Cubic Bézier curve splitting program

bezier-split.py

#!/usr/bin/env python3

# Copyright (C) 2020 Star Brilliant <coder@poorlab.com>
#
#            DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
#   TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
#
#  0. You just DO WHAT THE FUCK YOU WANT TO.

import sys
import typing

import numpy


def print_help() -> None:
    print('Cubic Bézier curve splitting program')
    print('Usage: {} x1,y1 x2,y2 x3,y3 x4,y4 split_point_x'.format(sys.argv[0]))
    print()
    print('If you have a cubic Bézier curve defined by Tikz syntax')
    print()
    print('  \draw (1,1) .. controls +(1,1) and +(-1,-1) .. (3,1)')
    print()
    print('or using absolute coordinates,')
    print()
    print('  \draw (1,1) .. controls (2,2) and (2,0) .. (3,1)')
    print()
    print('and you want to know what the two segments are if split at x=2.')
    print()
    print('you can call this program using the following arguments:')
    print()
    print('  {} 1,1 1,1 -1,-1 3,1 2'.format(sys.argv[0]))
    print()


def parse_point(s: str) -> typing.Tuple[float, float]:
    fields = str.split(s, ',', 2)
    x = float(fields[0])
    y = float(fields[1])
    return x, y


def main() -> None:
    if len(sys.argv) != 6:
        print_help()
        return

    a = numpy.asarray(parse_point(sys.argv[1]))
    b = numpy.asarray(parse_point(sys.argv[2]))
    c = numpy.asarray(parse_point(sys.argv[3]))
    d = numpy.asarray(parse_point(sys.argv[4]))
    x = float(sys.argv[5])

    b += a
    c += d

    t_all = numpy.roots(numpy.asarray([
        [-1,  3, -3, 1,  0],
        [ 3, -6,  3, 0,  0],
        [-3,  3,  0, 0,  0],
        [ 1,  0,  0, 0, -1],
    ]).dot(numpy.asarray([a[0], b[0], c[0], d[0], x])))
    t = numpy.abs(sorted(t_all, key=lambda x: numpy.abs(x - 0.5))[0])

    matrix_t = numpy.asarray([t*t*t, t*t, t, 1])
    matrix_abcd = numpy.asarray([a, b, c, d])

    b1 = matrix_t.dot(numpy.asarray([
        [ 0, 0, 0, 0],
        [ 0, 0, 0, 0],
        [-1, 1, 0, 0],
        [ 1, 0, 0, 0],
    ])).dot(matrix_abcd)
    c1 = matrix_t.dot(numpy.asarray([
        [ 0,  0, 0, 0],
        [ 1, -2, 1, 0],
        [-2,  2, 0, 0],
        [ 1,  0, 0, 0],
    ])).dot(matrix_abcd)

    mid = matrix_t.dot(numpy.asarray([
        [-1,  3, -3, 1],
        [ 3, -6,  3, 0],
        [-3,  3,  0, 0],
        [ 1,  0,  0, 0],
    ])).dot(matrix_abcd)

    b2 = matrix_t.dot(numpy.asarray([
        [0,  0,  0, 0],
        [0,  1, -2, 1],
        [0, -2,  2, 0],
        [0,  1,  0, 0],
    ])).dot(matrix_abcd)
    c2 = matrix_t.dot(numpy.asarray([
        [0, 0,  0, 0],
        [0, 0,  0, 0],
        [0, 0, -1, 1],
        [0, 0,  1, 0],
    ])).dot(matrix_abcd)

    b1 -= a
    c1 -= mid
    b2 -= mid
    c2 -= d

    print('Split at ({:.3f},{:.6f}), t = {:.6f}'.format(mid[0], mid[1], t))
    print()
    print('\\draw ({:.3f},{:.3f})'.format(a[0], a[1]))
    print('      .. controls +({:.3f},{:.3f}) and +({:.3f},{:.3f}) ..'.format(b1[0], b1[1], c1[0], c1[1]))
    print('      ({:.3f},{:.3f})'.format(mid[0], mid[1]))
    print('      .. controls +({:.3f},{:.3f}) and +({:.3f},{:.3f}) ..'.format(b2[0], b2[1], c2[0], c2[1]))
    print('      ({:.3f},{:.3f});'.format(d[0], d[1]))


if __name__ == '__main__':
    main()