# -*- coding: utf-8 -*-
#
#    Copyright © 2024 Simon Forman
#
#    This file is part of game
#
#    game is free software: you can redistribute it and/or modify
#    it under the terms of the GNU General Public License as published by
#    the Free Software Foundation, either version 3 of the License, or
#    (at your option) any later version.
#
#    game is distributed in the hope that it will be useful,
#    but WITHOUT ANY WARRANTY; without even the implied warranty of
#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#    GNU General Public License for more details.
#
#    You should have received a copy of the GNU General Public License
#    along with game.  If not see <http://www.gnu.org/licenses/>.
#
'''
Poisson Distribution
'''
from math import pi, sqrt, sin, cos, hypot
from random import random, randint


tau = 2 * pi


def poisson(w, h, d, test_points=30):
    '''
    Return a list of coordinates generated by a Poisson point process.

    Return a list of two-tuples, pairs of ints, representing points in a 2D
    plane.  The points are bounded by the width and height (w and h) and
    separated by a minimum distance of d.
    '''
    grid, x, y = Grid(d), randint(0, w), randint(0, h)
    grid.add(x, y)
    todo = [(x, y)]
    while todo:
        x, y = todo.pop(0)
        todo.extend(
            (nx, ny)
            for nx, ny in candidates(x, y, d, test_points)
            if 0 <= nx <= w and 0 <= ny <= h and grid.add(nx, ny)
            )
    return list(grid.grid.values())


class Grid(object):
    '''
    Keep track of points in a plane and efficiently check that added points
    are not nearer than a certain distance d to any others.
    '''

    def __init__(self, d):
        self.d = d
        self.r = d / sqrt(2) # A square of side r and diagonal d.
        self.grid = {}  # Map from grid "bins" to points, 1-to-1.

    def add(self, x, y):
        '''
        Add a point pair if it's not too close to any others and return a
        bool: True if the point was added, False if it was rejected.
        '''
        grid_coords = round(x / self.r), round(y / self.r)
        if any(hypot(x - nx, y - ny) < self.d
                     for nx, ny in self._neighborhood(grid_coords)):
            return False
        self.grid[grid_coords] = x, y
        return True

    def _neighborhood(self, coordinates):
        '''Return a list of the points in the neighborhood of (x, y).'''
        # Note, x and y here are grid coordinates, not plane coordinates.
        # This method returns plane coordinates.
        x, y = coordinates
        return filter(None, map(self.grid.get, [
                                    (x-1, y-2), (x, y-2), (x+1, y-2),
            (x-2, y-1), (x-1, y-1), (x, y-1), (x+1, y-1), (x+2, y-1),
            (x-2, y),   (x-1, y),   (x, y),   (x+1, y),   (x+2, y),
            (x-2, y+1), (x-1, y+1), (x, y+1), (x+1, y+1), (x+2, y+1),
                                    (x-1, y+2), (x, y+2), (x+1, y+2),
            ]))


def candidates(x, y, d, test_points):
    '''Generate points at a distance from (x, y) from d to 2*d.'''
    for _ in range(test_points):
        radius = d + random() * d
        angle = random() * tau
        yield (
            int(round(x + radius * cos(angle))),
            int(round(y + radius * sin(angle))),
            )


if __name__ == '__main__':
    from random import seed

    seed(23)

    WIDTH, HEIGHT, DISTANCE = 80, 24, 4

    P = set(poisson(WIDTH, HEIGHT, DISTANCE))

    for y in range(HEIGHT + 1):
        print(''.join(' *'[(x, y) in P] for x in range(WIDTH + 1)))