187 lines
6.2 KiB
Python
187 lines
6.2 KiB
Python
# tools/geometry.py
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from dataclasses import dataclass
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@dataclass
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class Point:
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"""Represents a 2D point in a Cartesian coordinate system."""
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x: float
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y: float
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class Line:
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"""Represents a finite line segment between two Points."""
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def __init__(self, p1: Point, p2: Point) -> None:
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self.p1 = p1
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self.p2 = p2
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def distance_to_point(self, point: Point) -> float:
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"""
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Calculates the shortest distance from this line segment to a given point.
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Uses vector projection to find the closest point on the segment.
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"""
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x1, y1 = self.p1.x, self.p1.y
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x2, y2 = self.p2.x, self.p2.y
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x3, y3 = point.x, point.y
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# If the line is actually just a single point
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if x1 == x2 and y1 == y2:
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return ((x1 - x3) ** 2 + (y1 - y3) ** 2) ** 0.5
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px, py = x2 - x1, y2 - y1
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norm = px * px + py * py
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# Calculate the projection scalar (u) of the point onto the line
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u = ((x3 - x1) * px + (y3 - y1) * py) / float(norm)
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# Clamp u to the [0, 1] range to ensure we stay on the line segment
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u = max(0.0, min(1.0, u))
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# Find the exact coordinates of the closest point on the segment
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closest_x = x1 + u * px
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closest_y = y1 + u * py
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# Return distance from the target point to the closest point
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dx, dy = closest_x - x3, closest_y - y3
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return (dx * dx + dy * dy) ** 0.5
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class LineString:
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"""Represents a path formed by a sequence of connected line segments."""
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def __init__(self, lines: list[list[float]]) -> None:
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if len(lines) < 2:
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raise ValueError("A LineString requires at least 2 coordinate pairs.")
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self.lineList: list[Line] = []
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for i in range(len(lines) - 1):
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p1 = Point(lines[i][0], lines[i][1])
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p2 = Point(lines[i + 1][0], lines[i + 1][1])
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self.lineList.append(Line(p1, p2))
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def distance_to(self, point: Point) -> float:
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"""Calculates the minimum distance from the given point to the LineString."""
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# Cleanly check the distance to all segments and return the smallest one
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return min(line.distance_to_point(point) for line in self.lineList)
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def is_intersecting(self, point: Point) -> bool:
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"""Checks if a given point lies exactly on the LineString."""
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return self.distance_to(point) == 0.0
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class Polygon:
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"""Represents a 2D shape enclosed by a series of connected points."""
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def __init__(self, points: list[list[float]]) -> None:
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self.listPoints: list[Point] = [Point(p[0], p[1]) for p in points]
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def on_line(self, l1: Line, p: Point) -> bool:
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"""Checks if collinear point 'p' lies strictly on the line segment 'l1'."""
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return min(l1.p1.x, l1.p2.x) <= p.x <= max(l1.p1.x, l1.p2.x) and min(
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l1.p1.y, l1.p2.y
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) <= p.y <= max(l1.p1.y, l1.p2.y)
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def direction(self, a: Point, b: Point, c: Point) -> int:
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"""
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Finds the orientation of an ordered triplet (a, b, c).
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Returns:
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0 : Collinear
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1 : Clockwise
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2 : Counterclockwise
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"""
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val = (b.y - a.y) * (c.x - b.x) - (b.x - a.x) * (c.y - b.y)
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if val == 0:
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return 0
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return 2 if val < 0 else 1
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def is_intersect(self, l1: Line, l2: Line) -> bool:
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"""Checks if line segment l1 intersects with line segment l2."""
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dir1 = self.direction(l1.p1, l1.p2, l2.p1)
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dir2 = self.direction(l1.p1, l1.p2, l2.p2)
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dir3 = self.direction(l2.p1, l2.p2, l1.p1)
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dir4 = self.direction(l2.p1, l2.p2, l1.p2)
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# General case intersection
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if dir1 != dir2 and dir3 != dir4:
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return True
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# Special collinear cases
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if dir1 == 0 and self.on_line(l1, l2.p1):
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return True
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if dir2 == 0 and self.on_line(l1, l2.p2):
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return True
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if dir3 == 0 and self.on_line(l2, l1.p1):
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return True
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if dir4 == 0 and self.on_line(l2, l1.p2):
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return True
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return False
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def contains(self, p: Point) -> bool:
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"""
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Determines if a point is strictly inside the Polygon using the Ray-Casting algorithm.
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Draws a horizontal line to the right of the point and counts edge intersections.
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"""
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n = len(self.listPoints)
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if n < 3:
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return False
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# Create a horizontal ray starting from the point and going infinitely right
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exline = Line(p, Point(99999.0, p.y))
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count = 0
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for i in range(n):
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side = Line(self.listPoints[i], self.listPoints[(i + 1) % n])
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if self.is_intersect(side, exline):
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# If the point is collinear with the side, check if it's strictly on the side
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if self.direction(side.p1, p, side.p2) == 0:
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return self.on_line(side, p)
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count += 1
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# If the number of intersections is odd, the point is inside the polygon
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return bool(count & 1)
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class MultiPolygon:
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"""Represents a collection of multiple separate Polygons."""
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def __init__(self, polygons: list) -> None:
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self.listPolygons: list[Polygon] = [Polygon(polygon[0]) for polygon in polygons]
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def contains(self, p: Point) -> bool:
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"""Returns True if the point is inside ANY of the contained Polygons."""
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for polygon in self.listPolygons:
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if polygon.contains(p):
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return True
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return False
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@dataclass
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class Coordinate:
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"""
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Custom type for the management of geographical coordinates.
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Provides utility to switch between lat/long and x/y point spaces.
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"""
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lat: float
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long: float
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@property
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def tuple(self) -> tuple[float, float]:
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"""Returns the coordinates as a (Latitude, Longitude) tuple."""
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return (self.lat, self.long)
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def to_Point(self, reversed: bool = False) -> Point:
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"""
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Returns Coordinates mapped to a Cartesian Point.
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Args:
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reversed (bool): If True, switches orientation so x=long, y=lat.
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Defaults to False (x=lat, y=long).
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"""
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return Point(self.long, self.lat) if reversed else Point(self.lat, self.long)
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