comparison: geometry.py
geometry.py
- changeset 14
- d383f319f35b
- parent 13
- 12d4ddc4bfd8
- child 15
- 45b3aeb25003
equal
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replaced
| 13:12d4ddc4bfd8 | 14:d383f319f35b |
|---|---|
| 316 ''' | 316 ''' |
| 317 return Matrix3x3([ | 317 return Matrix3x3([ |
| 318 sum(self[i, k] * other[k, j] for k in range(3)) | 318 sum(self[i, k] * other[k, j] for k in range(3)) |
| 319 for i, j in matrix_indices() | 319 for i, j in matrix_indices() |
| 320 ]) | 320 ]) |
| 321 def __add__(self, other): | |
| 322 return Matrix3x3([ | |
| 323 a + b | |
| 324 for a, b in zip(self.values, other.values) | |
| 325 ]) | |
| 326 def __mul__(self, scalar): | |
| 327 return Matrix3x3([ | |
| 328 x * scalar | |
| 329 for x in self.values | |
| 330 ]) | |
| 321 | 331 |
| 322 def complete_matrix(matrix, anchor): | 332 def complete_matrix(matrix, anchor): |
| 323 ''' | 333 ''' |
| 324 Combines a 3×3 matrix and an anchor vertex into a full 4×4 | 334 Combines a 3×3 matrix and an anchor vertex into a full 4×4 |
| 325 transformation matrix. | 335 transformation matrix. |
| 347 z = transformation_matrix[8] * vertex.x \ | 357 z = transformation_matrix[8] * vertex.x \ |
| 348 + transformation_matrix[9] * vertex.y \ | 358 + transformation_matrix[9] * vertex.y \ |
| 349 + transformation_matrix[10] * vertex.z \ | 359 + transformation_matrix[10] * vertex.z \ |
| 350 + transformation_matrix[11], | 360 + transformation_matrix[11], |
| 351 ) | 361 ) |
| 362 | |
| 363 def transform_to_xy(polygon): | |
| 364 ''' | |
| 365 Transforms the provided polygon into the XY plane. The polygon is | |
| 366 assumed to be planar. | |
| 367 | |
| 368 Implementation is based on this StackOverflow answer: | |
| 369 https://math.stackexchange.com/a/476311 | |
| 370 ''' | |
| 371 v1, v2, v3 = polygon.vertices[:3] | |
| 372 a, b = v3 - v2, v1 - v2 | |
| 373 normal = cross_product(a, b).normalized() | |
| 374 v = cross_product(normal, Vector(0, 0, 1)) | |
| 375 cosine = dot_product(normal, Vector(0, 0, 1)) | |
| 376 v_matrix = Matrix3x3([ | |
| 377 0, -v.z, v.y, | |
| 378 v.z, 0, -v.x, | |
| 379 -v.y, v.x, 0, | |
| 380 ]) | |
| 381 try: | |
| 382 rotation_matrix = Matrix3x3() | |
| 383 rotation_matrix += v_matrix | |
| 384 rotation_matrix += (v_matrix @ v_matrix) * (1 / (1 + cosine)) | |
| 385 except ZeroDivisionError: | |
| 386 rotation_matrix = Matrix3x3() | |
| 387 full_matrix = complete_matrix(rotation_matrix, Vertex(0, 0, 0)) | |
| 388 return Polygon([ | |
| 389 transform(vertex = vertex, transformation_matrix = full_matrix) | |
| 390 for vertex in polygon.vertices | |
| 391 ]) | |
| 392 | |
| 393 def vector_angle(vec_1, vec_2, normalized = False): | |
| 394 from math import acos, pi as π | |
| 395 cosine = dot_product(vec_1, vec_2) | |
| 396 try: | |
| 397 cosine /= vec_1.length() * vec_2.length() | |
| 398 except ZeroDivisionError: | |
| 399 return 0 | |
| 400 angle = acos(cosine) | |
| 401 if normalized and angle > π / 2: | |
| 402 angle = π - angle | |
| 403 return angle | |
| 404 | |
| 405 def split_quadrilateral(polygon): | |
| 406 assert(len(polygon.vertices) == 4) | |
| 407 vertices = IndexRing(polygon.vertices) | |
| 408 for i in (0, 1): | |
| 409 a, b = vertices[0 + i], vertices[1 + i] | |
| 410 c, d = vertices[2 + i], vertices[3 + i] | |
| 411 yield Polygon([a, b, c]), Polygon([b, c, d]) | |
| 412 | |
| 413 def triangle_plane_normal(polygon): | |
| 414 assert(len(polygon.vertices) == 3) | |
| 415 a, b, c = polygon.vertices[:3] | |
| 416 return cross_product(b - a, b - c) |
