3b1b-manim/once_useful_constructs/region.py

import numpy as np
import itertools as it
from PIL import Image
from copy import deepcopy

from mobject.mobject import Mobject
from utils.iterables import adjacent_pairs

from constants import *

# Warning: This is all now pretty depricated, and should not be expected to work

class Region(Mobject):
    CONFIG = {
        "display_mode" : "region"
    }
    def __init__(self, condition = (lambda x, y : True), **kwargs):
        """
        Condition must be a function which takes in two real
        arrays (representing x and y values of space respectively)
        and return a boolean array.  This can essentially look like
        a function from R^2 to {True, False}, but & and | must be
        used in place of "and" and "or"
        """
        Mobject.__init__(self, **kwargs)
        self.condition = condition

    def _combine(self, region, op):
        self.condition = lambda x, y : op(
            self.condition(x, y),
            region.condition(x, y)
        )

    def union(self, region):
        self._combine(region, lambda bg1, bg2 : bg1 | bg2)
        return self

    def intersect(self, region):
        self._combine(region, lambda bg1, bg2 : bg1 & bg2)
        return self

    def complement(self):
        self.bool_grid = ~self.bool_grid
        return self

class HalfPlane(Region):
    def __init__(self, point_pair, upper_left = True, *args, **kwargs):
        """
        point_pair of the form [(x_0, y_0,...), (x_1, y_1,...)]

        Pf upper_left is True, the side of the region will be
        everything on the upper left side of the line through
        the point pair
        """
        if not upper_left:
            point_pair = list(point_pair)
            point_pair.reverse()
        (x0, y0), (x1, y1) = point_pair[0][:2], point_pair[1][:2]
        def condition(x, y):
            return (x1 - x0)*(y - y0) > (y1 - y0)*(x - x0)
        Region.__init__(self, condition, *args, **kwargs)

def region_from_line_boundary(*lines, **kwargs):
    reg = Region(**kwargs)
    for line in lines:
        reg.intersect(HalfPlane(line, **kwargs))
    return reg

def region_from_polygon_vertices(*vertices, **kwargs):
    return region_from_line_boundary(*adjacent_pairs(vertices), **kwargs)


def plane_partition(*lines, **kwargs):
    """
    A 'line' is a pair of points [(x0, y0,...), (x1, y1,...)]

    Returns the list of regions of the plane cut out by
    these lines
    """
    result = []
    half_planes = [HalfPlane(line, **kwargs) for line in lines]
    complements = [deepcopy(hp).complement() for hp in half_planes]
    num_lines = len(lines)
    for bool_list in it.product(*[[True, False]]*num_lines):
        reg = Region(**kwargs)
        for i in range(num_lines):
            if bool_list[i]:
                reg.intersect(half_planes[i])
            else:
                reg.intersect(complements[i])
        if reg.bool_grid.any():
            result.append(reg)
    return result

def plane_partition_from_points(*points, **kwargs):
    """
    Returns list of regions cut out by the complete graph
    with points from the argument as vertices.  

    Each point comes in the form (x, y)
    """
    lines = [[p1, p2] for (p1, p2) in it.combinations(points, 2)]
    return plane_partition(*lines, **kwargs)