cleaned up some of the colouring geometry prototiles; added get_prototiles_from_vectors function

Author: DOSull

examples/scratch-pad.ipynb

@@ -331,7 +331,8 @@ def get_local_patch(self, r: int = 1,
     if not include_0:  # throw away the identity vector
       vecs.pop((0, 0, 0) if self.base_shape in (TileShape.HEXAGON,) else (0, 0))
     ids, tiles = [], []
-    # we need to add the translated prototiles in order of their distance from # tile 0, esp. in the square case, i.e. something like this:
+    # we need to add the translated prototiles in order of their distance from 
+    # tile 0, esp. in the square case, i.e. something like this:
     #
     #      5 4 3 4 5
     #      4 2 1 2 4

weavingspace/tileable.py

@@ -647,13 +647,13 @@ def setup_hex_colouring(unit:"TileUnit") -> None:
   elif unit.n == 5:
     hexagon = affine.rotate(hexagon, 30, origin = (0, 0))
     w, h = h, w
-    tr = [(-w, 3 * h / 8), (0, 3 * h / 8), ( w, 3 * h / 8), 
-          (-w / 2, -3 * h / 8), (w / 2, -3 * h / 8)]
+    tr = [(-w, h / 4), (0, h / 4), ( w, h / 4), 
+          (-w / 2, -h / 2), (w / 2, -h / 2)]
     hexes = [affine.translate(hexagon, v[0], v[1]) for v in tr]
     _setup_base_tile(unit, TileShape.HEXAGON)
     unit.prototile.geometry = [geom.Polygon([
-      (-9 * w / 8, -3 * h / 4), (-11 * w / 8, 0), (-9 * w / 8,  3 * h / 4), 
-      ( 9 * w / 8,  3 * h / 4), ( 11 * w / 8, 0), ( 9 * w / 8, -3 * h / 4) 
+      (-w, -3 * h / 4), (-3 * w / 2,  0), (-w,  3 * h / 4), 
+      ( w,  3 * h / 4), ( 3 * w / 2,  0), ( w, -3 * h / 4) 
     ])]
   elif unit.n == 6:
     hexagon = affine.rotate(hexagon, 30, origin = (0, 0))
@@ -686,12 +686,10 @@ def setup_hex_colouring(unit:"TileUnit") -> None:
     hexes = [affine.translate(hexagon, v[0], v[1]) for v in tr]
     _setup_base_tile(unit, TileShape.HEXAGON)
     unit.prototile.geometry = [geom.Polygon([
-      (-11 * w / 8, -7 * h / 8), (-13 * w / 8, -5 * h / 8), (-7 * w / 8,  11 * h / 8), 
-      ( 11 * w / 8,  7 * h / 8), ( 13 * w / 8,  5 * h / 8), ( 7 * w / 8, -11 * h / 8) 
+      (-3 * w / 2, -h), (-3 * w / 2, -h / 2), (-w,  5 * h / 4), 
+      ( 3 * w / 2,  h), ( 3 * w / 2,  h / 2), ( w, -5 * h / 4) 
     ])]
   elif unit.n == 9:
-    # Make a hexagon and displace in the direction of its
-    # own 6 corners, scaled as needed
     _setup_base_tile(unit, TileShape.HEXAGON)
     offsets = [
       (-3 * w / 4, -5 * h / 4), (0, -3 * h / 4), ( 3 * w / 4, -5 * h / 4),
@@ -737,8 +735,8 @@ def setup_square_colouring(unit:"TileUnit") -> None:
     _setup_base_tile(unit, TileShape.HEXAGON)
     x = s * np.sqrt(2)
     unit.prototile.geometry = [geom.Polygon([
-      (-5 * x / 8, -x / 2), (-7 * x / 8, 0), (-5 * x / 8,  x / 2), 
-      ( 5 * x / 8,  x / 2), ( 7 * x / 8, 0), ( 5 * x / 8, -x / 2), 
+      (-x / 2, -x / 2), (-x, 0), (-x / 2,  x / 2), 
+      ( x / 2,  x / 2), ( x, 0), ( x / 2, -x / 2), 
     ])]
   elif unit.n == 4:
     # Copy and translate square
@@ -753,7 +751,7 @@ def setup_square_colouring(unit:"TileUnit") -> None:
     _setup_base_tile(unit, TileShape.RECTANGLE)
     # Copy and translate square
     tr = [( 0, 0), 
-          (s,  0), (0, s),
+          ( s, 0), (0,  s),
           (-s, 0), (0, -s)]
     squares = [affine.translate(sq, v[0], v[1]) for v in tr]
     rotation = np.degrees(np.arctan2(1, 2))
@@ -780,10 +778,11 @@ def setup_square_colouring(unit:"TileUnit") -> None:
     squares = [affine.translate(sq, v[0], v[1]) for v in tr]
     squares = [affine.rotate(sq, -45, (0, 0)) for sq in squares]
     _setup_base_tile(unit, TileShape.HEXAGON)
-    unit.prototile.geometry = [affine.rotate(geom.Polygon([
-      (-11 * s  / 14, -23 * s / 14), (-17 * s / 14, -19 * s / 14), (-25 * s / 14,  5 * s / 14),
-      ( 11 * s  / 14,  23 * s / 14), ( 17 * s / 14,  19 * s / 14), ( 25 * s / 14, -5 * s / 14)
-    ]), -45, (0, 0))]
+    x = s * np.sqrt(2)
+    unit.prototile.geometry = [geom.Polygon([
+      (-x, -x / 2), (-3 * x / 2, 0), (-x / 2,  x),
+      ( x,  x / 2), ( 3 * x / 2, 0), ( x / 2, -x)
+    ])]
   elif unit.n == 8:
     # Copy and translate square
     tr = [(-s, -s), (0, -s), ( s, -s),
@@ -794,8 +793,8 @@ def setup_square_colouring(unit:"TileUnit") -> None:
     _setup_base_tile(unit, TileShape.HEXAGON)
     x  = s * np.sqrt(2)
     unit.prototile.geometry = [geom.Polygon([
-      (-3 * x / 4, -x), ( 3 * x / 4, -x), ( 5 * x / 4, 0),
-      ( 3 * x / 4,  x), (-3 * x / 4,  x), (-5 * x / 4, 0)
+      (-x / 2, -x), ( x / 2, -x), ( 3 * x / 2, 0),
+      ( x / 2,  x), (-x / 2,  x), (-3 * x / 2, 0)
     ])]
   elif unit.n == 9:
     # Copy and translate square

weavingspace/tiling_geometries.py

@@ -1129,3 +1129,46 @@ def get_intersection(line1:StraightLine,
   x = x if x_set else (line1.B * line2.C - line2.B * line1.C) / denominator
   y = y if y_set else (line1.C * line2.A - line2.C * line1.A) / denominator
   return geom.Point(x, y)
+
+def get_prototiles_from_vectors(v1:tuple[float], v2:tuple[float]):
+  # parallelogram exists regardless
+  parallelogram = geom.Polygon([
+    geom.Point(0, 0), v1, (v1[0]+v2[0], v1[1]+v2[1]), v2])
+  # pc = parallelogram.centroid
+  # parallelogram = affine.translate(geom.Polygon, xoff=-pc.x, yoff=-pc.y)
+  triangle1 = ensure_cw(geom.Polygon([(0, 0), v1, v2]))
+  triangle2 = ensure_cw(geom.Polygon([(0, 0), v1, (-v2[0], -v2[1])]))
+  angles1 = get_interior_angles(triangle1)
+  angles2 = get_interior_angles(triangle2)
+  triangle = triangle1 if max(angles1) <= max(angles2) else triangle2
+  c = incentre(triangle)
+  # c = triangle.centroid
+  t_corners = [geom.Point(p[0] - c.x, p[1] - c.y) 
+               for p in triangle.exterior.coords]
+  e_corners = [geom.Point(p.x + q.x, p.y + q.y) 
+               for p, q in zip(t_corners[:-1], t_corners[1:])]
+  hex_corners = []
+  for i in range(3):
+    hex_corners.extend([t_corners[i], e_corners[i]])
+  hex = geom.Polygon(hex_corners)
+  hex = affine.translate(hex, -hex.centroid.x, -hex.centroid.y)
+  return parallelogram, hex
+  
+  # p = [p for p in triangle.exterior.coords]
+  # e = [geom.Point(p2[0] - p1[0], p2[1] - p1[1]) 
+  #       for p1, p2 in zip(p[:-1], p[1:])]
+  # e = [e[0], geom.Point(-e[1].x, -e[1].y), e[2]]
+
+  # # L1 = get_straight_line(geom.Point(0, 0), e[0], True)
+  # # L2 = get_straight_line(geom.Point(0, 0), e[1], True)
+  # # L3 = get_straight_line(geom.Point(0, 0), e[2], True)
+  # # L4 = get_straight_line(geom.Point(0, 0), 
+  # #                         geom.Point(-e[0].x, -e[0].y), True)
+  # # c1 = get_intersection(L1, L2)
+  # # c2 = get_intersection(L2, L3)
+  # # c3 = get_intersection(L3, L4)
+  # # print(f'{c1=} {c2=} {c3=}')
+  # # hex = geom.Polygon([c1, c2, c3, geom.Point(-c1.x, -c1.y), 
+  # #                     geom.Point(-c2.x, -c2.y), geom.Point(-c3.x, -c3.y)])
+  # return parallelogram, hex
+