comparison: geometry.py
geometry.py
- changeset 7
- 0ab0d61ccee8
- parent 6
- 6da1e81c5652
- child 9
- fea8e9ae6f29
equal
deleted
inserted
replaced
| 6:6da1e81c5652 | 7:0ab0d61ccee8 |
|---|---|
| 1 def degree_rep(angle): | |
| 2 from math import degrees | |
| 3 return '∠ %.2f°' % degrees(angle) | |
| 4 | |
| 5 def position_vector(vertex): | |
| 6 assert isinstance(vertex, Vertex) | |
| 7 return Vector(*vertex.coordinates) | |
| 8 | |
| 9 def angle_magnitude_key(angle): | |
| 10 ''' | |
| 11 Returns how great an angle is. | |
| 12 ''' | |
| 13 from math import pi as π | |
| 14 normalized_angle = abs(angle) % (2 * π) | |
| 15 if normalized_angle > π: | |
| 16 normalized_angle = (2 * π) - normalized_angle | |
| 17 return normalized_angle | |
| 18 | |
| 1 class Vertex: | 19 class Vertex: |
| 2 def __init__(self, x, y, z): | 20 def __init__(self, x, y, z): |
| 3 if not all(is_real(coordinate) for coordinate in (x, y, z)): | 21 if not all(is_real(coordinate) for coordinate in (x, y, z)): |
| 4 raise ValueError(str.format('Bad vertex coordinates: {!r}', | 22 raise ValueError(str.format('Bad vertex coordinates: {!r}', |
| 5 (x, y, z), | 23 (x, y, z), |
| 17 ) | 35 ) |
| 18 @property | 36 @property |
| 19 def coordinates(self): | 37 def coordinates(self): |
| 20 return self.x, self.y, self.z | 38 return self.x, self.y, self.z |
| 21 def __add__(self, other): | 39 def __add__(self, other): |
| 22 return type(self)(self.x + other.x, self.y + other.y, self.z + other.z) | 40 assert not (type(self) == type(other) == Vertex) |
| 41 if type(self) == Vector and type(other) == Vector: | |
| 42 result_type = Vector | |
| 43 else: | |
| 44 result_type = Vertex | |
| 45 return result_type(self.x + other.x, self.y + other.y, self.z + other.z) | |
| 46 def __radd__(self, other): | |
| 47 return self + other | |
| 23 def __neg__(self): | 48 def __neg__(self): |
| 24 return type(self)(-self.x, -self.y, -self.z) | 49 return type(self)(-self.x, -self.y, -self.z) |
| 25 def __sub__(self, other): | 50 def __sub__(self, other): |
| 26 return self + (-other) | 51 result = self + (-position_vector(other)) |
| 52 if isinstance(other, Vertex): | |
| 53 return Vector(*result.coordinates) | |
| 54 else: | |
| 55 return result | |
| 27 def __mul__(self, scalar): | 56 def __mul__(self, scalar): |
| 57 assert is_real(scalar) | |
| 28 return type(self)(self.x * scalar, self.y * scalar, self.z * scalar) | 58 return type(self)(self.x * scalar, self.y * scalar, self.z * scalar) |
| 29 def __rmul__(self, other): | 59 def __rmul__(self, other): |
| 30 return self * other | 60 return self * other |
| 31 def __truediv__(self, scalar): | 61 def __truediv__(self, scalar): |
| 62 assert is_real(scalar) | |
| 32 return type(self)(self.x / scalar, self.y / scalar, self.z / scalar) | 63 return type(self)(self.x / scalar, self.y / scalar, self.z / scalar) |
| 33 def __floordiv__(self, scalar): | 64 def __floordiv__(self, scalar): |
| 65 assert is_real(scalar) | |
| 34 return type(self)(self.x // scalar, self.y // scalar, self.z // scalar) | 66 return type(self)(self.x // scalar, self.y // scalar, self.z // scalar) |
| 35 def __matmul__(self, transformation_matrix): | 67 def __matmul__(self, transformation_matrix): |
| 36 return transform(self, transformation_matrix) | 68 return transform(self, transformation_matrix) |
| 37 def __eq__(self, other): | 69 def __eq__(self, other): |
| 38 return self.coordinates == other.coordinates | 70 return self.coordinates == other.coordinates |
| 51 def __init__(self, v1, v2): | 83 def __init__(self, v1, v2): |
| 52 self.v1, self.v2 = v1, v2 | 84 self.v1, self.v2 = v1, v2 |
| 53 def __repr__(self): | 85 def __repr__(self): |
| 54 return str.format('LineSegment({!r}, {!r})', self.v1, self.v2) | 86 return str.format('LineSegment({!r}, {!r})', self.v1, self.v2) |
| 55 @property | 87 @property |
| 88 def length(self): | |
| 89 return self.v1.distance_to(self.v2) | |
| 90 @property | |
| 56 def vertices(self): | 91 def vertices(self): |
| 57 return self.v1, self.v2 | 92 return self.v1, self.v2 |
| 58 def __len__(self): | 93 def __len__(self): |
| 59 return 2 | 94 return 2 |
| 60 def __getitem__(self, index): | 95 def __getitem__(self, index): |
| 68 | 103 |
| 69 class Vector(Vertex): | 104 class Vector(Vertex): |
| 70 def __init__(self, x, y, z): | 105 def __init__(self, x, y, z): |
| 71 super().__init__(x, y, z) | 106 super().__init__(x, y, z) |
| 72 def __repr__(self): | 107 def __repr__(self): |
| 73 return str.format('Vector({!r}, {!r}. {!r})', self.x, self.y, self.z) | 108 return str.format('Vector({!r}, {!r}, {!r})', self.x, self.y, self.z) |
| 74 def length(self): | 109 def length(self): |
| 75 from math import sqrt | 110 from math import sqrt |
| 76 return sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2) | 111 return sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2) |
| 77 def normalized(self): | 112 def normalized(self): |
| 78 length = self.length() | 113 length = self.length() |
| 146 raise NotImplementedError | 181 raise NotImplementedError |
| 147 def __getitem__(self, index): | 182 def __getitem__(self, index): |
| 148 return self.vertices[index % len(self.vertices)] | 183 return self.vertices[index % len(self.vertices)] |
| 149 def __len__(self): | 184 def __len__(self): |
| 150 return len(self.vertices) | 185 return len(self.vertices) |
| 186 @property | |
| 187 def perimeter_lines(self): | |
| 188 for v1, v2 in pairs(self.vertices): | |
| 189 yield LineSegment(v1, v2) | |
| 190 @property | |
| 191 def smallest_angle(self): | |
| 192 from math import acos, inf | |
| 193 min_angle = inf | |
| 194 for v1, v2, v3 in pairs(self.vertices, count = 3): | |
| 195 vec1 = (position_vector(v3) - position_vector(v2)).normalized() | |
| 196 vec2 = (position_vector(v1) - position_vector(v2)).normalized() | |
| 197 cosine = dot_product(vec1, vec2) / vec1.length() / vec2.length() | |
| 198 min_angle = min(min_angle, angle_magnitude_key(acos(cosine))) | |
| 199 return min_angle | |
| 200 @property | |
| 201 def hairline_ratio(self): | |
| 202 lengths = [line.length for line in self.perimeter_lines] | |
| 203 return max(lengths) / min(lengths) | |
| 151 | 204 |
| 152 def is_real(number): | 205 def is_real(number): |
| 153 return isinstance(number, int) or isinstance(number, float) | 206 return isinstance(number, int) or isinstance(number, float) |
| 154 | 207 |
| 155 class Matrix3x3: | 208 class Matrix3x3: |
