Calculate angle distortions

impossolid/angle-distortion.py

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+import collections
+import math
+import sys
+
+def read_edge_distortions(filename):
+  vertices = set()
+  distortions = {}
+  with open(filename, 'r') as edge_file:
+    while edge_line := edge_file.readline():
+      line_parts = edge_line.rstrip().split(': ')
+      endpoints = tuple(sorted(line_parts[0].split(', ')))
+      vertices.update(endpoints)
+      if len(line_parts) > 1:
+        distortions[endpoints] = float(line_parts[1])
+      else:
+        distortions[endpoints] = 0
+  return (vertices, distortions)
+
+def find_triangles(vertices, edges):
+  triangles = []
+  for e in edges:
+    for v in vertices:
+      if e[1] < v:
+        if (e[0], v) in edges and (e[1], v) in edges:
+          triangles.append((e[0], e[1], v))
+  return triangles
+
+# use the law of cosines to get the angle distortion
+def angle_distortion(edge_distortions):
+  a, b, c = list(edge_distortions)
+  cos_angle_a = (1 + 2*(b + c - a) + b*b + c*c - a*a) / (2*(1 + b)*(1 + c))
+  return math.degrees(math.acos(cos_angle_a)) - 60
+
+if __name__ == '__main__':
+  if len(sys.argv) <= 1:
+    print('Pass the path to the file that lists the edge distortions')
+  else:
+    vertices, distortions = read_edge_distortions(sys.argv[1])
+    triangles = find_triangles(vertices, distortions.keys())
+    total_angle_distortion = 0
+    highest_angle_distortion = -math.inf
+    lowest_angle_distortion = math.inf
+    print('{} triangles\n'.format(len(triangles)))
+    for t in triangles:
+      print('Triangle {0}, {1}, {2}'.format(t[0], t[1], t[2]))
+      edge_distortions = collections.deque(
+        [distortions[(t[j], t[k])] for (j, k) in [(1, 2), (0, 2), (0, 1)]]
+      )
+      for k in range(3):
+        ang_distort = angle_distortion(edge_distortions)
+        total_angle_distortion += abs(ang_distort)
+        highest_angle_distortion = max(highest_angle_distortion, ang_distort)
+        lowest_angle_distortion = min(lowest_angle_distortion, ang_distort)
+        print('  {0}: {1}°'.format(t[k], ang_distort))
+        edge_distortions.rotate()
+      print()
+    print('Total angle distortion: {}°'.format(total_angle_distortion))
+    print('Highest angle distortion: {}°'.format(highest_angle_distortion))
+    print('Lowest angle distortion: {}°'.format(lowest_angle_distortion))