, Yout) = Color.XyzToXyy(X: x, Y: y, Z: z) + return (X, Y, Yout) + } + + // Converts the given color to CIE xyY space, taking into account + // a given reference white. (i.e. the monitor's white) + // (Note that the reference white is only used for black input.) + // x, y and Y are in [0..1] + public func XyyWhiteRef(wref: WhiteReference) -> (x: Float64, y: Float64, Y: Float64) { + let (X, Y2, Z) = self.Xyz() + let (x, y, Yout) = Color.XyzToXyyWhiteRef(X: X, Y: Y2, Z: Z, wref: wref) + return (x, y, Yout) + } + + // Generates a color by using data given in CIE xyY space. + // x, y and Y are in [0..1] + public static func Xyy(x: Float64, y: Float64, Y: Float64) -> Color { + let (X, Yout, Z) = Color.XyyToXyz(x: x, y: y, Y: Y) + return Color.Xyz(x: X, y: Yout, z: Z) + } + + /// L*a*b* /// + ////////////// + // http://en.wikipedia.org/wiki/Lab_color_space#CIELAB-CIEXYZ_conversions + // For L*a*b*, we need to L*a*b*<->XYZ->RGB and the first one is device dependent. + + public static func lab_f(_ t: Float64) -> Float64 { + if t > 6.0 / 29.0 * 6.0 / 29.0 * 6.0 / 29.0 { + return cbrt(t) + } + return t / 3.0 * 29.0 / 6.0 * 29.0 / 6.0 + 4.0 / 29.0 + } + + public static func XyzToLab(x: Float64, y: Float64, z: Float64) -> (l: Float64, a: Float64, b: Float64) { + // Use D65 white as reference point by default. + // http://www.fredmiranda.com/forum/topic/1035332 + // http://en.wikipedia.org/wiki/Standard_illuminant + return Color.XyzToLabWhiteRef(x: x, y: y, z: z, wref: D65) + } + + public static func XyzToLabWhiteRef(x: Float64, y: Float64, z: Float64, wref: WhiteReference) -> (l: Float64, a: Float64, b: Float64) { + let fy = Color.lab_f(y / wref.wref[1]) + let l = 1.16 * fy - 0.16 + let a = 5.0 * (Color.lab_f(x / wref.wref[0]) - fy) + let b = 2.0 * (fy - Color.lab_f(z / wref.wref[2])) + return (l, a, b) + } + + public static func lab_finv(_ t: Float64) -> Float64 { + if t > 6.0 / 29.0 { + return t * t * t + } + return 3.0 * 6.0 / 29.0 * 6.0 / 29.0 * (t - 4.0 / 29.0) + } + + public static func LabToXyz(l: Float64, a: Float64, b: Float64) -> (x: Float64, y: Float64, z: Float64) { + // D65 white (see above). + return Color.LabToXyzWhiteRef(l: l, a: a, b: b, wref: D65) + } + + public static func LabToXyzWhiteRef(l: Float64, a: Float64, b: Float64, wref: WhiteReference) -> (x: Float64, y: Float64, z: Float64) { + let l2 = (l + 0.16) / 1.16 + let x = wref.wref[0] * Color.lab_finv(l2 + a / 5.0) + let y = wref.wref[1] * Color.lab_finv(l2) + let z = wref.wref[2] * Color.lab_finv(l2 - b / 2.0) + return (x, y, z) + } + + // Converts the given color to CIE L*a*b* space using D65 as reference white. + public func Lab() -> (l: Float64, a: Float64, b: Float64) { + let (x, y, z) = self.Xyz() + return Color.XyzToLab(x: x, y: y, z: z) + } + + // Converts the given color to CIE L*a*b* space, taking into account + // a given reference white. (i.e. the monitor's white) + public func LabWhiteRef(wref: WhiteReference) -> (l: Float64, a: Float64, b: Float64) { + let (x, y, z) = self.Xyz() + return Color.XyzToLabWhiteRef(x: x, y: y, z: z, wref: wref) + } + + // Generates a color by using data given in CIE L*a*b* space using D65 as reference white. + // WARNING: many combinations of `l`, `a`, and `b` values do not have corresponding + // valid RGB values, check the FAQ in the README if you're unsure. + public static func Lab(l: Float64, a: Float64, b: Float64) -> Color { + let (x, y, z) = Color.LabToXyz(l: l, a: a, b: b) + return Color.Xyz(x: x, y: y, z: z) + } + + // Generates a color by using data given in CIE L*a*b* space, taking + // into account a given reference white. (i.e. the monitor's white) + public static func LabWhiteRef(l: Float64, a: Float64, b: Float64, wref: WhiteReference) -> Color { + let (x, y, z) = Color.LabToXyzWhiteRef(l: l, a: a, b: b, wref: wref) + return Color.Xyz(x: x, y: y, z: z) + } + + // DistanceLab is a good measure of visual similarity between two colors! + // A result of 0 would mean identical colors, while a result of 1 or higher + // means the colors differ a lot. + public func DistanceLab(_ c2: Color) -> Float64 { + let (l1, a1, b1) = Lab() + let (l2, a2, b2) = c2.Lab() + return (sq(l1 - l2) + sq(a1 - a2) + sq(b1 - b2)).squareRoot() + } + + // DistanceCIE76 is the same as DistanceLab. + public func DistanceCIE76(_ c2: Color) -> Float64 { + return self.DistanceLab(c2) + } + + // Uses the CIE94 formula to calculate color distance. More accurate than + // DistanceLab, but also more work. + public func DistanceCIE94(_ cr: Color) -> Float64 { + var (l1, a1, b1) = self.Lab() + var (l2, a2, b2) = cr.Lab() + + // NOTE: Since all those formulas expect L,a,b values 100x larger than we + // have them in this library, we either need to adjust all constants + // in the formula, or convert the ranges of L,a,b before, and then + // scale the distances down again. The latter is less error-prone. + (l1, a1, b1) = (l1 * 100.0, a1 * 100.0, b1 * 100.0) + (l2, a2, b2) = (l2 * 100.0, a2 * 100.0, b2 * 100.0) + + let kl = 1.0 // 2.0 for textiles + let kc = 1.0 + let kh = 1.0 + let k1 = 0.045 // 0.048 for textiles + let k2 = 0.015 // 0.014 for textiles. + + let deltaL = l1 - l2 + let c1 = (sq(a1) + sq(b1)).squareRoot() + let c2 = (sq(a2) + sq(b2)).squareRoot() + let deltaCab = c1 - c2 + + // Not taking Sqrt here for stability, and it's unnecessary. + let deltaHab2 = sq(a1 - a2) + sq(b1 - b2) - sq(deltaCab) + let sl = 1.0 + let sc = 1.0 + k1 * c1 + let sh = 1.0 + k2 * c1 + + let vL2 = sq(deltaL / (kl * sl)) + let vC2 = sq(deltaCab / (kc * sc)) + let vH2 = deltaHab2 / sq(kh * sh) + + return (vL2 + vC2 + vH2).squareRoot() * 0.01 // See above. + } + + // DistanceCIEDE2000 uses the Delta E 2000 formula to calculate color + // distance. It is more expensive but more accurate than both DistanceLab + // and DistanceCIE94. + public func DistanceCIEDE2000(_ cr: Color) -> Float64 { + return self.DistanceCIEDE2000klch(cr: cr, kl: 1.0, kc: 1.0, kh: 1.0) + } + + // DistanceCIEDE2000klch uses the Delta E 2000 formula with custom values + // for the weighting factors kL, kC, and kH. + public func DistanceCIEDE2000klch(cr: Color, kl: Float64, kc: Float64, kh: Float64) -> Float64 { + var (l1, a1, b1) = self.Lab() + var (l2, a2, b2) = cr.Lab() + + // As with CIE94, we scale up the ranges of L,a,b beforehand and scale + // them down again afterwards. + (l1, a1, b1) = (l1 * 100.0, a1 * 100.0, b1 * 100.0) + (l2, a2, b2) = (l2 * 100.0, a2 * 100.0, b2 * 100.0) + + let cab1 = (sq(a1) + sq(b1)).squareRoot() + let cab2 = (sq(a2) + sq(b2)).squareRoot() + let cabmean = (cab1 + cab2) / 2 + + let g = 0.5 * (1 - (pow(cabmean, 7) / (pow(cabmean, 7) + pow(25, 7))).squareRoot()) + let ap1 = (1 + g) * a1 + let ap2 = (1 + g) * a2 + let cp1 = (sq(ap1) + sq(b1)).squareRoot() + let cp2 = (sq(ap2) + sq(b2)).squareRoot() + + var hp1 = 0.0 + if b1 != ap1 || ap1 != 0 { + hp1 = atan2(b1, ap1) + if hp1 < 0 { + hp1 += Float64.pi * 2 + } + hp1 *= 180 / Float64.pi + } + var hp2 = 0.0 + if b2 != ap2 || ap2 != 0 { + hp2 = atan2(b2, ap2) + if hp2 < 0 { + hp2 += Float64.pi * 2 + } + hp2 *= 180 / Float64.pi + } + + let deltaLp = l2 - l1 + let deltaCp = cp2 - cp1 + var dhp = 0.0 + let cpProduct = cp1 * cp2 + if cpProduct != 0 { + dhp = hp2 - hp1 + if dhp > 180 { + dhp -= 360 + } else if dhp < -180 { + dhp += 360 + } + } + let deltaHp = 2 * cpProduct.squareRoot() * sin(dhp / 2 * Float64.pi / 180) + + let lpmean = (l1 + l2) / 2 + let cpmean = (cp1 + cp2) / 2 + var hpmean = hp1 + hp2 + if cpProduct != 0 { + hpmean /= 2 + if abs(hp1 - hp2) > 180 { + if hp1 + hp2 < 360 { + hpmean += 180 + } else { + hpmean -= 180 + } + } + } + + let t = 1 - 0.17 * cos((hpmean - 30) * Float64.pi / 180) + 0.24 * cos(2 * hpmean * Float64.pi / 180) + 0.32 * cos((3 * hpmean + 6) * Float64.pi / 180) - 0.2 * cos((4 * hpmean - 63) * Float64.pi / 180) + let deltaTheta = 30 * exp(-sq((hpmean - 275) / 25)) + let rc = 2 * (pow(cpmean, 7) / (pow(cpmean, 7) + pow(25, 7))).squareRoot() + let sl = 1 + (0.015 * sq(lpmean - 50)) / (20 + sq(lpmean - 50)).squareRoot() + let sc = 1 + 0.045 * cpmean + let sh = 1 + 0.015 * cpmean * t + let rt = -sin(2 * deltaTheta * Float64.pi / 180) * rc + + return (sq(deltaLp / (kl * sl)) + sq(deltaCp / (kc * sc)) + sq(deltaHp / (kh * sh)) + rt * (deltaCp / (kc * sc)) * (deltaHp / (kh * sh))).squareRoot() * 0.01 + } + + // BlendLab blends two colors in the L*a*b* color-space, which should result in a smoother blend. + // t == 0 results in c1, t == 1 results in c2 + public func BlendLab(c2: Color, t: Float64) -> Color { + let (l1, a1, b1) = self.Lab() + let (l2, a2, b2) = c2.Lab() + return Color.Lab(l: l1 + t * (l2 - l1), + a: a1 + t * (a2 - a1), + b: b1 + t * (b2 - b1)) + } + + /// L*u*v* /// + ////////////// + // http://en.wikipedia.org/wiki/CIELUV#XYZ_.E2.86.92_CIELUV_and_CIELUV_.E2.86.92_XYZ_conversions + // For L*u*v*, we need to L*u*v*<->XYZ<->RGB and the first one is device dependent. + + public static func XyzToLuv(x: Float64, y: Float64, z: Float64) -> (l: Float64, a: Float64, b: Float64) { + // Use D65 white as reference point by default. + // http://www.fredmiranda.com/forum/topic/1035332 + // http://en.wikipedia.org/wiki/Standard_illuminant + let (l, u, v) = Color.XyzToLuvWhiteRef(x: x, y: y, z: z, wref: D65) + return (l, u, v) + } + + public static func XyzToLuvWhiteRef(x: Float64, y: Float64, z: Float64, wref: WhiteReference) -> (l: Float64, u: Float64, v: Float64) { + let l, u, v: Float64 + if y / wref.wref[1] <= 6.0 / 29.0 * 6.0 / 29.0 * 6.0 / 29.0 { + l = y / wref.wref[1] * (29.0 / 3.0 * 29.0 / 3.0 * 29.0 / 3.0) / 100.0 + } else { + l = 1.16 * cbrt(y / wref.wref[1]) - 0.16 + } + let (ubis, vbis) = Color.xyz_to_uv(x: x, y: y, z: z) + let (un, vn) = Color.xyz_to_uv(x: wref.wref[0], y: wref.wref[1], z: wref.wref[2]) + u = 13.0 * l * (ubis - un) + v = 13.0 * l * (vbis - vn) + return (l, u, v) + } + + // For this part, we do as R's graphics.hcl does, not as wikipedia does. + // Or is it the same? + public static func xyz_to_uv(x: Float64, y: Float64, z: Float64) -> (u: Float64, v: Float64) { + var u, v: Float64 + let denom = x + 15.0 * y + 3.0 * z + if denom == 0.0 { + (u, v) = (0.0, 0.0) + } else { + u = 4.0 * x / denom + v = 9.0 * y / denom + } + return (u, v) + } + + public static func LuvToXyz(l: Float64, u: Float64, v: Float64) -> (x: Float64, y: Float64, z: Float64) { + // D65 white (see above). + return Color.LuvToXyzWhiteRef(l: l, u: u, v: v, wref: D65) + } + + public static func LuvToXyzWhiteRef(l: Float64, u: Float64, v: Float64, wref: WhiteReference) -> (x: Float64, y: Float64, z: Float64) { + var x, y, z: Float64 + z = 0.0 + + // y = wref[1] * lab_finv((l + 0.16) / 1.16) + if l <= 0.08 { + y = wref.wref[1] * l * 100.0 * 3.0 / 29.0 * 3.0 / 29.0 * 3.0 / 29.0 + } else { + y = wref.wref[1] * cub((l + 0.16) / 1.16) + } + + let (un, vn) = Color.xyz_to_uv(x: wref.wref[0], y: wref.wref[1], z: wref.wref[2]) + if l != 0.0 { + let ubis = u / (13.0 * l) + un + let vbis = v / (13.0 * l) + vn + x = y * 9.0 * ubis / (4.0 * vbis) + z = y * (12.0 - 3.0 * ubis - 20.0 * vbis) / (4.0 * vbis) + } else { + (x, y) = (0.0, 0.0) + } + + return (x, y, z) + } + + // Converts the given color to CIE L*u*v* space using D65 as reference white. + // L* is in [0..1] and both u* and v* are in about [-1..1] + public func Luv() -> (l: Float64, u: Float64, v: Float64) { + let (x, y, z) = self.Xyz() + let (l, u, v) = Color.XyzToLuv(x: x, y: y, z: z) + return (l, u, v) + } + + // Converts the given color to CIE L*u*v* space, taking into account + // a given reference white. (i.e. the monitor's white) + // L* is in [0..1] and both u* and v* are in about [-1..1] + public func LuvWhiteRef(wref: WhiteReference) -> (l: Float64, u: Float64, v: Float64) { + let (x, y, z) = self.Xyz() + let (l, u, v) = Color.XyzToLuvWhiteRef(x: x, y: y, z: z, wref: wref) + return (l, u, v) + } + + // Generates a color by using data given in CIE L*u*v* space using D65 as reference white. + // L* is in [0..1] and both u* and v* are in about [-1..1] + // WARNING: many combinations of `l`, `u`, and `v` values do not have corresponding + // valid RGB values, check the FAQ in the README if you're unsure. + public static func Luv(l: Float64, u: Float64, v: Float64) -> Color { + let (x, y, z) = Color.LuvToXyz(l: l, u: u, v: v) + return Color.Xyz(x: x, y: y, z: z) + } + + // Generates a color by using data given in CIE L*u*v* space, taking + // into account a given reference white. (i.e. the monitor's white) + // L* is in [0..1] and both u* and v* are in about [-1..1] + public static func LuvWhiteRef(l: Float64, u: Float64, v: Float64, wref: WhiteReference) -> Color { + let (x, y, z) = Color.LuvToXyzWhiteRef(l: l, u: u, v: v, wref: wref) + return Color.Xyz(x: x, y: y, z: z) + } + + // DistanceLuv is a good measure of visual similarity between two colors! + // A result of 0 would mean identical colors, while a result of 1 or higher + // means the colors differ a lot. + public func DistanceLuv(_ c2: Color) -> Float64 { + let (l1, u1, v1) = self.Luv() + let (l2, u2, v2) = c2.Luv() + return (sq(l1 - l2) + sq(u1 - u2) + sq(v1 - v2)).squareRoot() + } + + // BlendLuv blends two colors in the CIE-L*u*v* color-space, which should result in a smoother blend. + // t == 0 results in c1, t == 1 results in c2 + public func BlendLuv(c2: Color, t: Float64) -> Color { + let (l1, u1, v1) = self.Luv() + let (l2, u2, v2) = c2.Luv() + return Color.Luv(l: l1 + t * (l2 - l1), + u: u1 + t * (u2 - u1), + v: v1 + t * (v2 - v1)) + } + + /// HCL /// + /////////// + // HCL is nothing else than L*a*b* in cylindrical coordinates! + // (this was wrong on English wikipedia, I fixed it, let's hope the fix stays.) + // But it is widely popular since it is a "correct HSV" + // http://www.hunterlab.com/appnotes/an09_96a.pdf + + // Converts the given color to HCL space using D65 as reference white. + // H values are in [0..360], C and L values are in [0..1] although C can overshoot 1.0 + public func Hcl() -> (h: Float64, c: Float64, l: Float64) { + return self.HclWhiteRef(wref: D65) + } + + public static func LabToHcl(L: Float64, a: Float64, b: Float64) -> (h: Float64, c: Float64, l: Float64) { + let h: Float64 + // Oops, floating point workaround necessary if a ~= b and both are very small (i.e. almost zero). + if abs(b - a) > 1e-4, abs(a) > 1e-4 { + h = (57.29577951308232087721 * atan2(b, a) + 360.0).truncatingRemainder(dividingBy: 360.0) // Rad2Deg + } else { + h = 0.0 + } + let c = (sq(a) + sq(b)).squareRoot() + let l = L + return (h, c, l) + } + + // Converts the given color to HCL space, taking into account + // a given reference white. (i.e. the monitor's white) + // H values are in [0..360], C and L values are in [0..1] + public func HclWhiteRef(wref: WhiteReference) -> (h: Float64, c: Float64, l: Float64) { + let (L, a, b) = self.LabWhiteRef(wref: wref) + return Color.LabToHcl(L: L, a: a, b: b) + } + + // Generates a color by using data given in HCL space using D65 as reference white. + // H values are in [0..360], C and L values are in [0..1] + // WARNING: many combinations of `h`, `c`, and `l` values do not have corresponding + // valid RGB values, check the FAQ in the README if you're unsure. + public static func Hcl(h: Float64, c: Float64, l: Float64) -> Color { + return Color.HclWhiteRef(h: h, c: c, l: l, wref: D65) + } + + public static func HclToLab(h: Float64, c: Float64, l: Float64) -> (L: Float64, a: Float64, b: Float64) { + let H = 0.01745329251994329576 * h // Deg2Rad + let a = c * cos(H) + let b = c * sin(H) + let L = l + return (L, a, b) + } + + // Generates a color by using data given in HCL space, taking + // into account a given reference white. (i.e. the monitor's white) + // H values are in [0..360], C and L values are in [0..1] + public static func HclWhiteRef(h: Float64, c: Float64, l: Float64, wref: WhiteReference) -> Color { + let (L, a, b) = Color.HclToLab(h: h, c: c, l: l) + return Color.LabWhiteRef(l: L, a: a, b: b, wref: wref) + } + + // BlendHcl blends two colors in the CIE-L*C*h° color-space, which should result in a smoother blend. + // t == 0 results in c1, t == 1 results in c2 + public func BlendHcl(c2: Color, t: Float64) -> Color { + var (h1, c1, l1) = Hcl() + var (h2, c2, l2) = c2.Hcl() + + // https://github.com/lucasb-eyer/go-colorful/pull/60 + if c1 <= 0.00015, c2 >= 0.00015 { + h1 = h2 + } else if c2 <= 0.00015, c1 >= 0.00015 { + h2 = h1 + } + + // We know that h are both in [0..360] + return Color.Hcl(h: Color.interp_angle(a0: h1, a1: h2, t: t), c: c1 + t * (c2 - c1), l: l1 + t * (l2 - l1)).Clamped() + } + + // LuvLch + + // Converts the given color to LuvLCh space using D65 as reference white. + // h values are in [0..360], C and L values are in [0..1] although C can overshoot 1.0 + public func LuvLCh() -> (l: Float64, c: Float64, h: Float64) { + return LuvLChWhiteRef(wref: D65) + } + + public static func LuvToLuvLCh(L: Float64, u: Float64, v: Float64) -> (l: Float64, c: Float64, h: Float64) { + let l, c, h: Float64 + // Oops, floating point workaround necessary if u ~= v and both are very small (i.e. almost zero). + if abs(v - u) > 1e-4, abs(u) > 1e-4 { + h = (57.29577951308232087721 * atan2(v, u) + 360.0).truncatingRemainder(dividingBy: 360.0) // Rad2Deg + } else { + h = 0.0 + } + l = L + c = (sq(u) + sq(v)).squareRoot() + return (l, c, h) + } + + // Converts the given color to LuvLCh space, taking into account + // a given reference white. (i.e. the monitor's white) + // h values are in [0..360], c and l values are in [0..1] + public func LuvLChWhiteRef(wref: WhiteReference) -> (l: Float64, c: Float64, h: Float64) { + let (l, u, v) = LuvWhiteRef(wref: wref) + return Color.LuvToLuvLCh(L: l, u: u, v: v) + } + + // Generates a color by using data given in LuvLCh space using D65 as reference white. + // h values are in [0..360], C and L values are in [0..1] + // WARNING: many combinations of `l`, `c`, and `h` values do not have corresponding + // valid RGB values, check the FAQ in the README if you're unsure. + public func LuvLCh(l: Float64, c: Float64, h: Float64) -> Color { + return Color.LuvLChWhiteRef(l: l, c: c, h: h, wref: D65) + } + + public static func LuvLChToLuv(l: Float64, c: Float64, h: Float64) -> (L: Float64, u: Float64, v: Float64) { + let H = 0.01745329251994329576 * h // Deg2Rad + let u = c * cos(H) + let v = c * sin(H) + let L = l + return (L, u, v) + } + + // Generates a color by using data given in LuvLCh space, taking + // into account a given reference white. (i.e. the monitor's white) + // h values are in [0..360], C and L values are in [0..1] + public static func LuvLChWhiteRef(l: Float64, c: Float64, h: Float64, wref: WhiteReference) -> Color { + let (L, u, v) = Color.LuvLChToLuv(l: l, c: c, h: h) + return Color.LuvWhiteRef(l: L, u: u, v: v, wref: wref) + } + + // BlendLuvLCh blends two colors in the cylindrical CIELUV color space. + // t == 0 results in c1, t == 1 results in c2 + public func BlendLuvLCh(c2: Color, t: Float64) -> Color { + let (l1, c1, h1) = LuvLCh() + let (l2, c2, h2) = c2.LuvLCh() + + // We know that h are both in [0..360] + return LuvLCh(l: l1 + t * (l2 - l1), c: c1 + t * (c2 - c1), h: Color.interp_angle(a0: h1, a1: h2, t: t)) + } + + public var description: String { + return "R: \(R), G: \(G) B: \(B)" + } + + public static func == (c1: Color, c2: Color) -> Bool { + return c1.R == c2.R && + c1.G == c2.G && + c1.B == c2.B + } + + public static func < (c1: Color, c2: Color) -> Bool { + if c1.R != c2.R { + return c1.R < c2.R + } else if c1.G != c2.G { + return c1.G < c2.G + } else { + return c1.B < c2.B + } + } +} diff --git a/Sources/Colorful/happy_palettegen.swift b/Sources/Colorful/happy_palettegen.swift new file mode 100644 index 0000000..80c71f5 --- /dev/null +++ b/Sources/Colorful/happy_palettegen.swift @@ -0,0 +1,22 @@ + +// Uses the HSV color space to generate colors with similar S,V but distributed +// evenly along their Hue. This is fast but not always pretty. +// If you've got time to spare, use Lab (the non-fast below). +public func FastHappyPalette(_ colorsCount: Int) -> [Color] { + var colors = [Color](repeating: Color(), count: colorsCount) // make([]Color, colorsCount) + + for i in 0.. [Color] { + func pimpy(l: Float64, a: Float64, b: Float64) -> Bool { + let (_, c, _) = Color.LabToHcl(L: l, a: a, b: b) + return 0.3 <= c && 0.4 <= l && l <= 0.8 + } + + return try SoftPaletteEx(colorsCount: colorsCount, settings: SoftPaletteSettings(checkColorFn: pimpy, iterations: 50, manySamples: true)) +} diff --git a/Sources/Colorful/hsluv.swift b/Sources/Colorful/hsluv.swift new file mode 100644 index 0000000..12b9955 --- /dev/null +++ b/Sources/Colorful/hsluv.swift @@ -0,0 +1,209 @@ +// Source: https://github.com/hsluv/hsluv-go +// Under MIT License +// Modified so that Saturation and Luminance are in [0..1] instead of [0..100]. + +// HSLuv uses a rounded version of the D65. This has no impact on the final RGB +// values, but to keep high levels of accuracy for internal operations and when +// comparing to the test values, this modified white reference is used internally. +// +// See this GitHub thread for details on these values: +// https://github.com/hsluv/hsluv/issues/79 +import Foundation + +public var hSLuvD65: WhiteReference = WhiteReference(X: 0.95045592705167, Y: 1.0, Z: 1.089057750759878) + +extension Color { + public static func LuvLChToHSLuv(l: Float64, c: Float64, h: Float64) -> (h: Float64, s: Float64, l: Float64) { + // [-1..1] but the code expects it to be [-100..100] + let c: Float64 = c * 100.0 + let l: Float64 = l * 100.0 + + var s, max: Float64 + if l > 99.9999999 || l < 0.00000001 { + s = 0.0 + } else { + max = Color.maxChromaForLH(l: l, h: h) + s = c / max * 100.0 + } + return (h, clamp01(s / 100.0), clamp01(l / 100.0)) + } + + public static func HSLuvToLuvLCh(h: Float64, s: Float64, l: Float64) -> (L: Float64, C: Float64, h: Float64) { + let l: Float64 = l * 100.0 + let s: Float64 = s * 100.0 + + var c, max: Float64 + if l > 99.9999999 || l < 0.00000001 { + c = 0.0 + } else { + max = Color.maxChromaForLH(l: l, h: h) + c = max / 100.0 * s + } + + // c is [-100..100], but for LCh it's supposed to be almost [-1..1] + return (clamp01(l / 100.0), c / 100.0, h) + } + + public static func LuvLChToHPLuv(l: Float64, c: Float64, h: Float64) -> (h: Float64, s: Float64, l: Float64) { + // [-1..1] but the code expects it to be [-100..100] + let c: Float64 = c * 100.0 + let l: Float64 = l * 100.0 + + var s, max: Float64 + if l > 99.9999999 || l < 0.00000001 { + s = 0.0 + } else { + max = Color.maxSafeChromaForL(l) + s = c / max * 100.0 + } + return (h, s / 100.0, l / 100.0) + } + + public static func HPLuvToLuvLCh(h: Float64, s: Float64, l: Float64) -> (l: Float64, c: Float64, h: Float64) { + // [-1..1] but the code expects it to be [-100..100] + let l = l * 100.0 + let s = s * 100.0 + + var c, max: Float64 + if l > 99.9999999 || l < 0.00000001 { + c = 0.0 + } else { + max = Color.maxSafeChromaForL(l) + c = max / 100.0 * s + } + return (l / 100.0, c / 100.0, h) + } + + // HSLuv returns the Hue, Saturation and Luminance of the color in the HSLuv + // color space. Hue in [0..360], a Saturation [0..1], and a Luminance + // (lightness) in [0..1]. + public func HSLuv() -> (h: Float64, s: Float64, l: Float64) { + // sRGB -> Linear RGB -> CIEXYZ -> CIELUV -> LuvLCh -> HSLuv + var s: Float64 + var (l, c, h) = LuvLChWhiteRef(wref: hSLuvD65) + (h, s, l) = Color.LuvLChToHSLuv(l: l, c: c, h: h) + return (h, s, l) + } + + // HPLuv returns the Hue, Saturation and Luminance of the color in the HSLuv + // color space. Hue in [0..360], a Saturation [0..1], and a Luminance + // (lightness) in [0..1]. + // + // Note that HPLuv can only represent pastel colors, and so the Saturation + // value could be much larger than 1 for colors it can't represent. + public func HPLuv() -> (h: Float64, s: Float64, l: Float64) { + var s: Float64 + var (l, c, h) = LuvLChWhiteRef(wref: hSLuvD65) + (h, s, l) = Color.LuvLChToHPLuv(l: l, c: c, h: h) + return (h, s, l) + } + + // DistanceHPLuv calculates Euclidean distance in the HPLuv colorspace. No idea + // how useful this is. + + // The Hue value is divided by 100 before the calculation, so that H, S, and L + // have the same relative ranges. + public func DistanceHPLuv(c2: Color) -> Float64 { + let (h1, s1, l1) = HPLuv() + let (h2, s2, l2) = c2.HPLuv() + return (sq((h1 - h2) / 100.0) + sq(s1 - s2) + sq(l1 - l2)).squareRoot() + } + + // HSLuv creates a new Color from values in the HSLuv color space. + // Hue in [0..360], a Saturation [0..1], and a Luminance (lightness) in [0..1]. + // + // The returned color values are clamped (using .Clamped), so this will never output + // an invalid color. + public static func HSLuv(h: Float64, s: Float64, l: Float64) -> Color { + // HSLuv -> LuvLCh -> CIELUV -> CIEXYZ -> Linear RGB -> sRGB + var u, v: Float64 + var (l, c, h) = Color.HSLuvToLuvLCh(h: h, s: s, l: l) + (l, u, v) = Color.LuvLChToLuv(l: l, c: c, h: h) + let (x, y, z) = Color.LuvToXyzWhiteRef(l: l, u: u, v: v, wref: hSLuvD65) + let (r, g, b) = Color.XyzToLinearRgb(x: x, y: y, z: z) + return Color.LinearRgb(r: r, g: g, b: b).Clamped() + } + + // HPLuv creates a new Color from values in the HPLuv color space. + // Hue in [0..360], a Saturation [0..1], and a Luminance (lightness) in [0..1]. + // + // The returned color values are clamped (using .Clamped), so this will never output + // an invalid color. + public static func HPLuv(h: Float64, s: Float64, l: Float64) -> Color { + // HPLuv -> LuvLCh -> CIELUV -> CIEXYZ -> Linear RGB -> sRGB + var u, v: Float64 + var (l, c, h) = Color.HPLuvToLuvLCh(h: h, s: s, l: l) + (l, u, v) = Color.LuvLChToLuv(l: l, c: c, h: h) + let (x, y, z) = Color.LuvToXyzWhiteRef(l: l, u: u, v: v, wref: hSLuvD65) + let (r, g, b) = Color.XyzToLinearRgb(x: x, y: y, z: z) + return Color.LinearRgb(r: r, g: g, b: b).Clamped() + } + + static var m: [[Float64]] = [ + [3.2409699419045214, -1.5373831775700935, -0.49861076029300328], + [-0.96924363628087983, 1.8759675015077207, 0.041555057407175613], + [0.055630079696993609, -0.20397695888897657, 1.0569715142428786], + ] + + static let kappa = 903.2962962962963 + static let epsilon = 0.0088564516790356308 + + static func maxChromaForLH(l: Float64, h: Float64) -> Float64 { + let hRad = h / 360.0 * Float64.pi * 2.0 + var minLength = Float64.greatestFiniteMagnitude + for line in Color.getBounds(l) { + let length = lengthOfRayUntilIntersect(theta: hRad, x: line[0], y: line[1]) + if length > 0.0, length < minLength { + minLength = length + } + } + return minLength + } + + static func getBounds(_ l: Float64) -> [[Float64]] { + var sub2: Float64 + var ret = [[Float64]](repeating: [Float64](repeating: Float64(), count: 2), count: 6) + let sub1 = pow(l + 16.0, 3.0) / 1_560_896.0 + if sub1 > epsilon { + sub2 = sub1 + } else { + sub2 = l / kappa + } + for (i, _) in m.enumerated() { + for k in 0 ..< 2 { + let top1: Float64 = (284_517.0 * m[i][0] - 94839.0 * m[i][2]) * sub2 + let top2: Float64 = (838_422.0 * m[i][2] + 769_860.0 * m[i][1] + 731_718.0 * m[i][0]) * l * sub2 - 769_860.0 * Float64(k) * l + let bottom: Float64 = (632_260.0 * m[i][2] - 126_452.0 * m[i][1]) * sub2 + 126_452.0 * Float64(k) + ret[i * 2 + k][0] = top1 / bottom + ret[i * 2 + k][1] = top2 / bottom + } + } + return ret + } + + static func lengthOfRayUntilIntersect(theta: Float64, x: Float64, y: Float64) -> Float64 { + return y / (sin(theta) - x * cos(theta)) + } + + static func maxSafeChromaForL(_ l: Float64) -> Float64 { + var minLength = Float64.greatestFiniteMagnitude + for line in Color.getBounds(l) { + let m1 = line[0] + let b1 = line[1] + let x = Color.intersectLineLine(x1: m1, y1: b1, x2: -1.0 / m1, y2: 0.0) + let dist = Color.distanceFromPole(x: x, y: b1 + x * m1) + if dist < minLength { + minLength = dist + } + } + return minLength + } + + static func intersectLineLine(x1: Float64, y1: Float64, x2: Float64, y2: Float64) -> Float64 { + return (y1 - y2) / (x2 - x1) + } + + static func distanceFromPole(x: Float64, y: Float64) -> Float64 { + return (pow(x, 2.0) + pow(y, 2.0)).squareRoot() + } +} diff --git a/Sources/Colorful/soft_palettegen.swift b/Sources/Colorful/soft_palettegen.swift new file mode 100644 index 0000000..841ed89 --- /dev/null +++ b/Sources/Colorful/soft_palettegen.swift @@ -0,0 +1,221 @@ + +struct lab_t: Equatable { + var L, A, B: Float64 + init(L: Float64 = 0.0, A: Float64 = 0.0, B: Float64 = 0.0) { + self.L = L + self.A = A + self.B = B + } + static func == (lhs: lab_t, rhs: lab_t) -> Bool { + return lhs.L == rhs.L && + lhs.A == rhs.A && + lhs.B == rhs.B + } +} + +public func randomIntInRange(min: Int, max: Int) -> Int { + return Int.random(in: min...max) +} + +public typealias CheckColorFn = (Float64, Float64, Float64) -> Bool + +public struct SoftPaletteSettings { + // A function which can be used to restrict the allowed color-space. + var CheckColor: CheckColorFn? + + // The higher, the better quality but the slower. Usually two figures. + var Iterations: Int + + // Use up to 160000 or 8000 samples of the L*a*b* space (and thus calls to CheckColor). + // Set this to true only if your CheckColor shapes the Lab space weirdly. + var ManySamples: Bool + + public init(checkColorFn: CheckColorFn?, iterations: Int, manySamples: Bool) { + self.CheckColor = checkColorFn + self.Iterations = iterations + self.ManySamples = manySamples + } +} + + +// An example error we can throw +public enum SoftPaletteError: Error { + case tooManyColorsRequested(String) +} + +// Yeah, windows-stype Foo, FooEx, screw you golang... +// Uses K-means to cluster the color-space and return the means of the clusters +// as a new palette of distinctive colors. Falls back to K-medoid if the mean +// happens to fall outside of the color-space, which can only happen if you +// specify a CheckColor function. +public func SoftPaletteEx(colorsCount: Int, settings: SoftPaletteSettings) throws -> [Color] { + + // Checks whether it's a valid RGB and also fulfills the potentially provided constraint. + func checkIfRGBValid(col: lab_t) -> Bool { + let c = Color.Lab(l: col.L, a: col.A, b: col.B) + return c.IsValid() && (settings.CheckColor == nil || settings.CheckColor!(col.L, col.A, col.B)) + } + + let check = checkIfRGBValid + + // Sample the color space. These will be the points k-means is run on. + var dl = 0.05 + var dab = 0.1 + if settings.ManySamples { + dl = 0.01 + dab = 0.05 + } + + var samples: [lab_t] = [lab_t]() + samples.reserveCapacity(Int(1.0/dl*2.0/dab*2.0/dab)) + + for l in stride(from: 0.0, through: 1.0, by: dl) { + for a in stride(from: -1.0, through: 1.0, by: dab) { + for b in stride(from: -1.0, through: 1.0, by: dab) { + if check(lab_t(L: l, A: a, B: b)) { + samples.append(lab_t(L: l, A: a, B: b)) + } + } + } + } + + // That would cause some infinite loops down there... + if samples.count < colorsCount { + throw SoftPaletteError.tooManyColorsRequested(String(format: "palettegen: more colors requested (%@) than samples available (%@). Your requested color count may be wrong, you might want to use many samples or your constraint function makes the valid color space too small", colorsCount, samples.count)) + } else if samples.count == colorsCount { + return labs2cols(samples) // Oops? + } + + // We take the initial means out of the samples, so they are in fact medoids. + // This helps us avoid infinite loops or arbitrary cutoffs with too restrictive constraints. + // means := make([]lab_t, colorsCount) + var means = [lab_t](repeating: lab_t(), count: colorsCount) + for i in 0.. 0 { + newmean.L /= Float64(nsamples) + newmean.A /= Float64(nsamples) + newmean.B /= Float64(nsamples) + } else { + // That mean doesn't have any samples? Get a new mean from the sample list! + var inewmean: Int = randomIntInRange(min: 0, max: samples_used.count) + while samples_used[inewmean] { + inewmean = randomIntInRange(min: 0, max: samples_used.count) + } + newmean = samples[inewmean] + samples_used[inewmean] = true + } + + // But now we still need to check whether the new mean is an allowed color. + if nsamples > 0 && check(newmean) { + // It does, life's good (TM) + means[imean] = newmean + } else { + // New mean isn't an allowed color or doesn't have any samples! + // Switch to medoid mode and pick the closest (unused) sample. + // This should always find something thanks to len(samples) >= colorsCount + var mindist = Float64.infinity + for (isample, sample) in samples.enumerated() { + if !samples_used[isample] { + let dist = lab_dist(lab1: sample, lab2: newmean) + if dist < mindist { + mindist = dist + newmean = sample + } + } + } + } + } + } + return labs2cols(means) +} + + +// A wrapper which uses common parameters. +public func SoftPalette(_ colorsCount: Int) throws -> [Color] { + let settings = SoftPaletteSettings(checkColorFn: nil, iterations: 50, manySamples: false) + do { + return try SoftPaletteEx(colorsCount: colorsCount, settings: settings) + } catch let error { + throw error + } +} + + +func In(haystack: [lab_t], upto: Int, needle: lab_t) -> Bool { + var i = 0 + while (i < upto && i < haystack.count) { + if haystack[i] == needle { + return true + } + i += 1 + } + return false +} + +let LAB_DELTA = 1e-6 + +func lab_eq(lab1: lab_t, lab2: lab_t) -> Bool { + return abs(lab1.L-lab2.L) < LAB_DELTA && + abs(lab1.A-lab2.A) < LAB_DELTA && + abs(lab1.B-lab2.B) < LAB_DELTA +} + +// That's faster than using colorful's DistanceLab since we would have to +// convert back and forth for that. Here is no conversion. +func lab_dist(lab1: lab_t, lab2: lab_t) -> Float64 { + return (sq(lab1.L-lab2.L) + sq(lab1.A-lab2.A) + sq(lab1.B-lab2.B)).squareRoot() +} + +func labs2cols(_ labs: [lab_t]) -> [Color] { + var cols = [Color](repeating: Color(), count: labs.count) + + for (k, v) in labs.enumerated() { + cols[k] = Color.Lab(l: v.L, a: v.A, b: v.B) + } + + return cols +} diff --git a/Sources/Colorful/sort.swift b/Sources/Colorful/sort.swift new file mode 100644 index 0000000..76d15f0 --- /dev/null +++ b/Sources/Colorful/sort.swift @@ -0,0 +1,194 @@ +import Foundation + +typealias edgeIdxs = [Int] +typealias edgeDistance = [edgeIdxs:Float64] + +class Element: Equatable { + weak var parent: Element? + var rank: Int = 0 + + init() { + self.parent = self + } + + static func == (lhs: Element, rhs: Element) -> Bool { + let lhsAddress = Unmanaged.passUnretained(lhs) + let rhsAddress = Unmanaged.passUnretained(rhs) + return lhsAddress.toOpaque() == rhsAddress.toOpaque() + } + + func find() -> Element { + var e: Element = self + while e.parent != e { + e.parent = e.parent!.parent + e = e.parent! + } + return e + } +} + +// allToAllDistancesCIEDE2000 computes the CIEDE2000 distance between each pair of +// colors. It returns a map from a pair of indices (u, v) with u < v to a +// distance. +func allToAllDistancesCIEDE2000(_ cs: [Color]) -> edgeDistance { + let nc = cs.count + var m: edgeDistance = [:] + for u in 0..<(nc-1) { + var v = u + 1 + while v < nc { + m[[u, v]] = cs[u].DistanceCIEDE2000(cs[v]) + v += 1 + } + } + return m +} + +// sortEdges sorts all edges in a distance map by increasing vertex distance. +func sortEdges(_ m: edgeDistance) -> [edgeIdxs] { + var es: [edgeIdxs] = [edgeIdxs]() + es.reserveCapacity(m.count) + for uv in m.keys { + es.append(uv) + } + es.sort(by: { itemA, itemB in + m[itemA]! < m[itemB]! + }) + return es +} + +// union establishes the union of two sets when given an element from each set. +// Afterwards, the original sets no longer exist as separate entities. +func union(e1: Element, e2: Element) { + // Ensure the two elements aren't already part of the same union. + let e1Root = e1.find() + let e2Root = e2.find() + if e1Root == e2Root { + return + } + + // Create a union by making the shorter tree point to the root of the + // larger tree. + if e1Root.rank < e2Root.rank { + e1Root.parent = e2Root + } else if e1Root.rank > e2Root.rank { + e2Root.parent = e1Root + } else { + e2Root.parent = e1Root + e1Root.rank += 1 + } +} + +// traverseMST walks a minimum spanning tree in prefix order. +func traverseMST(mst: [edgeIdxs:Any], root: Int) -> [Int] { + // Compute a list of neighbors for each vertex. + var neighs: [Int:[Int]] = [:] + for uv in mst.keys { + let (u, v) = (uv[0], uv[1]) + if neighs[u] == nil { + neighs[u] = [v] + } else { + neighs[u]!.append(v) + } + } + + for (u, var vs) in neighs { + vs.sort() + + for (index, _) in neighs[u]!.enumerated() { + if index >= vs.count { + break + } + neighs[u]![index] = vs[index] + } + } + + // Walk the tree from a given vertex. + var order: [Int] = [] + order.reserveCapacity(neighs.count) + var visited: [Int: Bool] = [:] + func walkFrom(_ r: Int) { + // Visit the starting vertex. + order.append(r) + visited[r] = true + + // Recursively visit each child in turn. + for c in neighs[r] ?? [] { + if !(visited[c] ?? false) { + walkFrom(c) + } + } + } + + walkFrom(root) + return order +} + +// minSpanTree computes a minimum spanning tree from a vertex count and a +// distance-sorted edge list. It returns the subset of edges that belong to +// the tree, including both (u, v) and (v, u) for each edge. +func minSpanTree(nc: Int, es: [edgeIdxs]) -> [edgeIdxs:Any] { + // Start with each vertex in its own set. + + var elts : [Element] = [Element]() + for _ in 0.. [Color] { + // Do nothing in trivial cases. + var newCs: [Color] = [Color](repeating: Color(), count: cs.count) + if cs.count < 2 { + newCs.append(contentsOf: cs[0...1]) + return newCs + } + + // Compute the distance from each color to every other color. + let dists = allToAllDistancesCIEDE2000(cs) + + // Produce a list of edges in increasing order of the distance between + // their vertices. + let edges = sortEdges(dists) + + // Construct a minimum spanning tree from the list of edges. + let mst = minSpanTree(nc: cs.count, es: edges) + + // Find the darkest color in the list. + let black: Color = Color() + var dIdx: Int = 0 // Index of darkest color + var light = Float64.greatestFiniteMagnitude // Lightness of darkest color (distance from black) + for (i, c) in cs.enumerated() { + let d = black.DistanceCIEDE2000(c) + if d < light { + dIdx = i + light = d + } + } + + // Traverse the tree starting from the darkest color. + let idxs = traverseMST(mst: mst, root: dIdx) + + // Convert the index list to a list of colors, overwriting the input. + for (i, idx) in idxs.enumerated() { + newCs[i] = cs[idx] + } + + return newCs +} diff --git a/Sources/Colorful/warm_palettegen.swift b/Sources/Colorful/warm_palettegen.swift new file mode 100644 index 0000000..007b172 --- /dev/null +++ b/Sources/Colorful/warm_palettegen.swift @@ -0,0 +1,21 @@ +// Uses the HSV color space to generate colors with similar S,V but distributed +// evenly along their Hue. This is fast but not always pretty. +// If you've got time to spare, use Lab (the non-fast below). +public func FastWarmPalette(_ colorsCount: Int) -> [Color] { + var colors = [Color](repeating: Color(), count: colorsCount) + + for i in 0.. [Color] { + func warmy(l: Float64, a: Float64, b: Float64) -> Bool { + let (_, c, _) = Color.LabToHcl(L: l, a: a, b: b) + return 0.1 <= c && c <= 0.4 && 0.2 <= l && l <= 0.5 + } + + return try SoftPaletteEx(colorsCount: colorsCount, settings: SoftPaletteSettings(checkColorFn: warmy, iterations: 50, manySamples: true)) +} diff --git a/Sources/Demos/Benchmark/main.swift b/Sources/Demos/Benchmark/main.swift new file mode 100644 index 0000000..344d996 --- /dev/null +++ b/Sources/Demos/Benchmark/main.swift @@ -0,0 +1,77 @@ +import Foundation +import Colorful + +let TESTS_COUNT = 10000 + +func BenchmarkColorToLinear() { + measure(label: "ColorToLinear", tests: TESTS_COUNT) { + let (r, g, b) = Color(R: randomFloat64(), G: randomFloat64(), B: randomFloat64()).LinearRgb() + _ = r + _ = g + _ = b + } +} + +func BenchmarkFastColorToLinear() { + measure(label: "FastColorToLinear", tests: TESTS_COUNT) { + let (r, g, b) = Color(R: randomFloat64(), G: randomFloat64(), B: randomFloat64()).FastLinearRgb() + _ = r + _ = g + _ = b + } +} + +func BenchmarkLinearToColor() { + measure(label: "LinearToColor", tests: TESTS_COUNT) { + let c = Color.LinearRgb(r: randomFloat64(), g: randomFloat64(), b: randomFloat64()) + _ = c + } +} + +func BenchmarkFastLinearToColor() { + measure(label: "FastLinearToColor", tests: TESTS_COUNT) { + let c = Color.FastLinearRgb(r: randomFloat64(), g: randomFloat64(), b: randomFloat64()) + _ = c + } +} + +BenchmarkColorToLinear() +BenchmarkFastColorToLinear() +BenchmarkLinearToColor() +BenchmarkFastLinearToColor() + +//-------------------------------------------------------- +// this benchmarking function has been taken from: +// https://stackoverflow.com/a/53403129 +//-------------------------------------------------------- +@_transparent @discardableResult public func measure(label: String? = nil, tests: Int = 1, printResults output: Bool = true, setup: @escaping () -> Void = { return }, _ block: @escaping () -> Void) -> Double { + + guard tests > 0 else { fatalError("Number of tests must be greater than 0") } + + var avgExecutionTime : CFAbsoluteTime = 0 + for _ in 1...tests { + setup() + let start = CFAbsoluteTimeGetCurrent() + block() + let end = CFAbsoluteTimeGetCurrent() + avgExecutionTime += end - start + } + + avgExecutionTime /= CFAbsoluteTime(tests) + + if output { + let avgTimeStr = "\(avgExecutionTime)".replacingOccurrences(of: "e|E", with: " × 10^", options: .regularExpression, range: nil) + + if let label = label { + print(label, "▿") + print("\tExecution time: \(avgTimeStr)s") + print("\tNumber of tests: \(tests)\n") + } else { + print("Execution time: \(avgTimeStr)s") + print("Number of tests: \(tests)\n") + } + } + + return avgExecutionTime +} + diff --git a/Sources/Demos/ColorBlend/clamped.png b/Sources/Demos/ColorBlend/clamped.png new file mode 100644 index 0000000000000000000000000000000000000000..69e880d3570e481060ff55c21cd86d627709303e GIT binary patch literal 6305 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+import AppKit + +import Colorful +import DemoShared + +let blocks = 10 +let blockw = 40 + +let (image, imageRep) = createImageRep(NSSize(width: blocks*blockw, height: 200)) + +let c1 = try! Color.Hex("#fdffcc") +let c2 = try! Color.Hex("#242a42") + +// Use these colors to get invalid RGB in the gradient. +// let c1 = try! Color.Hex("#EEEF61") +// let c2 = try! Color.Hex("#1E3140") + +var col = Color() +for i in 0..*Jv41*BY5)(7gOlcwO*s@=QQOQy&``Ee|V@Zi{Eo04I z3DbfsF}6{*NHb_GGtJ=j-t*pb-rjrP_q^x#{C>~xkLUS5=lst3eV!-&JlaB#Uy2_9 z00^Rx25N-hn#A52KUP;P>_6Q?W!=9YVGf;bo##|6G1E60zRE9nWTIP6s4URJN2NF7$m zzU<6y^c9wSY^M63p?mp%X8l#lj$70IYgjvayKhvS?B_GtKpf9A(EhOyx8Pqec^!;! zYZfmEp&XQbIM)@tH40Mo9)89#mOgp^090@=Z0j(`5;l3Iik1nQo5&f4Ie@)Stx(xgAwqMk0%k%}(v^HkAD$_N9-1d2%$3L=pWOPPtCm-n- z{d`3G2xQvg6)S{WR1Lq9Kc3vblwZ9pG^?f`)3^vaf%|r(z-SFu$4J=`9i5v_)41Ee z)cqwy3`tjHe6YJLqKMBdF>?7Z26w4Tno;-ZavnarhWDS%P@?9)VfBPXF{6>Uy*OVA zIWW7(@Mw;4z^lQ$B9r35rmq6G(YjD)uCb58ZpMxWUc8tw*S`X3F7!Zyj=xfNu>=Hs z_ReW&HM8+Z=8Avp`7!En2oAg6m3Gzf4sG2Oa63``)76OYylN98**Kc0BxjU?fAN z?gyXZj~;sMR{34!z4zLedbKTmu9>s8gsQxq?!Yqk8XF5ANuI_ppY2*3h|u1pyK(w- zWL(dA>U9F6+eoX$ssSGc%x8zHzzyt@{L=-1Gvee$pezZ#Y_aPYBw-C}^A=P|^>+MG z=?Hv4ta-kods(c3O=@P4^_ml&3-Mm-_$|Be2D+7#%bz_@18>+6EY$Ou@7uyEPBD^H z4NCzxB&KuwPx92-?F(#Q+g}>$p%9|4!S<8vgbMB)*4Uz`=K*(^1->AdREr39$?A&i 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%.17f\tand c2: %.17f", c1a.DistanceRgb(c1b), c2a.DistanceRgb(c2b))) +print(String(format: "DistanceLab: c1: %.17f\tand c2: %.17f", c1a.DistanceLab(c1b), c2a.DistanceLab(c2b))) +print(String(format: "DistanceLuv: c1: %.17f\tand c2: %.17f", c1a.DistanceLuv(c1b), c2a.DistanceLuv(c2b))) +print(String(format: "DistanceCIE76: c1: %.17f\tand c2: %.17f", c1a.DistanceCIE76(c1b), c2a.DistanceCIE76(c2b))) +print(String(format: "DistanceCIE94: c1: %.17f\tand c2: %.17f", c1a.DistanceCIE94(c1b), c2a.DistanceCIE94(c2b))) +print(String(format: "DistanceCIEDE2000: c1: %.17f\tand c2: %.17f", c1a.DistanceCIEDE2000(c1b), c2a.DistanceCIEDE2000(c2b))) diff --git a/Sources/Demos/ColorGens/colorgens.png b/Sources/Demos/ColorGens/colorgens.png new file mode 100644 index 0000000000000000000000000000000000000000..2db460123004fc40537ae50a624306bc499b608c GIT binary patch literal 2317 zcmeAS@N?(olHy`uVBq!ia0y~yVB8C2Z{c79lKm#B`9O-XILO_JVcj{Imq3n7YJ_K+ 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Foundation +import AppKit + +import Colorful +import DemoShared + +let blocks = 10 +let blockw = 40 +let space = 5 + +let (image, imageRep) = createImageRep(NSSize(width: blocks*blockw+space*(blocks-1), height: 4*(blockw+space))) + +for i in 0..>`?!5iv1}v5hfB+awevM)s^@6g9?- zWt5PeFk>0}PIfcHFy_aH_kZ}k$J>YNzRvr+ujBr3-RE&!=W%1~Y%GNZWCQ>JfUwm+ zR~!IAc$C!@6Q?kqr9K~|6Qj0qZT@rq zor}OEzY~deX6iYIUf1%8+g0$1pFBKw&E5n^HaBju7&!N*gZQU09{Udp#zL0Hpe$aV zukvD|7f#pM|Q5*p`mZZIbU2+x$9T^=NgZU?F`pHI*_Mv ztyrTS4#_WS`OD29HkX_gK-i(Ld*}-)#fcJE`pdjJbjS1ZZ?m-%o`(a?%@lP;Dle_| zomHq=H*SWX(R=4LvK?}-t-|{&Xk&rafQhYAPqn+P;EtRNY`Jv)qjCQv>P)=gc*hgwVPs}ujuufSM%kv52tyK}#j6_x{>jaFU{g`MI zbr}y`z08@2swx)gq_1ZBv`^=%rAt+?Sw_U0sNL^-p@zC;?l<%a-W1o!kPUhdWOOUo zI!QEQ=@O*HYv=syTo?-^B(vEV&5bf#FPs!$OmiloiG*IQUiLiB~Q&@~&xaN4!n#BJ7# zn`t(0^*GXkf{qHVgsiC!)eVt1+nbJtGQG$a=KD8FtygI+d4rlg+7bbg1tIL0KOr@l z;!*#sY=;fJTe%jnR2x;t(!;Sil`u-J?b0u@Hitc%sjU$4=jL1Av6%!ayf{28w4*_e zQIE8#CUmTs=FzHsp&K)jYJQFdPj?DEV58fd^^5f#=)8`Fo4ct|O@o@U0sIo9L`26q 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zicKsdj!$bXB*E<-C{`m^35AB5GD4)DxY>OCTtGc7`Z-dj87mn>YEm^_qNp~&HdnI~h&o(k# zIB3p~B^RMVL+@A(KSL)EZJWQv=Q&o)$3NYlrO6~XH8A`=$x9!NKBnl1i|`r%v+tg> z?Clj#$$WrRy$|mHDD0jHeY9ki5it141m7VVjPNCk<7e}g=D?cXm0%Q#%xmjZ0vyJ| zdoomQshEhkHvagq1FL%I#J>CF74kVSqRab`E~})tZ$wX>t^@p27ih6Ril@}-06%JO lub=*1{JR_fue7nsl{z [Color] { + var cs: [Color] = [Color](repeating: Color(), count: n) + for (i, _) in cs.enumerated() { + cs[i] = Color( + R: randomFloat64(), + G: randomFloat64(), + B: randomFloat64() + ) + } + return cs +} + +// drawStripes creates an image with three sets of stripes. +func drawStripes(cs1: [Color], cs2: [Color], cs3: [Color], ht: Int, sep: Int) -> NSImage { + let (image, imageRep) = createImageRep(NSSize(width: cs1.count, height: 3*ht+2*sep)) + for (c, _) in cs1.enumerated() { + for r in 0..Px#L}ge>W=%~1DgXcg2mk?xX#fNO00031000^Q000001E2u_0{{R30RRC20H6W@ z1ONa40RR91D4+uX1ONa40RR950000001(DNe*gdp2T4RhRCodHok4cvI1EJPv`#h$ zos&-DVe)!mDl#QX0REz?SCL4AjY6RS(z5;d_wmm{{97LnV%cR`7iwW>-EWVXr4?h$ 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z&O-K=T`Z5u7&9jVpvS+$UUNh5eJ97bhFNVDOt}OXRy=MhBXYM8C?HUKi=`6?br%0wc2H|4@KG))(E&Prp0t?n2WJ@i`!UaUAru1A^Xd&%i=FcvTlG-XSsA>x0OXd zdwYOU(6Bp@ARv#;xC1%HC}@VE4g&Jn30Ie(t^%v9#tY62>Pnm(WKAgu` zjG;7M8q`dCyM93~H|0|E*aDKGk2^*it08hh+0+Dt^4P52Az;ca7l{;D_l$C75lbfv z$Q}_g?g{qQW_1RU_H2U6CD(!INhY>i)Y~6_%I%Lo_w=mb9=CVGJpP3Csp}_IB>pQP z(%uryJK@nKc0-sD+V>C znH;Mzt;V3{$i-ySvVK5&7%q>^>bwfvTV5Y>MS?l4ZeP?1r7`%GhW5D6w!ACuLpW57 z+ff8lkeg)Y#c^brYPl>Rqo~A=xk$v~Ik1MM6DA;>WI|Fcs9dYt+dQ+YkWe#?wO%7&k4It?I))vvImV%J92paA1mw;@z!*~}^m021z1D~Hc%-O#W1Pp- zJ8gQ60J(Q!wlJi}dAT~W?7n)0PUu)87sP6;1EJbm?u4H6nBmsa8UbcyY$riB0uaJBm|X Color { + var t: Float64 = t + for i in 0.. Color { + do { + return try! Color.Hex(s) + } +} + + +// The "keypoints" of the gradient. +let keypoints: [GradientKeyPoint] = [ + GradientKeyPoint(Col: MustParseHex("#9e0142"), Pos: 0.0), + GradientKeyPoint(Col: MustParseHex("#d53e4f"), Pos: 0.1), + GradientKeyPoint(Col: MustParseHex("#f46d43"), Pos: 0.2), + GradientKeyPoint(Col: MustParseHex("#fdae61"), Pos: 0.3), + GradientKeyPoint(Col: MustParseHex("#fee090"), Pos: 0.4), + GradientKeyPoint(Col: MustParseHex("#ffffbf"), Pos: 0.5), + GradientKeyPoint(Col: MustParseHex("#e6f598"), Pos: 0.6), + GradientKeyPoint(Col: MustParseHex("#abdda4"), Pos: 0.7), + GradientKeyPoint(Col: MustParseHex("#66c2a5"), Pos: 0.8), + GradientKeyPoint(Col: MustParseHex("#3288bd"), Pos: 0.9), + GradientKeyPoint(Col: MustParseHex("#5e4fa2"), Pos: 1.0), +] + +let gradient = Gradient(keypoints) + +let h = 1024 +let w = 40 + +let (image, imageRep) = createImageRep(NSSize(width: w, height: h)) + +var y = h - 1 +while y >= 0 { + let c = gradient.GetInterpolatedColorFor(Float64(y) / Float64(h)) + drawRect(imageRep: imageRep, rect: NSRect(x: 0, y: y, width: w, height: 1), color: c) + y -= 1 +} + +_ = savePNG(image: image, path: "Sources/Demos/GradientGen/gradientgen.png") diff --git a/Sources/Demos/PaletteGens/main.swift b/Sources/Demos/PaletteGens/main.swift new file mode 100644 index 0000000..52c2bba --- /dev/null +++ b/Sources/Demos/PaletteGens/main.swift @@ -0,0 +1,62 @@ +import Foundation +import AppKit + +import Colorful +import DemoShared + +let colors = 10 +let blockw = 40 +let space = 5 + + +func isbrowny(l: Float64, a: Float64, b: Float64) -> Bool { + let (h, c, L) = Color.LabToHcl(L: l, a: a, b: b) + return 10.0 < h && h < 50.0 && 0.1 < c && c < 0.5 && L < 0.5 +} + +let (image, imageRep) = createImageRep(NSSize(width: colors*blockw+space*(colors-1), height: 6*blockw+8*space)) + + +var warm: [Color] = [] +var happy: [Color] = [] +var soft: [Color] = [] +var brownies: [Color] = [] + +do { + warm = try WarmPalette(colors) +} catch let error { + print("Error generating warm palette: \(error)") +} + +let fwarm = FastWarmPalette(colors) + +do { + happy = try HappyPalette(colors) +} catch let error { + print("Error generating happy palette: \(error)") +} + +let fhappy = FastHappyPalette(colors) + +do { + soft = try SoftPalette(colors) +} catch let error { + print("Error generating soft palette: \(error)") +} + +do { + brownies = try SoftPaletteEx(colorsCount: colors, settings: SoftPaletteSettings(checkColorFn: isbrowny, iterations: 50, manySamples: true)) +} catch let error { + print("Error generating brownies palette: \(error)") +} + +for i in 0..I%?TySZt1aQ!zNfj_cBw-5)S{re% zc957z!njTeiHNZkj8R*mNEX}zh=c+rpe#{YViZWfJlH3fC;MQ1IQM+_obTK@bASKy z|L)CO5f$k*YT_saLA>aT!dD>(s)05hhk=pEW7;U_P|m8zP(*2%{19%!H%8N$%a$Qu zLX1OD(Iy1zN`W>J8iI_FqsR#8QP-Fp^Kur|$VdDek9Q@WDtF@{$VWTq;S0V^N4p!F zYU<%w#^lM3DJ82G8%`@s^ctbxq_Uhej>D!q6v>I0qwZ92+?jBJc zHP&Y@oJq%{7;G@Mk6A@XULd4J(b!gnzYnq2PfiZ$`N0!|O~quASOIxRt~aV_NQsQa 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image.tiffRepresentation!) + let pngData = imageRep?.representation(using: .png, properties: [:]) + do { + try pngData?.write(to: URL(fileURLWithPath: path)) + } + catch { + return false + } + return true +} + +public func createImageRep(_ size: NSSize) -> (NSImage, NSBitmapImageRep) { + let image = NSImage(size: size) + + let imageRep = NSBitmapImageRep(bitmapDataPlanes: nil, + pixelsWide: Int(image.size.width), + pixelsHigh: Int(image.size.height), + bitsPerSample: 8, + samplesPerPixel: 3, + hasAlpha: false, + isPlanar: false, + colorSpaceName: .deviceRGB, + bytesPerRow: 0, bitsPerPixel: 0)! + + image.addRepresentation(imageRep) + return (image, imageRep) +} + +public func drawRect(imageRep: NSBitmapImageRep, rect: NSRect, color: Color) { + let (r, g, b) = color.RGB255() + var col: [Int] = [Int(r), Int(g), Int(b)] + for posx in stride(from: 0, to: rect.size.width, by: 1) { + for posy in stride(from: 0, to: rect.size.height, by: 1) { + imageRep.setPixel(&col, atX: Int(rect.origin.x+posx), y: Int(rect.origin.y+posy)) + } + } +} + +public func setPixel(imageRep: NSBitmapImageRep, pos: NSPoint, color: Color) { + let (r, g, b) = color.RGB255() + var col: [Int] = [Int(r), Int(g), Int(b)] + imageRep.setPixel(&col, atX: Int(pos.x), y: Int(pos.y)) +} diff --git a/Tests/ColorfulTests/Resources/hsluv-snapshot-rev4.json b/Tests/ColorfulTests/Resources/hsluv-snapshot-rev4.json new file mode 100644 index 0000000..16354ab --- /dev/null +++ b/Tests/ColorfulTests/Resources/hsluv-snapshot-rev4.json @@ -0,0 +1 @@ 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\ No newline at end of file diff --git a/Tests/ColorfulTests/swift_colorfulTests.swift b/Tests/ColorfulTests/swift_colorfulTests.swift new file mode 100644 index 0000000..ad59bb7 --- /dev/null +++ b/Tests/ColorfulTests/swift_colorfulTests.swift @@ -0,0 +1,639 @@ +import class Foundation.Bundle +import XCTest + +@testable import Colorful + +// Checks whether the relative error is below eps +func almosteq_eps(v1: Float64, v2: Float64, eps: Float64) -> Bool { + if abs(v1) > delta { + return abs((v1 - v2) / v1) < eps + } + return true +} + +// Checks whether the relative error is below the 8bit RGB delta, which should be good enough. +let delta = 1.0 / 256.0 + +func almosteq(v1: Float64, v2: Float64) -> Bool { + return almosteq_eps(v1: v1, v2: v2, eps: delta) +} + +struct TestVals { + let c: Color + let hsl: [Float64] + let hsv: [Float64] + let hex: String + let xyz: [Float64] + let xyy: [Float64] + let lab: [Float64] + let lab50: [Float64] + let luv: [Float64] + let luv50: [Float64] + let hcl: [Float64] + let hcl50: [Float64] + let rgba: [UInt32] + let rgb255: [uint8] +} + +let vals: [TestVals] = [ + TestVals(c: Color(R: 1.0, G: 1.0, B: 1.0), hsl: [0.0, 0.0, 1.00], hsv: [0.0, 0.0, 1.0], hex: "#ffffff", xyz: [0.950470, 1.000000, 1.088830], xyy: [0.312727, 0.329023, 1.000000], lab: [1.000000, 0.000000, 0.000000], lab50: [1.000000, -0.023881, -0.193622], luv: [1.00000, 0.00000, 0.00000], luv50: [1.00000, -0.14716, -0.25658], hcl: [0.0000, 0.000000, 1.000000], hcl50: [262.9688, 0.195089, 1.000000], rgba: [65535, 65535, 65535, 65535], rgb255: [255, 255, 255]), + TestVals(c: Color(R: 0.5, G: 1.0, B: 1.0), hsl: [180.0, 1.0, 0.75], hsv: [180.0, 0.5, 1.0], hex: "#80ffff", xyz: [0.626296, 0.832848, 1.073634], xyy: [0.247276, 0.328828, 0.832848], lab: [0.931390, -0.353319, -0.108946], lab50: [0.931390, -0.374100, -0.301663], luv: [0.93139, -0.53909, -0.11630], luv50: [0.93139, -0.67615, -0.35528], hcl: [197.1371, 0.369735, 0.931390], hcl50: [218.8817, 0.480574, 0.931390], rgba: [32768, 65535, 65535, 65535], rgb255: [128, 255, 255]), + TestVals(c: Color(R: 1.0, G: 0.5, B: 1.0), hsl: [300.0, 1.0, 0.75], hsv: [300.0, 0.5, 1.0], hex: "#ff80ff", xyz: [0.669430, 0.437920, 0.995150], xyy: [0.318397, 0.208285, 0.437920], lab: [0.720892, 0.651673, -0.422133], lab50: [0.720892, 0.630425, -0.610035], luv: [0.72089, 0.60047, -0.77626], luv50: [0.72089, 0.49438, -0.96123], hcl: [327.0661, 0.776450, 0.720892], hcl50: [315.9417, 0.877257, 0.720892], rgba: [65535, 32768, 65535, 65535], rgb255: [255, 128, 255]), + TestVals(c: Color(R: 1.0, G: 1.0, B: 0.5), hsl: [60.0, 1.0, 0.75], hsv: [60.0, 0.5, 1.0], hex: "#ffff80", xyz: [0.808654, 0.943273, 0.341930], xyy: [0.386203, 0.450496, 0.943273], lab: [0.977637, -0.165795, 0.602017], lab50: [0.977637, -0.188424, 0.470410], luv: [0.97764, 0.05759, 0.79816], luv50: [0.97764, -0.08628, 0.54731], hcl: [105.3975, 0.624430, 0.977637], hcl50: [111.8287, 0.506743, 0.977637], rgba: [65535, 65535, 32768, 65535], rgb255: [255, 255, 128]), + TestVals(c: Color(R: 0.5, G: 0.5, B: 1.0), hsl: [240.0, 1.0, 0.75], hsv: [240.0, 0.5, 1.0], hex: "#8080ff", xyz: [0.345256, 0.270768, 0.979954], xyy: [0.216329, 0.169656, 0.270768], lab: [0.590453, 0.332846, -0.637099], lab50: [0.590453, 0.315806, -0.824040], luv: [0.59045, -0.07568, -1.04877], luv50: [0.59045, -0.16257, -1.20027], hcl: [297.5843, 0.718805, 0.590453], hcl50: [290.9689, 0.882482, 0.590453], rgba: [32768, 32768, 65535, 65535], rgb255: [128, 128, 255]), + TestVals(c: Color(R: 1.0, G: 0.5, B: 0.5), hsl: [0.0, 1.0, 0.75], hsv: [0.0, 0.5, 1.0], hex: "#ff8080", xyz: [0.527613, 0.381193, 0.248250], xyy: [0.455996, 0.329451, 0.381193], lab: [0.681085, 0.483884, 0.228328], lab50: [0.681085, 0.464258, 0.110043], luv: [0.68108, 0.92148, 0.19879], luv50: [0.68106, 0.82106, 0.02393], hcl: [25.2610, 0.535049, 0.681085], hcl50: [13.3347, 0.477121, 0.681085], rgba: [65535, 32768, 32768, 65535], rgb255: [255, 128, 128]), + TestVals(c: Color(R: 0.5, G: 1.0, B: 0.5), hsl: [120.0, 1.0, 0.75], hsv: [120.0, 0.5, 1.0], hex: "#80ff80", xyz: [0.484480, 0.776121, 0.326734], xyy: [0.305216, 0.488946, 0.776121], lab: [0.906026, -0.600870, 0.498993], lab50: [0.906026, -0.619946, 0.369365], luv: [0.90603, -0.58869, 0.76102], luv50: [0.90603, -0.72202, 0.52855], hcl: [140.2920, 0.781050, 0.906026], hcl50: [149.2134, 0.721640, 0.906026], rgba: [32768, 65535, 32768, 65535], rgb255: [128, 255, 128]), + TestVals(c: Color(R: 0.5, G: 0.5, B: 0.5), hsl: [0.0, 0.0, 0.50], hsv: [0.0, 0.0, 0.5], hex: "#808080", xyz: [0.203440, 0.214041, 0.233054], xyy: [0.312727, 0.329023, 0.214041], lab: [0.533890, 0.000000, 0.000000], lab50: [0.533890, -0.014285, -0.115821], luv: [0.53389, 0.00000, 0.00000], luv50: [0.53389, -0.07857, -0.13699], hcl: [0.0000, 0.000000, 0.533890], hcl50: [262.9688, 0.116699, 0.533890], rgba: [32768, 32768, 32768, 65535], rgb255: [128, 128, 128]), + TestVals(c: Color(R: 0.0, G: 1.0, B: 1.0), hsl: [180.0, 1.0, 0.50], hsv: [180.0, 1.0, 1.0], hex: "#00ffff", xyz: [0.538014, 0.787327, 1.069496], xyy: [0.224656, 0.328760, 0.787327], lab: [0.911132, -0.480875, -0.141312], lab50: [0.911132, -0.500630, -0.333781], luv: [0.91113, -0.70477, -0.15204], luv50: [0.91113, -0.83886, -0.38582], hcl: [196.3762, 0.501209, 0.911132], hcl50: [213.6923, 0.601698, 0.911132], rgba: [0, 65535, 65535, 65535], rgb255: [0, 255, 255]), + TestVals(c: Color(R: 1.0, G: 0.0, B: 1.0), hsl: [300.0, 1.0, 0.50], hsv: [300.0, 1.0, 1.0], hex: "#ff00ff", xyz: [0.592894, 0.284848, 0.969638], xyy: [0.320938, 0.154190, 0.284848], lab: [0.603242, 0.982343, -0.608249], lab50: [0.603242, 0.961939, -0.794531], luv: [0.60324, 0.84071, -1.08683], luv50: [0.60324, 0.75194, -1.24161], hcl: [328.2350, 1.155407, 0.603242], hcl50: [320.4444, 1.247640, 0.603242], rgba: [65535, 0, 65535, 65535], rgb255: [255, 0, 255]), + TestVals(c: Color(R: 1.0, G: 1.0, B: 0.0), hsl: [60.0, 1.0, 0.50], hsv: [60.0, 1.0, 1.0], hex: "#ffff00", xyz: [0.770033, 0.927825, 0.138526], xyy: [0.419320, 0.505246, 0.927825], lab: [0.971393, -0.215537, 0.944780], lab50: [0.971393, -0.237800, 0.847398], luv: [0.97139, 0.07706, 1.06787], luv50: [0.97139, -0.06590, 0.81862], hcl: [102.8512, 0.969054, 0.971393], hcl50: [105.6754, 0.880131, 0.971393], rgba: [65535, 65535, 0, 65535], rgb255: [255, 255, 0]), + TestVals(c: Color(R: 0.0, G: 0.0, B: 1.0), hsl: [240.0, 1.0, 0.50], hsv: [240.0, 1.0, 1.0], hex: "#0000ff", xyz: [0.180437, 0.072175, 0.950304], xyy: [0.150000, 0.060000, 0.072175], lab: [0.322970, 0.791875, -1.078602], lab50: [0.322970, 0.778150, -1.263638], luv: [0.32297, -0.09405, -1.30342], luv50: [0.32297, -0.14158, -1.38629], hcl: [306.2849, 1.338076, 0.322970], hcl50: [301.6248, 1.484014, 0.322970], rgba: [0, 0, 65535, 65535], rgb255: [0, 0, 255]), + TestVals(c: Color(R: 0.0, G: 1.0, B: 0.0), hsl: [120.0, 1.0, 0.50], hsv: [120.0, 1.0, 1.0], hex: "#00ff00", xyz: [0.357576, 0.715152, 0.119192], xyy: [0.300000, 0.600000, 0.715152], lab: [0.877347, -0.861827, 0.831793], lab50: [0.877347, -0.879067, 0.739170], luv: [0.87735, -0.83078, 1.07398], luv50: [0.87735, -0.95989, 0.84887], hcl: [136.0160, 1.197759, 0.877347], hcl50: [139.9409, 1.148534, 0.877347], rgba: [0, 65535, 0, 65535], rgb255: [0, 255, 0]), + TestVals(c: Color(R: 1.0, G: 0.0, B: 0.0), hsl: [0.0, 1.0, 0.50], hsv: [0.0, 1.0, 1.0], hex: "#ff0000", xyz: [0.412456, 0.212673, 0.019334], xyy: [0.640000, 0.330000, 0.212673], lab: [0.532408, 0.800925, 0.672032], lab50: [0.532408, 0.782845, 0.621518], luv: [0.53241, 1.75015, 0.37756], luv50: [0.53241, 1.67180, 0.24096], hcl: [39.9990, 1.045518, 0.532408], hcl50: [38.4469, 0.999566, 0.532408], rgba: [65535, 0, 0, 65535], rgb255: [255, 0, 0]), + TestVals(c: Color(R: 0.0, G: 0.0, B: 0.0), hsl: [0.0, 0.0, 0.00], hsv: [0.0, 0.0, 0.0], hex: "#000000", xyz: [0.000000, 0.000000, 0.000000], xyy: [0.312727, 0.329023, 0.000000], lab: [0.000000, 0.000000, 0.000000], lab50: [0.000000, 0.000000, 0.000000], luv: [0.00000, 0.00000, 0.00000], luv50: [0.00000, 0.00000, 0.00000], hcl: [0.0000, 0.000000, 0.000000], hcl50: [0.0000, 0.000000, 0.000000], rgba: [0, 0, 0, 65535], rgb255: [0, 0, 0]), +] + +struct ShortHex { + var c: Color + var hex: String +} + +var shorthexvals: [ShortHex] = [ + ShortHex(c: Color(R: 1.0, G: 1.0, B: 1.0), hex: "#fff"), + ShortHex(c: Color(R: 0.6, G: 1.0, B: 1.0), hex: "#9ff"), + ShortHex(c: Color(R: 1.0, G: 0.6, B: 1.0), hex: "#f9f"), + ShortHex(c: Color(R: 1.0, G: 1.0, B: 0.6), hex: "#ff9"), + ShortHex(c: Color(R: 0.6, G: 0.6, B: 1.0), hex: "#99f"), + ShortHex(c: Color(R: 1.0, G: 0.6, B: 0.6), hex: "#f99"), + ShortHex(c: Color(R: 0.6, G: 1.0, B: 0.6), hex: "#9f9"), + ShortHex(c: Color(R: 0.6, G: 0.6, B: 0.6), hex: "#999"), + ShortHex(c: Color(R: 0.0, G: 1.0, B: 1.0), hex: "#0ff"), + ShortHex(c: Color(R: 1.0, G: 0.0, B: 1.0), hex: "#f0f"), + ShortHex(c: Color(R: 1.0, G: 1.0, B: 0.0), hex: "#ff0"), + ShortHex(c: Color(R: 0.0, G: 0.0, B: 1.0), hex: "#00f"), + ShortHex(c: Color(R: 0.0, G: 1.0, B: 0.0), hex: "#0f0"), + ShortHex(c: Color(R: 1.0, G: 0.0, B: 0.0), hex: "#f00"), + ShortHex(c: Color(R: 0.0, G: 0.0, B: 0.0), hex: "#000"), +] + +struct DistStruct { + let c1: Color + let c2: Color + let d76: Float64 // That's also dLab + let d94: Float64 + let d00: Float64 +} + +// Ground-truth from http://www.brucelindbloom.com/index.html?ColorDifferenceCalcHelp.html +var dists: [DistStruct] = [ + DistStruct(c1: Color(R: 1.0, G: 1.0, B: 1.0), c2: Color(R: 1.0, G: 1.0, B: 1.0), d76: 0.0, d94: 0.0, d00: 0.0), + DistStruct(c1: Color(R: 0.0, G: 0.0, B: 0.0), c2: Color(R: 0.0, G: 0.0, B: 0.0), d76: 0.0, d94: 0.0, d00: 0.0), + + // Just pairs of values of the table way above. + DistStruct(c1: Color.Lab(l: 1.000000, a: 0.000000, b: 0.000000), c2: Color.Lab(l: 0.931390, a: -0.353319, b: -0.108946), d76: 0.37604638, d94: 0.37604638, d00: 0.23528129), + DistStruct(c1: Color.Lab(l: 0.720892, a: 0.651673, b: -0.422133), c2: Color.Lab(l: 0.977637, a: -0.165795, b: 0.602017), d76: 1.33531088, d94: 0.65466377, d00: 0.75175896), + DistStruct(c1: Color.Lab(l: 0.590453, a: 0.332846, b: -0.637099), c2: Color.Lab(l: 0.681085, a: 0.483884, b: 0.228328), d76: 0.88317072, d94: 0.42541075, d00: 0.37688153), + DistStruct(c1: Color.Lab(l: 0.906026, a: -0.600870, b: 0.498993), c2: Color.Lab(l: 0.533890, a: 0.000000, b: 0.000000), d76: 0.86517280, d94: 0.41038323, d00: 0.39960503), + DistStruct(c1: Color.Lab(l: 0.911132, a: -0.480875, b: -0.141312), c2: Color.Lab(l: 0.603242, a: 0.982343, b: -0.608249), d76: 1.56647162, d94: 0.87431457, d00: 0.57983482), + DistStruct(c1: Color.Lab(l: 0.971393, a: -0.215537, b: 0.944780), c2: Color.Lab(l: 0.322970, a: 0.791875, b: -1.078602), d76: 2.35146891, d94: 1.11858192, d00: 1.03426977), + DistStruct(c1: Color.Lab(l: 0.877347, a: -0.861827, b: 0.831793), c2: Color.Lab(l: 0.532408, a: 0.800925, b: 0.672032), d76: 1.70565338, d94: 0.68800270, d00: 0.86608245), +] + +struct AngleVals { + let a0: Float64 + let a1: Float64 + let t: Float64 + let at: Float64 +} + +// For testing angular interpolation internal function +// NOTE: They are being tested in both directions. +var anglevals: [AngleVals] = [ + AngleVals(a0: 0.0, a1: 1.0, t: 0.0, at: 0.0), + AngleVals(a0: 0.0, a1: 1.0, t: 0.25, at: 0.25), + AngleVals(a0: 0.0, a1: 1.0, t: 0.5, at: 0.5), + AngleVals(a0: 0.0, a1: 1.0, t: 1.0, at: 1.0), + AngleVals(a0: 0.0, a1: 90.0, t: 0.0, at: 0.0), + AngleVals(a0: 0.0, a1: 90.0, t: 0.25, at: 22.5), + AngleVals(a0: 0.0, a1: 90.0, t: 0.5, at: 45.0), + AngleVals(a0: 0.0, a1: 90.0, t: 1.0, at: 90.0), + AngleVals(a0: 0.0, a1: 178.0, t: 0.0, at: 0.0), // Exact 0-180 is ambiguous. + AngleVals(a0: 0.0, a1: 178.0, t: 0.25, at: 44.5), + AngleVals(a0: 0.0, a1: 178.0, t: 0.5, at: 89.0), + AngleVals(a0: 0.0, a1: 178.0, t: 1.0, at: 178.0), + AngleVals(a0: 0.0, a1: 182.0, t: 0.0, at: 0.0), // Exact 0-180 is ambiguous. + AngleVals(a0: 0.0, a1: 182.0, t: 0.25, at: 315.5), + AngleVals(a0: 0.0, a1: 182.0, t: 0.5, at: 271.0), + AngleVals(a0: 0.0, a1: 182.0, t: 1.0, at: 182.0), + AngleVals(a0: 0.0, a1: 270.0, t: 0.0, at: 0.0), + AngleVals(a0: 0.0, a1: 270.0, t: 0.25, at: 337.5), + AngleVals(a0: 0.0, a1: 270.0, t: 0.5, at: 315.0), + AngleVals(a0: 0.0, a1: 270.0, t: 1.0, at: 270.0), + AngleVals(a0: 0.0, a1: 359.0, t: 0.0, at: 0.0), + AngleVals(a0: 0.0, a1: 359.0, t: 0.25, at: 359.75), + AngleVals(a0: 0.0, a1: 359.0, t: 0.5, at: 359.5), + AngleVals(a0: 0.0, a1: 359.0, t: 1.0, at: 359.0), +] + +class swift_colorfulTests: XCTestCase { + /// RGBA /// + //////////// + + func testRGBAConversion() { + for (_, tt) in vals.enumerated() { + let (r, g, b, a) = tt.c.RGBA() + if r != tt.rgba[0] || g != tt.rgba[1] || b != tt.rgba[2] || a != tt.rgba[3] { + XCTFail("\(r)!=\(tt.rgba[0]) or \(g)!=\(tt.rgba[1]) or \(b)!=\(tt.rgba[2]) or \(a)!=\(tt.rgba[3])") + } + } + } + + /// RGB255 /// + //////////// + + func testRGB255Conversion() { + for (_, tt) in vals.enumerated() { + let (r, g, b) = tt.c.RGB255() + if r != tt.rgb255[0] || g != tt.rgb255[1] || b != tt.rgb255[2] { + XCTFail("\(r)!=\(tt.rgb255[0]) or \(g)!=\(tt.rgb255[1]) or \(b)!=\(tt.rgb255[2])") + } + } + } + + /// HSV /// + /////////// + + func testHsvCreation() { + for (i, tt) in vals.enumerated() { + let c = Color.Hsv(H: tt.hsv[0], S: tt.hsv[1], V: tt.hsv[2]) + if !c.AlmostEqualRgb(tt.c) { + XCTFail(String(format: "%i. Hsv(%@) => (%@), want %@ (delta %f)", i, tt.hsv.description, c.description, tt.c.description, delta)) + } + } + } + + func testHsvConversion() { + for (i, tt) in vals.enumerated() { + let (h, s, v) = tt.c.Hsv() + if !almosteq(v1: h, v2: tt.hsv[0]) || !almosteq(v1: s, v2: tt.hsv[1]) || !almosteq(v1: v, v2: tt.hsv[2]) { + XCTFail(String(format: "%i. %@.Hsv() => (%@), want %@ (delta %f)", i, tt.c.description, [h, s, v].description, tt.hsv.description, delta)) + } + } + } + + /// HSL /// + /////////// + + func testHslCreation() { + for (i, tt) in vals.enumerated() { + let c = Color.Hsl(h: tt.hsl[0], s: tt.hsl[1], l: tt.hsl[2]) + if !c.AlmostEqualRgb(tt.c) { + XCTFail(String(format: "%i. Hsl(%@) => (%@), want %@ (delta %f)", i, tt.hsl.description, c.description, tt.c.description, delta)) + } + } + } + + func testHslConversion() { + for (i, tt) in vals.enumerated() { + let (h, s, l) = tt.c.Hsl() + if !almosteq(v1: h, v2: tt.hsl[0]) || !almosteq(v1: s, v2: tt.hsl[1]) || !almosteq(v1: l, v2: tt.hsl[2]) { + XCTFail(String(format: "%i. %@.Hsl() => (%@), want %@ (delta %f)", i, tt.c.description, [h, s, l].description, tt.hsl.description, delta)) + } + } + } + + /// Hex /// + /////////// + + func testHexCreation() { + for (i, tt) in vals.enumerated() { + var c: Color + do { + c = try Color.Hex(tt.hex) + } catch { + XCTFail("testHexCreation failed!") + continue + } + if !c.AlmostEqualRgb(tt.c) { + XCTFail(String(format: "%i. Hex(%@) => (%@), want %@ (delta %f)", i, tt.hex, c.description, tt.c.description, delta)) + } + } + } + + func testHEXCreation() { + for (i, tt) in vals.enumerated() { + var c: Color + do { + c = try Color.Hex(tt.hex.uppercased()) + } catch { + XCTFail("testHEXCreation failed!") + continue + } + if !c.AlmostEqualRgb(tt.c) { + XCTFail(String(format: "%i. HEX(%@) => (%@), want %@ (delta %f)", i, tt.hex.uppercased(), c.description, tt.c.description, delta)) + } + } + } + + func testShortHexCreation() { + for (i, tt) in shorthexvals.enumerated() { + var c: Color + do { + c = try Color.Hex(tt.hex) + } catch { + XCTFail("testShortHexCreation failed!") + continue + } + + if !c.AlmostEqualRgb(tt.c) { + XCTFail(String(format: "%i. Hex(%@) => (%@), want %@ (delta %f)", i, tt.hex, c.description, tt.c.description, delta)) + } + } + } + + func testShortHEXCreation() { + for (i, tt) in shorthexvals.enumerated() { + var c: Color + do { + c = try Color.Hex(tt.hex.uppercased()) + } catch { + XCTFail("testShortHEXCreation failed!") + continue + } + + if !c.AlmostEqualRgb(tt.c) { + XCTFail(String(format: "%i. Hex(%@) => (%@), want %@ (delta %f)", i, tt.hex.uppercased(), c.description, tt.c.description, delta)) + } + } + } + + func testHexConversion() { + for (i, tt) in vals.enumerated() { + let hex = tt.c.Hex() + if hex != tt.hex { + XCTFail(String(format: "%i. %@.Hex() => (%@), want %@ (delta %f)", i, tt.c.description, hex, tt.hex, delta)) + } + } + } + + /// Linear /// + ////////////// + + // LinearRgb itself is implicitly tested by XYZ conversions below (they use it). + // So what we do here is just test that the FastLinearRgb approximation is "good enough" + func testFastLinearRgb() { + let eps = 6.0 / 255.0 // We want that "within 6 RGB values total" is "good enough". + + for r in stride(from: 0.0, to: 256.0, by: 1.0) { + for g in stride(from: 0.0, to: 256.0, by: 1.0) { + for b in stride(from: 0.0, to: 256.0, by: 1.0) { + let c = Color(R: r / 255.0, G: g / 255.0, B: b / 255.0) + let (r_want, g_want, b_want) = c.LinearRgb() + let (r_appr, g_appr, b_appr) = c.FastLinearRgb() + var (dr, dg, db) = (abs(r_want-r_appr), abs(g_want-g_appr), abs(b_want-b_appr)) + if dr+dg+db > eps { + XCTFail(String(format: "FastLinearRgb not precise enough for %@: differences are (%f, %f, %f), allowed total difference is %f", c.description, dr, dg, db, eps)) + return + } + + let c_want = Color.LinearRgb(r: r/255.0, g: g/255.0, b: b/255.0) + let c_appr = Color.FastLinearRgb(r: r/255.0, g: g/255.0, b: b/255.0) + (dr, dg, db) = (abs(c_want.R-c_appr.R), abs(c_want.G-c_appr.G), abs(c_want.B-c_appr.B)) + if dr+dg+db > eps { + XCTFail(String(format: "FastLinearRgb not precise enough for (%f, %f, %f): differences are (%f, %f, %f), allowed total difference is %f", r, g, b, dr, dg, db, eps)) + return + } + } + } + } + } + + /// XYZ /// + /////////// + func testXyzCreation() { + for (i, tt) in vals.enumerated() { + let c = Color.Xyz(x: tt.xyz[0], y: tt.xyz[1], z: tt.xyz[2]) + if !c.AlmostEqualRgb(tt.c) { + XCTFail(String(format: "%i. Xyz(%@) => (%@), want %@ (delta %f)", i, tt.xyz.description, c.description, tt.c.description, delta)) + } + } + } + + func testXyzConversion() { + for (i, tt) in vals.enumerated() { + let (x, y, z) = tt.c.Xyz() + if !almosteq(v1: x, v2: tt.xyz[0]) || !almosteq(v1: y, v2: tt.xyz[1]) || !almosteq(v1: z, v2: tt.xyz[2]) { + XCTFail(String(format: "%i. %@.Xyz() => (%@), want %@ (delta %f)", i, tt.c.description, [x, y, z].description, tt.xyz.description, delta)) + } + } + } + + /// xyY /// + /////////// + func testXyyCreation() { + for (i, tt) in vals.enumerated() { + let c = Color.Xyy(x: tt.xyy[0], y: tt.xyy[1], Y: tt.xyy[2]) + if !c.AlmostEqualRgb(tt.c) { + XCTFail(String(format: "%i. Xyy(%@) => (%@), want %@ (delta %f)", i, tt.xyy.description, c.description, tt.c.description, delta)) + } + } + } + + func testXyyConversion() { + for (i, tt) in vals.enumerated() { + let (x, y, Y) = tt.c.Xyy() + if !almosteq(v1: x, v2: tt.xyy[0]) || !almosteq(v1: y, v2: tt.xyy[1]) || !almosteq(v1: Y, v2: tt.xyy[2]) { + XCTFail(String(format: "%i. %@.Xyy() => (%@), want %@ (delta %f)", i, tt.c.description, [x, y, Y].description, tt.xyy.description, delta)) + } + } + } + + /// L*a*b* /// + ////////////// + func testLabCreation() { + for (i, tt) in vals.enumerated() { + let c = Color.Lab(l: tt.lab[0], a: tt.lab[1], b: tt.lab[2]) + if !c.AlmostEqualRgb(tt.c) { + XCTFail(String(format: "%i. Lab(%@) => (%@), want %@ (delta %f)", i, tt.lab.description, c.description, tt.c.description, delta)) + } + } + } + + func testLabConversion() { + for (i, tt) in vals.enumerated() { + let (l, a, b) = tt.c.Lab() + if !almosteq(v1: l, v2: tt.lab[0]) || !almosteq(v1: a, v2: tt.lab[1]) || !almosteq(v1: b, v2: tt.lab[2]) { + XCTFail(String(format: "%i. %@.Lab() => (%@), want %@ (delta %f)", i, tt.c.description, [l, a, b].description, tt.lab.description, delta)) + } + } + } + + func testLabWhiteRefCreation() { + for (i, tt) in vals.enumerated() { + let c = Color.LabWhiteRef(l: tt.lab50[0], a: tt.lab50[1], b: tt.lab50[2], wref: D50) + if !c.AlmostEqualRgb(tt.c) { + XCTFail(String(format: "%i. LabWhiteRef(%@, D50) => (%@), want %@ (delta %f)", i, tt.lab50.description, c.description, tt.c.description, delta)) + } + } + } + + func testLabWhiteRefConversion() { + for (i, tt) in vals.enumerated() { + let (l, a, b) = tt.c.LabWhiteRef(wref: D50) + if !almosteq(v1: l, v2: tt.lab50[0]) || !almosteq(v1: a, v2: tt.lab50[1]) || !almosteq(v1: b, v2: tt.lab50[2]) { + XCTFail(String(format: "%i. %@.LabWhiteRef(D50) => (%@), want %@ (delta %f)", i, tt.c.description, [l, a, b].description, tt.lab50.description, delta)) + } + } + } + + /// L*u*v* /// + ////////////// + func testLuvCreation() { + for (i, tt) in vals.enumerated() { + let c = Color.Luv(l: tt.luv[0], u: tt.luv[1], v: tt.luv[2]) + if !c.AlmostEqualRgb(tt.c) { + XCTFail(String(format: "%i. Luv(%@) => (%@), want %@ (delta %f)", i, tt.luv.description, c.description, tt.c.description, delta)) + } + } + } + + func testLuvConversion() { + for (i, tt) in vals.enumerated() { + let (l, u, v) = tt.c.Luv() + if !almosteq(v1: l, v2: tt.luv[0]) || !almosteq(v1: u, v2: tt.luv[1]) || !almosteq(v1: v, v2: tt.luv[2]) { + XCTFail(String(format: "%i. %@.Luv() => (%@), want %@ (delta %f)", i, tt.c.description, [l, u, v].description, tt.luv.description, delta)) + } + } + } + + func testLuvWhiteRefCreation() { + for (i, tt) in vals.enumerated() { + let c = Color.LuvWhiteRef(l: tt.luv50[0], u: tt.luv50[1], v: tt.luv50[2], wref: D50) + if !c.AlmostEqualRgb(tt.c) { + XCTFail(String(format: "%i. LuvWhiteRef(%@, D50) => (%@), want %@ (delta %f)", i, tt.luv50.description, c.description, tt.c.description, delta)) + } + } + } + + func testLuvWhiteRefConversion() { + for (i, tt) in vals.enumerated() { + let (l, u, v) = tt.c.LuvWhiteRef(wref: D50) + if !almosteq(v1: l, v2: tt.luv50[0]) || !almosteq(v1: u, v2: tt.luv50[1]) || !almosteq(v1: v, v2: tt.luv50[2]) { + XCTFail(String(format: "%i. %@.LuvWhiteRef(D50) => (%@), want %@ (delta %f)", i, tt.c.description, [l, u, v].description, tt.luv50.description, delta)) + } + } + } + + /// HCL /// + /////////// + // CIE-L*a*b* in polar coordinates. + func testHclCreation() { + for (i, tt) in vals.enumerated() { + let c = Color.Hcl(h: tt.hcl[0], c: tt.hcl[1], l: tt.hcl[2]) + if !c.AlmostEqualRgb(tt.c) { + XCTFail(String(format: "%i. Hcl(%@) => (%@), want %@ (delta %f)", i, tt.hcl.description, c.description, tt.c.description, delta)) + } + } + } + + func testHclConversion() { + for (i, tt) in vals.enumerated() { + let (h, c, l) = tt.c.Hcl() + if !almosteq(v1: h, v2: tt.hcl[0]) || !almosteq(v1: c, v2: tt.hcl[1]) || !almosteq(v1: l, v2: tt.hcl[2]) { + XCTFail(String(format: "%i. %@.Hcl() => (%@), want %@ (delta %f)", i, tt.c.description, [h, c, l].description, tt.hcl.description, delta)) + } + } + } + + func testHclWhiteRefCreation() { + for (i, tt) in vals.enumerated() { + let c = Color.HclWhiteRef(h: tt.hcl50[0], c: tt.hcl50[1], l: tt.hcl50[2], wref: D50) + if !c.AlmostEqualRgb(tt.c) { + XCTFail(String(format: "%i. HclWhiteRef(%@, D50) => (%@), want %@ (delta %f)", i, tt.hcl50.description, c.description, tt.c.description, delta)) + } + } + } + + func testHclWhiteRefConversion() { + for (i, tt) in vals.enumerated() { + let (h, c, l) = tt.c.HclWhiteRef(wref: D50) + if !almosteq(v1: h, v2: tt.hcl50[0]) || !almosteq(v1: c, v2: tt.hcl50[1]) || !almosteq(v1: l, v2: tt.hcl50[2]) { + XCTFail(String(format: "%i. %@.HclWhiteRef(D50) => (%@), want %@ (delta %f)", i, tt.c.description, [h, c, l].description, tt.hcl50.description, delta)) + } + } + } + + /// Test distances /// + ////////////////////// + + func testLabDistance() { + for (i, tt) in dists.enumerated() { + let d = tt.c1.DistanceCIE76(tt.c2) + if !almosteq(v1: d, v2: tt.d76) { + XCTFail(String(format: "%i. %@.DistanceCIE76(%@) => (%f), want %f (delta %f)", i, tt.c1.description, tt.c2.description, d, tt.d76, delta)) + } + } + } + + func testCIE94Distance() { + for (i, tt) in dists.enumerated() { + let d = tt.c1.DistanceCIE94(tt.c2) + if !almosteq(v1: d, v2: tt.d94) { + XCTFail(String(format: "%i. %@.DistanceCIE94(%@) => (%f), want %f (delta %f)", i, tt.c1.description, tt.c2.description, d, tt.d94, delta)) + } + } + } + + func testCIEDE2000Distance() { + for (i, tt) in dists.enumerated() { + let d = tt.c1.DistanceCIEDE2000(tt.c2) + if !almosteq(v1: d, v2: tt.d00) { + XCTFail(String(format: "%i. %@.DistanceCIEDE2000(%@) => (%f), want %f (delta %f)", i, tt.c1.description, tt.c2.description, d, tt.d00, delta)) + } + } + } + /// Test utilities /// + ////////////////////// + + func testClamp() { + let c_orig = Color(R: 1.1, G: -0.1, B: 0.5) + let c_want = Color(R: 1.0, G: 0.0, B: 0.5) + if c_orig.Clamped() != c_want { + XCTFail(String(format: "%@.Clamped() => %@, want %@", c_orig.description, c_orig.Clamped().description, c_want.description)) + } + } + + // func testMakeColor() { + // c_orig_nrgba := color.NRGBA{123, 45, 67, 255} + // c_ours, ok := MakeColor(c_orig_nrgba) + // r, g, b := c_ours.RGB255() + // if r != 123 || g != 45 || b != 67 || !ok { + // t.Errorf("NRGBA->Colorful->RGB255 error: %v became (%v, %v, %v, %t)", c_orig_nrgba, r, g, b, ok) + // } + + // c_orig_nrgba64 := color.NRGBA64{123 << 8, 45 << 8, 67 << 8, 0xffff} + // c_ours, ok = MakeColor(c_orig_nrgba64) + // r, g, b = c_ours.RGB255() + // if r != 123 || g != 45 || b != 67 || !ok { + // t.Errorf("NRGBA64->Colorful->RGB255 error: %v became (%v, %v, %v, %t)", c_orig_nrgba64, r, g, b, ok) + // } + + // c_orig_gray := color.Gray{123} + // c_ours, ok = MakeColor(c_orig_gray) + // r, g, b = c_ours.RGB255() + // if r != 123 || g != 123 || b != 123 || !ok { + // t.Errorf("Gray->Colorful->RGB255 error: %v became (%v, %v, %v, %t)", c_orig_gray, r, g, b, ok) + // } + + // c_orig_gray16 := color.Gray16{123 << 8} + // c_ours, ok = MakeColor(c_orig_gray16) + // r, g, b = c_ours.RGB255() + // if r != 123 || g != 123 || b != 123 || !ok { + // t.Errorf("Gray16->Colorful->RGB255 error: %v became (%v, %v, %v, %t)", c_orig_gray16, r, g, b, ok) + // } + + // c_orig_rgba := color.RGBA{255, 255, 255, 0} + // c_ours, ok = MakeColor(c_orig_rgba) + // r, g, b = c_ours.RGB255() + // if r != 0 || g != 0 || b != 0 || ok { + // t.Errorf("RGBA->Colorful->RGB255 error: %v became (%v, %v, %v, %t)", c_orig_rgba, r, g, b, ok) + // } + // } + + /// Issues raised on github /// + /////////////////////////////// + + // https://github.com/lucasb-eyer/go-colorful/issues/11 + func testIssue11() { + let c1hex = "#1a1a46" + let c2hex = "#666666" + + do { + let c1 = try Color.Hex(c1hex) + let c2 = try Color.Hex(c2hex) + + var blend = c1.BlendHsv(c2: c2, t: 0).Hex() + if blend != c1hex { + XCTFail(String(format: "Issue11: %@ --Hsv-> %@ = %@, want %@", c1hex, c2hex, blend, c1hex)) + } + blend = c1.BlendHsv(c2: c2, t: 1).Hex() + if blend != c2hex { + XCTFail(String(format: "Issue11: %@ --Hsv-> %@ = %@, want %@", c1hex, c2hex, blend, c2hex)) + } + + blend = c1.BlendLuv(c2: c2, t: 0).Hex() + if blend != c1hex { + XCTFail(String(format: "Issue11: %@ --Luv-> %@ = %@, want %@", c1hex, c2hex, blend, c1hex)) + } + blend = c1.BlendLuv(c2: c2, t: 1).Hex() + if blend != c2hex { + XCTFail(String(format: "Issue11: %@ --Luv-> %@ = %@, want %@", c1hex, c2hex, blend, c2hex)) + } + + blend = c1.BlendRgb(c2: c2, t: 0).Hex() + if blend != c1hex { + XCTFail(String(format: "Issue11: %@ --Rgb-> %@ = %@, want %@", c1hex, c2hex, blend, c1hex)) + } + blend = c1.BlendRgb(c2: c2, t: 1).Hex() + if blend != c2hex { + XCTFail(String(format: "Issue11: %@ --Rgb-> %@ = %@, want %@", c1hex, c2hex, blend, c2hex)) + } + + blend = c1.BlendLinearRgb(c2: c2, t: 0).Hex() + if blend != c1hex { + XCTFail(String(format: "Issue11: %@ --LinearRgb-> %@ = %@, want %@", c1hex, c2hex, blend, c1hex)) + } + blend = c1.BlendLinearRgb(c2: c2, t: 1).Hex() + if blend != c2hex { + XCTFail(String(format: "Issue11: %@ --LinearRgb-> %@ = %@, want %@", c1hex, c2hex, blend, c2hex)) + } + + blend = c1.BlendLab(c2: c2, t: 0).Hex() + if blend != c1hex { + XCTFail(String(format: "Issue11: %@ --Lab-> %@ = %@, want %@", c1hex, c2hex, blend, c1hex)) + } + blend = c1.BlendLab(c2: c2, t: 1).Hex() + if blend != c2hex { + XCTFail(String(format: "Issue11: %@ --Lab-> %@ = %@, want %@", c1hex, c2hex, blend, c2hex)) + } + + blend = c1.BlendHcl(c2: c2, t: 0).Hex() + if blend != c1hex { + XCTFail(String(format: "Issue11: %@ --Hcl-> %@ = %@, want %@", c1hex, c2hex, blend, c1hex)) + } + blend = c1.BlendHcl(c2: c2, t: 1).Hex() + if blend != c2hex { + XCTFail(String(format: "Issue11: %@ --Hcl-> %@ = %@, want %@", c1hex, c2hex, blend, c2hex)) + } + + blend = c1.BlendLuvLCh(c2: c2, t: 0).Hex() + if blend != c1hex { + XCTFail(String(format: "Issue11: %@ --LuvLCh-> %@ = %@, want %@", c1hex, c2hex, blend, c1hex)) + } + blend = c1.BlendLuvLCh(c2: c2, t: 1).Hex() + if blend != c2hex { + XCTFail(String(format: "Issue11: %@ --LuvLCh-> %@ = %@, want %@", c1hex, c2hex, blend, c2hex)) + } + } catch { + XCTFail("testIssue11 failed!") + } + } + + func testInterpolation() { + // Forward + for (i, tt) in anglevals.enumerated() { + let res = Color.interp_angle(a0: tt.a0, a1: tt.a1, t: tt.t) + if !almosteq_eps(v1: res, v2: tt.at, eps: 1e-15) { + XCTFail(String(format: "%i. interp_angle(%f, %f, %f) => (%f), want %f", i, tt.a0, tt.a1, tt.t, res, tt.at)) + } + } + // Backward + for (i, tt) in anglevals.enumerated() { + let res = Color.interp_angle(a0: tt.a1, a1: tt.a0, t: 1.0-tt.t) + if !almosteq_eps(v1: res, v2: tt.at, eps: 1e-15) { + XCTFail(String(format: "%i. interp_angle(%f, %f, %f) => (%f), want %f", i, tt.a1, tt.a0, 1.0-tt.t, res, tt.at)) + } + } + } + +} diff --git a/Tests/ColorfulTests/swift_hsluvTests.swift b/Tests/ColorfulTests/swift_hsluvTests.swift new file mode 100644 index 0000000..73c6fbf --- /dev/null +++ b/Tests/ColorfulTests/swift_hsluvTests.swift @@ -0,0 +1,153 @@ +import class Foundation.Bundle +import XCTest + +@testable import Colorful + +struct Values: Codable { + var lch: [Float64] + var luv: [Float64] + var rgb: [Float64] + var xyz: [Float64] + var hpluv: [Float64] + var hsluv: [Float64] +} + +func loadValuesFromJson(filename fileName: String) -> [String: Values]? { + if let url = Bundle.module.url(forResource: fileName, withExtension: "") { + do { + let data = try Data(contentsOf: url) + let decoder = JSONDecoder() + let jsonData: [String: Values] = try decoder.decode([String: Values].self, from: data) + return jsonData + } catch { + print("error:\(error)") + } + } + return nil +} + +var mapping: [String: Values] = .init() + +func fromHex(_ s: String) -> Color { + let c = try! Color.Hex(s) + return c +} + +func compareHex(result: String , expected: String, method: String, hex: String) { + if result != expected { + XCTFail(String(format: "result: %@ expected: %@, testing %s with test case %s", result, expected, method, hex)) + } +} + +// const delta = 0.00000001 +let hsluvTestDelta = 0.0000000001 // Two more zeros than the original delta, because values are divided by 100 + +func compareTuple(result: [Float64], expected: [Float64], method: String, hex: String) { + var err = false + var errs = [Bool](repeatElement(false, count: 3)) + for i in 0 ..< 3 { + if abs(result[i] - expected[i]) > hsluvTestDelta { + err = true + errs[i] = true + } + } + if err { + var resultOutput = "[" + for i in 0 ..< 3 { + resultOutput += String(format: "%f", arguments: [result[i]]) + if errs[i] { + resultOutput += " *" + } + if i < 2 { + resultOutput += ", " + } + } + resultOutput += "]" + XCTFail(String(format: "result: %s expected: %@, testing %s with test case %s", resultOutput, expected, method, hex)) + } +} + +extension swift_colorfulTests { + func testHSLuv() { + let snapshot = loadValuesFromJson(filename: "hsluv-snapshot-rev4.json") + for (hex, var colorValues) in snapshot! { + // print("Testing public methods for test case %s", hex) + + // Adjust color values to be in the ranges this library uses + colorValues.hsluv[1] /= 100.0 + colorValues.hsluv[2] /= 100.0 + colorValues.hpluv[1] /= 100.0 + colorValues.hpluv[2] /= 100.0 + + var col = Color.HSLuv(h: colorValues.hsluv[0], s: colorValues.hsluv[1], l: colorValues.hsluv[2]) + compareHex(result: col.Hex(), expected: hex, method: "HsluvToHex", hex: hex) + + col = Color.HSLuv(h: colorValues.hsluv[0],s: colorValues.hsluv[1],l: colorValues.hsluv[2]) + compareTuple(result: [col.R, col.G, col.B], expected: colorValues.rgb, method: "HsluvToRGB", hex: hex) + + var hsl = fromHex(hex).HSLuv() + compareTuple(result: [hsl.h, hsl.s, hsl.l], expected: colorValues.hsluv, method: "HsluvFromHex", hex: hex) + + hsl = Color(R: colorValues.rgb[0], G: colorValues.rgb[1], B: colorValues.rgb[2]).HSLuv() + compareTuple(result: [hsl.h, hsl.s, hsl.l], expected: colorValues.hsluv, method: "HsluvFromRGB", hex: hex) + + col = Color.HPLuv(h: colorValues.hpluv[0],s: colorValues.hpluv[1],l: colorValues.hpluv[2]) + compareHex(result: col.Hex(), expected: hex, method: "HpluvToHex", hex: hex) + + col = Color.HPLuv(h: colorValues.hpluv[0], s: colorValues.hpluv[1], l: colorValues.hpluv[2]) + compareTuple(result: [col.R, col.G, col.B], expected: colorValues.rgb, method: "HpluvToRGB", hex: hex) + + hsl = fromHex(hex).HPLuv() + compareTuple(result: [hsl.h, hsl.s, hsl.l], expected: colorValues.hpluv, method: "HpluvFromHex", hex: hex) + + hsl = Color(R: colorValues.rgb[0], G: colorValues.rgb[1], B: colorValues.rgb[2]).HPLuv() + compareTuple(result: [hsl.h, hsl.s, hsl.l], expected: colorValues.hpluv, method: "HpluvFromRGB", hex: hex) + + // print("Testing internal methods for test case %s", hex) + + colorValues.lch[0] /= 100.0 + colorValues.lch[1] /= 100.0 + colorValues.luv[0] /= 100.0 + colorValues.luv[1] /= 100.0 + colorValues.luv[2] /= 100.0 + + col = Color.LuvLChWhiteRef(l: colorValues.lch[0], c: colorValues.lch[1], h: colorValues.lch[2], wref: hSLuvD65) + compareTuple(result: [col.R, col.G, col.B], expected: colorValues.rgb, method: "convLchRgb", hex: hex) + + var lch = Color(R: colorValues.rgb[0], G: colorValues.rgb[1], B: colorValues.rgb[2]).LuvLChWhiteRef(wref: hSLuvD65) + compareTuple(result: [lch.l, lch.c, lch.h], expected: colorValues.lch, method: "convRgbLch", hex: hex) + + let luv = Color.XyzToLuvWhiteRef(x: colorValues.xyz[0], y: colorValues.xyz[1], z: colorValues.xyz[2], wref: hSLuvD65) + compareTuple(result: [luv.l, luv.u, luv.v], expected: colorValues.luv, method: "convXyzLuv", hex: hex) + + var xyz = Color.LuvToXyzWhiteRef(l: colorValues.luv[0], u: colorValues.luv[1], v: colorValues.luv[2], wref: hSLuvD65) + compareTuple(result: [xyz.x, xyz.y, xyz.z], expected: colorValues.xyz, method: "convLuvXyz", hex: hex) + + lch = Color.LuvToLuvLCh(L: colorValues.luv[0], u: colorValues.luv[1], v: colorValues.luv[2]) + compareTuple(result: [lch.l, lch.c, lch.h], expected: colorValues.lch, method: "convLuvLch", hex: hex) + + let Luv = Color.LuvLChToLuv(l: colorValues.lch[0], c: colorValues.lch[1], h: colorValues.lch[2]) + compareTuple(result: [Luv.L, Luv.u, Luv.v], expected: colorValues.luv, method: "convLchLuv", hex: hex) + + + let LCh = Color.HSLuvToLuvLCh(h: colorValues.hsluv[0],s: colorValues.hsluv[1],l: colorValues.hsluv[2]) + compareTuple(result: [LCh.L, LCh.C, LCh.h], expected: colorValues.lch, method: "convHsluvLch", hex: hex) + + hsl = Color.LuvLChToHSLuv(l: colorValues.lch[0], c: colorValues.lch[1], h: colorValues.lch[2]) + compareTuple(result: [hsl.h, hsl.s, hsl.l], expected: colorValues.hsluv, method: "convLchHsluv", hex: hex) + + lch = Color.HPLuvToLuvLCh(h: colorValues.hpluv[0], s: colorValues.hpluv[1], l: colorValues.hpluv[2]) + compareTuple(result: [lch.l, lch.c, lch.h], expected: colorValues.lch, method: "convHpluvLch", hex: hex) + + hsl = Color.LuvLChToHPLuv(l: colorValues.lch[0],c: colorValues.lch[1],h: colorValues.lch[2]) + compareTuple(result: [hsl.h, hsl.s, hsl.l], expected: colorValues.hpluv, method: "convLchHpluv", hex: hex) + + let rgb = Color.XyzToLinearRgb(x: colorValues.xyz[0], y: colorValues.xyz[1], z: colorValues.xyz[2]) + col = Color.LinearRgb(r: rgb.r, g: rgb.g, b: rgb.b) + compareTuple(result: [col.R, col.G, col.B], expected: colorValues.rgb, method: "convXyzRgb", hex: hex) + + xyz = Color(R: colorValues.rgb[0], G: colorValues.rgb[1], B: colorValues.rgb[2]).Xyz() + compareTuple(result: [xyz.x, xyz.y, xyz.z], expected: colorValues.xyz, method: "convRgbXyz", hex: hex) + } + } +} diff --git a/Tests/ColorfulTests/swift_sortTests.swift b/Tests/ColorfulTests/swift_sortTests.swift new file mode 100644 index 0000000..3aaa3c8 --- /dev/null +++ b/Tests/ColorfulTests/swift_sortTests.swift @@ -0,0 +1,36 @@ +import class Foundation.Bundle +import XCTest + +@testable import Colorful + +extension swift_colorfulTests { + // testSortSimple tests the sorting of a small set of colors. + func testSortSimple() { + // Sort a list of reds and blues. + var In: [Color] = [] + In.reserveCapacity(6) + + for i in 0..<3 { + In.append(Color(R: 1.0 - Float64(i+1)*0.25, G: 0.0, B: 0.0)) // Reds + In.append(Color(R: 0.0, G: 0.0, B: 1.0 - Float64(i+1)*0.25)) // Blues + } + + let out = Sorted(In) + + // Ensure the output matches what we expected. + let exp: [Color] = [ + Color(R: 0.25, G: 0.0, B: 0.0), + Color(R: 0.50, G: 0.0, B: 0.0), + Color(R: 0.75, G: 0.0, B: 0.0), + Color(R: 0.0, G: 0.0, B: 0.25), + Color(R: 0.0, G: 0.0, B: 0.50), + Color(R: 0.0, G: 0.0, B: 0.75), + ] + + for (i, e) in exp.enumerated() { + if out[i] != e { + XCTFail(String(format: "%@. Sorted(%@) want (%@)", i, out[i].description, e.description)) + } + } + } +} \ No newline at end of file