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551cc83 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 | from __future__ import annotations
import math
from dataclasses import dataclass
@dataclass(frozen=True)
class Box:
x_min: float
y_min: float
x_max: float
y_max: float
@property
def width(self) -> float:
return max(0.0, self.x_max - self.x_min)
@property
def height(self) -> float:
return max(0.0, self.y_max - self.y_min)
@property
def area(self) -> float:
return self.width * self.height
def intersection(self, other: "Box") -> "Box | None":
x_min = max(self.x_min, other.x_min)
y_min = max(self.y_min, other.y_min)
x_max = min(self.x_max, other.x_max)
y_max = min(self.y_max, other.y_max)
if x_max <= x_min or y_max <= y_min:
return None
return Box(x_min=x_min, y_min=y_min, x_max=x_max, y_max=y_max)
def contains_point(self, x: float, y: float) -> bool:
return self.x_min <= x <= self.x_max and self.y_min <= y <= self.y_max
def to_polygon(self) -> tuple[tuple[float, float], ...]:
return (
(self.x_min, self.y_min),
(self.x_max, self.y_min),
(self.x_max, self.y_max),
(self.x_min, self.y_max),
)
def to_list(self) -> list[float]:
return [self.x_min, self.y_min, self.x_max, self.y_max]
def signed_polygon_area(points: list[tuple[float, float]] | tuple[tuple[float, float], ...]) -> float:
if len(points) < 3:
return 0.0
area = 0.0
for index, point in enumerate(points):
next_point = points[(index + 1) % len(points)]
area += point[0] * next_point[1] - next_point[0] * point[1]
return area / 2.0
def polygon_area(points: list[tuple[float, float]] | tuple[tuple[float, float], ...]) -> float:
return abs(signed_polygon_area(points))
def polygon_bounds(points: list[tuple[float, float]] | tuple[tuple[float, float], ...]) -> Box:
return Box(
x_min=min(point[0] for point in points),
y_min=min(point[1] for point in points),
x_max=max(point[0] for point in points),
y_max=max(point[1] for point in points),
)
def rotated_rectangle_points(
x: float,
y: float,
width: float,
height: float,
rotation_degrees: float,
) -> tuple[tuple[float, float], ...]:
rotation_radians = math.radians(rotation_degrees)
cos_theta = math.cos(rotation_radians)
sin_theta = math.sin(rotation_radians)
return (
(x, y),
(x + width * cos_theta, y + width * sin_theta),
(x + width * cos_theta - height * sin_theta, y + width * sin_theta + height * cos_theta),
(x - height * sin_theta, y + height * cos_theta),
)
def point_in_convex_polygon(
point: tuple[float, float],
polygon: tuple[tuple[float, float], ...],
) -> bool:
if len(polygon) < 3:
return False
orientation = 1 if signed_polygon_area(polygon) >= 0 else -1
point_x, point_y = point
for index, start in enumerate(polygon):
end = polygon[(index + 1) % len(polygon)]
cross = ((end[0] - start[0]) * (point_y - start[1])) - (
(end[1] - start[1]) * (point_x - start[0])
)
if orientation * cross < -1e-9:
return False
return True
def line_intersection(
line1_start: tuple[float, float],
line1_end: tuple[float, float],
line2_start: tuple[float, float],
line2_end: tuple[float, float],
) -> tuple[float, float]:
x1, y1 = line1_start
x2, y2 = line1_end
x3, y3 = line2_start
x4, y4 = line2_end
denominator = ((x1 - x2) * (y3 - y4)) - ((y1 - y2) * (x3 - x4))
if abs(denominator) < 1e-12:
return line1_end
determinant1 = (x1 * y2) - (y1 * x2)
determinant2 = (x3 * y4) - (y3 * x4)
x = ((determinant1 * (x3 - x4)) - ((x1 - x2) * determinant2)) / denominator
y = ((determinant1 * (y3 - y4)) - ((y1 - y2) * determinant2)) / denominator
return (x, y)
def polygon_intersection(
subject_polygon: tuple[tuple[float, float], ...] | list[tuple[float, float]],
clip_polygon: tuple[tuple[float, float], ...],
) -> list[tuple[float, float]]:
output = list(subject_polygon)
if len(output) < 3 or len(clip_polygon) < 3:
return []
orientation = 1 if signed_polygon_area(clip_polygon) >= 0 else -1
def is_inside(point: tuple[float, float], edge_start: tuple[float, float], edge_end: tuple[float, float]) -> bool:
cross = ((edge_end[0] - edge_start[0]) * (point[1] - edge_start[1])) - (
(edge_end[1] - edge_start[1]) * (point[0] - edge_start[0])
)
return orientation * cross >= -1e-9
for index, clip_start in enumerate(clip_polygon):
clip_end = clip_polygon[(index + 1) % len(clip_polygon)]
input_points = output
output = []
if not input_points:
break
previous_point = input_points[-1]
for current_point in input_points:
current_inside = is_inside(current_point, clip_start, clip_end)
previous_inside = is_inside(previous_point, clip_start, clip_end)
if current_inside:
if not previous_inside:
output.append(
line_intersection(previous_point, current_point, clip_start, clip_end)
)
output.append(current_point)
elif previous_inside:
output.append(
line_intersection(previous_point, current_point, clip_start, clip_end)
)
previous_point = current_point
return output
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