Multiple reduction copy machine

mrcm.py

import copy
from math import sqrt

from python.common.polygon import Polygon
from python.common.polygon_group import PolygonGroup
from python.common.svg import Svg
from python.less9.transformations import *

def triangle(size, origin=False):
    pol = Polygon([(0, 0), (1, 0), (0.5, sqrt(3) / 2), (0, 0)])
    if origin:
        pol.apply_transformation(translation(-0.5, -sqrt(3) / 4))
    return pol.apply_transformation(scaling(size, size))


def square(size, origin=False):
    sq = Polygon([(0, 1), (1, 1), (1, 0), (0, 0), (0, 1)])
    if origin:
        sq.apply_transformation(translation(-0.5, -0.5))
    return sq.apply_transformation(scaling(size, size))


def sierpinsky_triangle(size=1000):
    transformations = [scaling(0.5, 0.5),
                       combine(scaling(0.5, 0.5), translation(size / 2, (size) * (sqrt(3) / 2))),
                       combine(scaling(0.5, 0.5), translation(size, 0))]
    mrcm(triangle(size, True), transformations, 7, name="sierpinsky")


def serp_relatives(transformations, size=1000, name="relatives"):
    start_polygon = square(size, True)
    scale = scaling(0.5, 0.5)
    moves = [translation(-size / 2, size / 2), translation(size / 2, size / 2), translation(size / 2, -size / 2)]
    trans = list(map(lambda x: combine(scale, x[0], x[1]), zip(moves, transformations)))
    mrcm(start_polygon, trans, 7, name)


def merge_groups(groups):
    top_group = PolygonGroup()
    for group in groups:
        for polygon in group.polygons:
            top_group.polygons.append(polygon)
    return top_group


def mrcm(polygon, transformations, iterations, name="multiple_reduction"):
    group = PolygonGroup([polygon])
    for iteration in range(iterations):
        groups = []
        for transformation in transformations:
            copy_group = copy.deepcopy(group)
            copy_group.apply_transformation(transformation)
            groups.append(copy_group)
        group = merge_groups(groups)

    svg = Svg()
    group.draw_to_svg(svg)
    svg.save("output/" + name)
    return group


def tree(size, r, angle, name="tree"):
    scale = scaling(r, r)
    r1 = rotation(angle)
    r2 = rotation(-angle)
    transformations = [combine(scale, r1, translation(0, size / 2)),
                       combine(scale, r2, translation(0, size / 2)),
                       np.identity(3)]
    mrcm(Polygon([(0, -0.5), (0, 0.5)]).apply_transformation(scaling(size, size)), transformations, 8, name)