From 6c4e59d184eadb17b5b6e208347b32bdd3f09753 Mon Sep 17 00:00:00 2001
From: John Honniball <coredump@virginmedia.com>
Date: Fri, 11 Sep 2020 13:26:47 +0100
Subject: [PATCH] Fill upper right sub-plot and modify lower right. Add
 half-ellipse function.

---
 TODO.md   |  2 +-
 ellipse.c | 53 ++++++++++++++++++++++++++++++++++++++++++++++++-----
 2 files changed, 49 insertions(+), 6 deletions(-)

diff --git a/TODO.md b/TODO.md
index d361edd..0b56c1d 100644
--- a/TODO.md
+++ b/TODO.md
@@ -108,7 +108,7 @@ E.g. op, pconic, hconic.
 * Convert Tarim's C++ 'spiro' to C and make it use the library too.
 * Finish off some of the incomplete plots. E.g. hexagon, fraserspiral,
 flake, qrplot, spiralsq, twist, zigzag.
-* Fill the empty sub-plots in 'circle4', 'ellipse' and 'piscis'.
+* Fill the empty sub-plots in 'circle4' and 'piscis'.
 * Clean up the various 'dala' drawings. Eliminate the 'dala2c' variant
 by adding colour to 'dala2.c'.
 * Add run-time variation to 'dala2.c'.
diff --git a/ellipse.c b/ellipse.c
index 2e9e931..65167bc 100644
--- a/ellipse.c
+++ b/ellipse.c
@@ -11,6 +11,7 @@ void plot_ll(const double xc, const double yc, const double r1, const double r2)
 void plot_lr(const double xc, const double yc, const double r1, const double r2);
 void plot_ul(const double xc, const double yc, const double r1, const double r2);
 void plot_ur(const double xc, const double yc, const double r1, const double r2);
+void half_ellipse(const double x0, const double y0, const double a, const double b, const double theta);
 
 
 int main(int argc, char * const argv[])
@@ -84,18 +85,24 @@ void plot_ll(const double xc, const double yc, const double r1, const double r2)
 void plot_lr(const double xc, const double yc, const double r1, const double r2)
 {
    /* Inspired by "Japanese Optical and Geometrical Art" by
-      Hajime Ouchi, ISBN 0-486-23553-X, page 23, bottom */
+      Hajime Ouchi, ISBN 0-486-23553-X, page 85, lower right */
    int i;
-   const double delta = (2.0 * M_PI) / 8.0;
+   const int n = 8;
+   const double delta = (2.0 * M_PI) / (double)n;
    const double radius = r2 / 2.0;
+   const double r3 = radius * sqrt(2.0);
    
-   for (i = 0; i < 8; i++) {
+   for (i = 0; i < n; i++) {
       const double theta = delta * (double)i;
       
       const double x = xc + (radius * cos(theta));
       const double y = yc + (radius * sin(theta));
+      const double x1 = xc + (r3 * cos(theta + delta));
+      const double y1 = yc + (r3 * sin(theta + delta));
       
-      ellipse(x, y, r1 / 2.0, r2 / 2.0, theta);
+      half_ellipse(x, y, r2 / 2.0, r1 / 2.0, theta - (M_PI / 2.0));
+      moveto(x1, y1);
+      lineto(xc, yc);
    }
 }
 
@@ -116,7 +123,21 @@ void plot_ul(const double xc, const double yc, const double r1, const double r2)
 
 void plot_ur(const double xc, const double yc, const double r1, const double r2)
 {
-   circle(xc, yc, r2);
+   int i;
+   const int n = 11;
+   const double delta = (2.0 * M_PI) / (double)n;
+   const double radius = r2 / 2.0;
+   
+// circle(xc, yc, r2);
+
+   for (i = 0; i < n; i++) {
+      const double theta = delta * (double)i;
+      
+      const double x = xc + (radius * cos(theta));
+      const double y = yc + (radius * sin(theta));
+      
+      half_ellipse(x, y, r2 / 2.0, r1 / 2.0, theta);
+   }
 #if 0
    int i;
 
@@ -163,3 +184,25 @@ void ellipse_foci(const double x1, const double y1, const double x2, const doubl
    
    ellipse(x0, y0, a, b, theta);
 }
+
+
+void half_ellipse(const double x0, const double y0, const double a, const double b, const double theta)
+{
+   const int npts = 36;
+   const double delta = M_PI / (double)npts;
+   const double sintheta = sin(theta);
+   const double costheta = cos(theta);
+   int i;
+   
+   for (i = 0; i <= npts; i++) {
+      const double t = (double)i * delta;
+      
+      const double x = (a * cos(t) * costheta) - (b * sin(t) * sintheta);
+      const double y = (a * cos(t) * sintheta) + (b * sin(t) * costheta);
+      
+      if (i == 0)
+         moveto(x0 + x, y0 + y);
+      else
+         lineto(x0 + x, y0 + y);
+   }
+}