377 lines
15 KiB
Python
377 lines
15 KiB
Python
from __future__ import annotations
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from dataclasses import dataclass
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from enum import Enum
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from math import gcd, sqrt, inf, atan2, degrees
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from .math import round_half_up
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from typing import Union, List, Optional
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class DistanceAlgorithm(Enum):
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MANHATTAN = 0
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EUCLIDEAN = 1
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PYTHAGOREAN = 1
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CHEBYSHEV = 2
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CHESSBOARD = 2
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@dataclass(frozen=True)
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class Coordinate:
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x: int
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y: int
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z: Optional[int] = None
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def getDistanceTo(self, target: Coordinate, algorithm: DistanceAlgorithm = DistanceAlgorithm.EUCLIDEAN,
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includeDiagonals: bool = False) -> Union[int, float]:
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"""
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Get distance to target Coordinate
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:param target:
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:param algorithm: Calculation Algorithm (s. DistanceAlgorithm)
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:param includeDiagonals: in Manhattan Mode specify if diagonal
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movements are allowed (counts as 1.4 in 2D, 1.7 in 3D)
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:return: Distance to Target
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"""
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if algorithm == DistanceAlgorithm.EUCLIDEAN:
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if self.z is None:
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return sqrt(abs(self.x - target.x) ** 2 + abs(self.y - target.y) ** 2)
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else:
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return sqrt(abs(self.x - target.x) ** 2 + abs(self.y - target.y) ** 2 + abs(self.z - target.z) ** 2)
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elif algorithm == DistanceAlgorithm.CHEBYSHEV:
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if self.z is None:
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return max(abs(target.x - self.x), abs(target.y - self.y))
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else:
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return max(abs(target.x - self.x), abs(target.y - self.y), abs(target.z - self.z))
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elif algorithm == DistanceAlgorithm.MANHATTAN:
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if not includeDiagonals:
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if self.z is None:
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return abs(self.x - target.x) + abs(self.y - target.y)
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else:
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return abs(self.x - target.x) + abs(self.y - target.y) + abs(self.z - target.z)
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else:
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dist = [abs(self.x - target.x), abs(self.y - target.y)]
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if self.z is None:
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o_dist = max(dist) - min(dist)
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return o_dist + 1.4 * min(dist)
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else:
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dist.append(abs(self.z - target.z))
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d_steps = min(dist)
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dist.remove(min(dist))
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dist = [x - d_steps for x in dist]
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o_dist = max(dist) - min(dist)
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return 1.7 * d_steps + o_dist + 1.4 * min(dist)
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def inBoundaries(self, minX: int, minY: int, maxX: int, maxY: int, minZ: int = -inf, maxZ: int = inf) -> bool:
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if self.z is None:
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return minX <= self.x <= maxX and minY <= self.y <= maxY
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else:
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return minX <= self.x <= maxX and minY <= self.y <= maxY and minZ <= self.z <= maxZ
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def getCircle(self, radius: int = 1, algorithm: DistanceAlgorithm = DistanceAlgorithm.EUCLIDEAN,
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minX: int = -inf, minY: int = -inf, maxX: int = inf, maxY: int = inf,
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minZ: int = -inf, maxZ: int = inf) -> list[Coordinate]:
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ret = []
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if self.z is None: # mode 2D
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for x in range(self.x - radius * 2, self.x + radius * 2 + 1):
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for y in range(self.y - radius * 2, self.y + radius * 2 + 1):
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target = Coordinate(x, y)
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if not target.inBoundaries(minX, minY, maxX, maxY):
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continue
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dist = round_half_up(self.getDistanceTo(target, algorithm=algorithm, includeDiagonals=False))
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if dist == radius:
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ret.append(target)
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else:
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for x in range(self.x - radius * 2, self.x + radius * 2 + 1):
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for y in range(self.y - radius * 2, self.y + radius * 2 + 1):
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for z in range(self.z - radius * 2, self.z + radius * 2 + 1):
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target = Coordinate(x, y)
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if not target.inBoundaries(minX, minY, maxX, maxY, minZ, maxZ):
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continue
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dist = round_half_up(self.getDistanceTo(target, algorithm=algorithm, includeDiagonals=False))
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if dist == radius:
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ret.append(target)
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return ret
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def getNeighbours(self, includeDiagonal: bool = True, minX: int = -inf, minY: int = -inf,
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maxX: int = inf, maxY: int = inf, minZ: int = -inf, maxZ: int = inf) -> list[Coordinate]:
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"""
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Get a list of neighbouring coordinates.
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:param includeDiagonal: include diagonal neighbours
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:param minX: ignore all neighbours that would have an X value below this
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:param minY: ignore all neighbours that would have an Y value below this
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:param minZ: ignore all neighbours that would have an Z value below this
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:param maxX: ignore all neighbours that would have an X value above this
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:param maxY: ignore all neighbours that would have an Y value above this
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:param maxZ: ignore all neighbours that would have an Z value above this
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:return: list of Coordinate
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"""
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if self.z is None:
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if includeDiagonal:
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nb_list = [(-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 1), (1, -1), (1, 0), (1, 1)]
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else:
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nb_list = [(-1, 0), (1, 0), (0, -1), (0, 1)]
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for dx, dy in nb_list:
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if minX <= self.x + dx <= maxX and minY <= self.y + dy <= maxY:
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yield self.__class__(self.x + dx, self.y + dy)
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else:
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if includeDiagonal:
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nb_list = [(x, y, z) for x in [-1, 0, 1] for y in [-1, 0, 1] for z in [-1, 0, 1]]
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nb_list.remove((0, 0, 0))
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else:
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nb_list = [(-1, 0, 0), (0, -1, 0), (1, 0, 0), (0, 1, 0), (0, 0, 1), (0, 0, -1)]
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for dx, dy, dz in nb_list:
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if minX <= self.x + dx <= maxX and minY <= self.y + dy <= maxY and minZ <= self.z + dz <= maxZ:
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yield self.__class__(self.x + dx, self.y + dy, self.z + dz)
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def getAngleTo(self, target: Coordinate, normalized: bool = False) -> float:
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"""normalized returns an angle going clockwise with 0 starting in the 'north'"""
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if self.z is not None:
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raise NotImplementedError() # which angle?!?!
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dx = target.x - self.x
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dy = target.y - self.y
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if not normalized:
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return degrees(atan2(dy, dx))
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else:
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angle = degrees(atan2(dx, dy))
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if dx >= 0:
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return 180.0 - angle
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else:
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return 180.0 + abs(angle)
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def getLineTo(self, target: Coordinate) -> List[Coordinate]:
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diff = target - self
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if self.z is None:
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steps = gcd(diff.x, diff.y)
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step_x = diff.x // steps
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step_y = diff.y // steps
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return [self.__class__(self.x + step_x * i, self.y + step_y * i) for i in range(steps + 1)]
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else:
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steps = gcd(diff.x, diff.y, diff.z)
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step_x = diff.x // steps
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step_y = diff.y // steps
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step_z = diff.z // steps
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return [self.__class__(self.x + step_x * i, self.y + step_y * i, self.z + step_z * i) for i in range(steps + 1)]
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def reverse(self) -> Coordinate:
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if self.z is None:
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return self.__class__(-self.x, -self.y)
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else:
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return self.__class__(-self.x, -self.y, -self.z)
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def __add__(self, other: Coordinate) -> Coordinate:
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if self.z is None:
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return self.__class__(self.x + other.x, self.y + other.y)
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else:
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return self.__class__(self.x + other.x, self.y + other.y, self.z + other.z)
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def __sub__(self, other: Coordinate) -> Coordinate:
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if self.z is None:
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return self.__class__(self.x - other.x, self.y - other.y)
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else:
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return self.__class__(self.x - other.x, self.y - other.y, self.z - other.z)
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def __eq__(self, other):
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return self.x == other.x and self.y == other.y and self.z == other.z
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def __gt__(self, other):
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if self.z is None:
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return self.x > other.x and self.y > other.y
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else:
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return self.x > other.x and self.y > other.y and self.z > other.z
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def __ge__(self, other):
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if self.z is None:
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return self.x >= other.x and self.y >= other.y
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else:
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return self.x >= other.x and self.y >= other.y and self.z >= other.z
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def __lt__(self, other):
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if self.z is None:
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return self.x < other.x and self.y < other.y
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else:
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return self.x < other.x and self.y < other.y and self.z < other.z
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def __le__(self, other):
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if self.z is None:
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return self.x <= other.x and self.y <= other.y
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else:
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return self.x <= other.x and self.y <= other.y and self.z <= other.z
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def __str__(self):
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if self.z is None:
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return "(%d,%d)" % (self.x, self.y)
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else:
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return "(%d,%d,%d)" % (self.x, self.y, self.z)
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def __repr__(self):
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if self.z is None:
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return "%s(x=%d, y=%d)" % (self.__class__.__name__, self.x, self.y)
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else:
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return "%s(x=%d, y=%d, z=%d)" % (self.__class__.__name__, self.x, self.y, self.z)
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@classmethod
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def generate(cls, from_x: int, to_x: int, from_y: int, to_y: int,
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from_z: int = None, to_z: int = None) -> List[Coordinate]:
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if from_z is None or to_z is None:
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return [cls(x, y) for x in range(from_x, to_x + 1) for y in range(from_y, to_y + 1)]
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else:
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return [
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cls(x, y, z)
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for x in range(from_x, to_x + 1)
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for y in range(from_y, to_y + 1)
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for z in range(from_z, to_z + 1)
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]
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class HexCoordinate(Coordinate):
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"""
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https://www.redblobgames.com/grids/hexagons/#coordinates-cube
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Treat as 3d Coordinate
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+y -x +z
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y x z
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yxz
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z x y
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-z +x -y
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"""
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neighbour_vectors = {
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'ne': Coordinate(-1, 0, 1),
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'nw': Coordinate(-1, 1, 0),
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'e': Coordinate(0, -1, 1),
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'w': Coordinate(0, 1, -1),
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'sw': Coordinate(1, 0, -1),
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'se': Coordinate(1, -1, 0),
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}
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def __init__(self, x: int, y: int, z: int):
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assert (x + y + z) == 0
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super().__init__(x, y, z)
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def get_length(self) -> int:
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return (abs(self.x) + abs(self.y) + abs(self.z)) // 2
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def getDistanceTo(self, target: Coordinate, algorithm: DistanceAlgorithm = DistanceAlgorithm.EUCLIDEAN,
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includeDiagonals: bool = True) -> Union[int, float]:
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# includeDiagonals makes no sense in a hex grid, it's just here for signature reasons
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if algorithm == DistanceAlgorithm.MANHATTAN:
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return (self - target).get_length()
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def getNeighbours(self, includeDiagonal: bool = True, minX: int = -inf, minY: int = -inf,
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maxX: int = inf, maxY: int = inf, minZ: int = -inf, maxZ: int = inf) -> list[Coordinate]:
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# includeDiagonals makes no sense in a hex grid, it's just here for signature reasons
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return [
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self + x for x in self.neighbour_vectors.values()
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if minX <= (self + x).x <= maxX and minY <= (self + x).y <= maxY and minZ <= (self + x).z <= maxZ
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]
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HexCoordinateR = HexCoordinate
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class HexCoordinateF(HexCoordinate):
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"""
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https://www.redblobgames.com/grids/hexagons/#coordinates-cube
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Treat as 3d Coordinate
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+y -x
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y x
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-z z yxz z +z
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x y
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+x -y
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"""
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neighbour_vectors = {
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'ne': Coordinate(-1, 0, 1),
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'nw': Coordinate(0, 1, -1),
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'n': Coordinate(-1, 1, 0),
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's': Coordinate(1, -1, 0),
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'sw': Coordinate(1, 0, -1),
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'se': Coordinate(0, -1, 1),
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}
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def __init__(self, x: int, y: int, z: int):
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super().__init__(x, y, z)
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class Shape:
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def __init__(self, top_left: Coordinate, bottom_right: Coordinate):
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"""
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in 2D mode: top_left is the upper left corner and bottom_right the lower right
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(top_left.x <= bottom_right.x and top_left.y <= bottom_right.y)
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in 3D mode: same logic applied, just for 3D Coordinates
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top_left is the upper left rear corner and bottom_right the lower right front
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(top_left.x <= bottom_right.x and top_left.y <= bottom_right.y and top_left.z <= bottom_right.z)
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"""
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self.top_left = top_left
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self.bottom_right = bottom_right
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self.mode_3d = top_left.z is not None and bottom_right.z is not None
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def __len__(self):
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if not self.mode_3d:
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return (self.bottom_right.x - self.top_left.x + 1) * (self.bottom_right.y - self.top_left.y + 1)
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else:
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return (
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(self.bottom_right.x - self.top_left.x + 1)
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* (self.bottom_right.y - self.top_left.y + 1)
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* (self.bottom_right.z - self.top_left.z + 1)
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)
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def intersection(self, other: Shape) -> Union[Shape, None]:
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"""
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returns a Shape of the intersecting part, or None if the Shapes don't intersect
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"""
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if self.mode_3d != other.mode_3d:
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raise ValueError("Cannot calculate intersection between 2d and 3d shape")
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if not self.mode_3d:
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intersect_top_left = Coordinate(
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self.top_left.x if self.top_left.x > other.top_left.x else other.top_left.x,
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self.top_left.y if self.top_left.y > other.top_left.y else other.top_left.y,
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)
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intersect_bottom_right = Coordinate(
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self.bottom_right.x if self.bottom_right.x < other.bottom_right.x else other.bottom_right.x,
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self.bottom_right.y if self.bottom_right.y < other.bottom_right.y else other.bottom_right.y,
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)
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else:
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intersect_top_left = Coordinate(
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self.top_left.x if self.top_left.x > other.top_left.x else other.top_left.x,
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self.top_left.y if self.top_left.y > other.top_left.y else other.top_left.y,
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self.top_left.z if self.top_left.z > other.top_left.z else other.top_left.z,
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)
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intersect_bottom_right = Coordinate(
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self.bottom_right.x if self.bottom_right.x < other.bottom_right.x else other.bottom_right.x,
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self.bottom_right.y if self.bottom_right.y < other.bottom_right.y else other.bottom_right.y,
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self.bottom_right.z if self.bottom_right.z < other.bottom_right.z else other.bottom_right.z,
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)
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if intersect_top_left <= intersect_bottom_right:
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return self.__class__(intersect_top_left, intersect_bottom_right)
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def __and__(self, other):
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return self.intersection(other)
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def __rand__(self, other):
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return self.intersection(other)
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def __str__(self):
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return "%s(%s -> %s)" % (self.__class__.__name__, self.top_left, self.bottom_right)
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def __repr__(self):
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return "%s(%s, %s)" % (self.__class__.__name__, self.top_left, self.bottom_right)
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class Square(Shape):
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def __init__(self, top_left, bottom_right):
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super().__init__(top_left, bottom_right)
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self.mode_3d = False
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class Cube(Shape):
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def __init__(self, top_left, bottom_right):
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if top_left.z is None or bottom_right.z is None:
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raise ValueError("Both Coordinates need to be 3D")
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super().__init__(top_left, bottom_right)
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