Megagon SVG!

generate.py

#!/usr/bin/env python3


# NOTE
# LAYERS is a non-empty list of integers.
# The n-gon can be determine by calc_ngon(LAYERS), e.g.,
#LAYERS = [1, 2, 2]                      # heptagon (not constructible)
#LAYERS = [1, 4, 3]                      # heptadecagon (17 sides)
#LAYERS = [2, 2, 3, 2]                   # tetracontadigon (42)
#LAYERS = [4, 1, 4, 3, 2, 2]             # 360-gon
#LAYERS = [4, 3, 2, 4, 3, 2]             # chiliagon (1,000)
#LAYERS = [1, 9, 10, 10, 10]             # myriagon (10,000)
#LAYERS = [1, 16, 15, 16, 16]            # 65537-gon
LAYERS = [100, 99, 100]                 # megagon (1,000,000)

# NOTE
# Otherwise, just use NGON to describe the polygon,
# and let the program determine a pattern for LAYERS automatically.
#NGON = 17

PADDING = 50
RADIUS = 700
PRECISION = 9



##############################################################################

import sys
from types import SimpleNamespace as namespace
from math import sin, cos, tan, radians
from operator import mul
from functools import reduce
from itertools import product
from collections import Counter


def translate(center, x, y):
    return x+center, y+center

def _rotate(angle, x, y):
    return x*cos(angle) - y*sin(angle), x*sin(angle) + y*cos(angle)

def rotate(x, y, angle, center):
    return translate(center, *_rotate(angle, *translate(-center, x, y)))


def iter_primes(memo=namespace(pi=0, ps=[2, 3])):
    k = 0
    while True:
        while len(memo.ps) <= k:
            head = memo.ps[memo.pi]**2 + 1
            memo.pi += 1
            tail = memo.ps[memo.pi]**2
            seive = list(range(head, tail))
            for p in memo.ps[:memo.pi]:
                size = 1 + (tail - head + (head % -p)) // p
                seive[-head%p::p] = [0] * size
            memo.ps += (p for p in seive if p)
        yield memo.ps[k]
        k += 1

def factors(n):
    if n == 1:
        return [1]
    fs = []
    for p in iter_primes():
        if p**2 > n:
            break
        while n % p == 0:
            fs += [p]
            n //= p
    if n > 1:
        fs += [n]
    return fs

def divisors(n):
    gfs = ({p**i for i in range(k+1)} for p, k in Counter(factors(n)).items())
    return sorted(reduce(mul, ts) for ts in product(*gfs))


def calc_ngon(layers):
    r = 1
    for v in reversed(layers):
        r *= v
        r += 1
    return r - 1

def calc_layers(ngon, memo=[()]):
    while len(memo) < ngon+1:
        row = [(d, *memo[len(memo)//d-1]) for d in divisors(len(memo))]
        memo += [min(row, key=lambda r: (sum(r), len(r)))]
    return memo[ngon]



class Polygon(object):
    def __init__(self, data):
        if isinstance(data, int):
            self.ngon = data
            self.rel_pieces = calc_layers(data)
        elif isinstance(data, list) or isinstance(data, iter):
            self.rel_pieces = data
            self.ngon = calc_ngon(data)
        else:
            raise KeyError('initial data for polygon must be int or list of int.')
        if self.ngon < 3:
            raise KeyError('its absurd to draw a polygon with number of sides less than 3.')
        self.angle = 360/self.ngon
        self.abs_pieces = [self.rel_pieces[0]]
        self.tot_pieces = [self.rel_pieces[0]]
        self._init_pieces_info()

    def _init_pieces_info(self):
        for i in range(1, len(self.rel_pieces)):
            self.abs_pieces += [self.abs_pieces[i-1] * self.rel_pieces[i]]
            self.tot_pieces += [self.tot_pieces[i-1] + self.abs_pieces[i]]

    def base_group(self, radius, padding):
        center = radius + padding
        x = center - (radius * tan(radians(self.angle/2)))
        y = padding
        spec = []
        for _ in range(self.rel_pieces[0]+1):
            spec += f'{round(x, PRECISION)},{round(y, PRECISION)}',
            x, y = rotate(x, y, radians(self.angle), center)
        return f'<g id="a0"><polyline points="{" ".join(spec)}" stroke="#000" fill="none" /></g>\n'

    def make_group(self, k, radius, padding, precision):
        if k == 0:
            return self.base_group(radius, padding)
        center = radius + padding
        theta = self.angle * self.abs_pieces[k-1]
        s = f'<g id="a{k}">\n'
        for i in range(1, 1+self.rel_pieces[k]):
            rot = round(theta*i, precision)
            s += f'<use xlink:href="#a{k-1}" transform="rotate({rot} {center} {center})" />\n'
        s += '</g>\n'
        return s

    def svg(self, radius, padding, precision):
        size = 2 * (radius + padding)
        header = 'xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"'
        s = f'<!-- {self.ngon}-gon with layers {self.rel_pieces}. -->\n'
        s += f'<svg {header} height="{size}" width="{size}">\n'
        for i, _ in enumerate(self.rel_pieces):
            s += self.make_group(i, radius, padding, precision)
        s += '</svg>'
        return s



if __name__ == '__main__':
    if len(sys.argv) == 2:
        print(Polygon(int(sys.argv[1])).svg(RADIUS, PADDING, PRECISION))
    elif len(sys.argv) > 2:
        print(Polygon(list(map(int, sys.argv[1:]))).svg(RADIUS, PADDING, PRECISION))
    elif 'LAYERS' in globals():
        print(Polygon(LAYERS).svg(RADIUS, PADDING, PRECISION))
    elif 'NGON' in globals():
        print(Polygon(NGON).svg(RADIUS, PADDING, PRECISION))
    else:
        raise NotImplementedError

heptadecagon.svg

<!-- 17-gon with layers (1, 4, 3). -->
<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" height="1500" width="1500">
<g id="a0"><polyline points="619.147322024,50 880.852677976,50.0" stroke="#000" fill="none" /></g>
<g id="a1">
<use xlink:href="#a0" transform="rotate(21.176470588 750 750)" />
<use xlink:href="#a0" transform="rotate(42.352941176 750 750)" />
<use xlink:href="#a0" transform="rotate(63.529411765 750 750)" />
<use xlink:href="#a0" transform="rotate(84.705882353 750 750)" />
</g>
<g id="a2">
<use xlink:href="#a1" transform="rotate(84.705882353 750 750)" />
<use xlink:href="#a1" transform="rotate(169.411764706 750 750)" />
<use xlink:href="#a1" transform="rotate(254.117647059 750 750)" />
</g>
</svg>

megagon.svg