110 lines
3.5 KiB
Python
110 lines
3.5 KiB
Python
# -*- coding: utf-8 -*-
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#
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# Copyright © 2024 Simon Forman
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#
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# This file is part of game
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#
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# game is free software: you can redistribute it and/or modify
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# it under the terms of the GNU General Public License as published by
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# the Free Software Foundation, either version 3 of the License, or
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# (at your option) any later version.
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#
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# game is distributed in the hope that it will be useful,
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# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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# GNU General Public License for more details.
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#
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# You should have received a copy of the GNU General Public License
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# along with game. If not see <http://www.gnu.org/licenses/>.
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#
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'''
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Poisson Distribution
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'''
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from math import pi, sqrt, sin, cos, hypot
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from random import random, randint
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tau = 2 * pi
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def poisson(w, h, d, test_points=30):
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'''
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Return a list of coordinates generated by a Poisson point process.
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Return a list of two-tuples, pairs of ints, representing points in a 2D
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plane. The points are bounded by the width and height (w and h) and
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separated by a minimum distance of d.
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'''
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grid, x, y = Grid(d), randint(0, w), randint(0, h)
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grid.add(x, y)
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todo = [(x, y)]
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while todo:
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x, y = todo.pop(0)
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todo.extend(
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(nx, ny)
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for nx, ny in candidates(x, y, d, test_points)
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if 0 <= nx <= w and 0 <= ny <= h and grid.add(nx, ny)
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)
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return list(grid.grid.values())
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class Grid(object):
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'''
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Keep track of points in a plane and efficiently check that added points
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are not nearer than a certain distance d to any others.
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'''
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def __init__(self, d):
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self.d = d
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self.r = d / sqrt(2) # A square of side r and diagonal d.
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self.grid = {} # Map from grid "bins" to points, 1-to-1.
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def add(self, x, y):
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'''
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Add a point pair if it's not too close to any others and return a
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bool: True if the point was added, False if it was rejected.
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'''
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grid_coords = round(x / self.r), round(y / self.r)
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if any(hypot(x - nx, y - ny) < self.d
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for nx, ny in self._neighborhood(grid_coords)):
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return False
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self.grid[grid_coords] = x, y
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return True
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def _neighborhood(self, coordinates):
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'''Return a list of the points in the neighborhood of (x, y).'''
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# Note, x and y here are grid coordinates, not plane coordinates.
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# This method returns plane coordinates.
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x, y = coordinates
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return filter(None, map(self.grid.get, [
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(x-1, y-2), (x, y-2), (x+1, y-2),
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(x-2, y-1), (x-1, y-1), (x, y-1), (x+1, y-1), (x+2, y-1),
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(x-2, y), (x-1, y), (x, y), (x+1, y), (x+2, y),
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(x-2, y+1), (x-1, y+1), (x, y+1), (x+1, y+1), (x+2, y+1),
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(x-1, y+2), (x, y+2), (x+1, y+2),
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]))
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def candidates(x, y, d, test_points):
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'''Generate points at a distance from (x, y) from d to 2*d.'''
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for _ in range(test_points):
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radius = d + random() * d
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angle = random() * tau
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yield (
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int(round(x + radius * cos(angle))),
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int(round(y + radius * sin(angle))),
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)
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if __name__ == '__main__':
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from random import seed
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seed(23)
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WIDTH, HEIGHT, DISTANCE = 80, 24, 4
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P = set(poisson(WIDTH, HEIGHT, DISTANCE))
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for y in range(HEIGHT + 1):
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print(''.join(' *'[(x, y) in P] for x in range(WIDTH + 1)))
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