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| import svgpathtools | |
| import numpy as np | |
| import math | |
| def split_cubic(c, t): | |
| c0, c1 = svgpathtools.split_bezier(c, t) | |
| return svgpathtools.CubicBezier(c0[0], c0[1], c0[2], c0[3]), svgpathtools.CubicBezier(c1[0], c1[1], c1[2], c1[3]) | |
| def cubic_to_quadratic(curve): | |
| # Best L2 approximation | |
| m = (-curve.start + 3 * curve.control1 + 3 * curve.control2 - curve.end) / 4.0 | |
| return svgpathtools.QuadraticBezier(curve.start, m, curve.end) | |
| def convert_and_write_svg(cubic, filename): | |
| cubic_path = svgpathtools.Path(cubic) | |
| cubic_ctrl = svgpathtools.Path(svgpathtools.Line(cubic.start, cubic.control1), | |
| svgpathtools.Line(cubic.control1, cubic.control2), | |
| svgpathtools.Line(cubic.control2, cubic.end)) | |
| cubic_color = (50, 50, 200) | |
| cubic_ctrl_color = (150, 150, 150) | |
| r = 4.0 | |
| paths = [cubic_path, cubic_ctrl] | |
| colors = [cubic_color, cubic_ctrl_color] | |
| dots = [cubic_path[0].start, cubic_path[0].control1, cubic_path[0].control2, cubic_path[0].end] | |
| ncols = ['green', 'green', 'green', 'green'] | |
| nradii = [r, r, r, r] | |
| stroke_widths = [3.0, 1.5] | |
| def add_quadratic(q): | |
| paths.append(q) | |
| q_ctrl = svgpathtools.Path(svgpathtools.Line(q.start, q.control), | |
| svgpathtools.Line(q.control, q.end)) | |
| paths.append(q_ctrl) | |
| colors.append((200, 50, 50)) # q_color | |
| colors.append((150, 150, 150)) # q_ctrl_color | |
| dots.append(q.start) | |
| dots.append(q.control) | |
| dots.append(q.end) | |
| ncols.append('purple') | |
| ncols.append('purple') | |
| ncols.append('purple') | |
| nradii.append(r) | |
| nradii.append(r) | |
| nradii.append(r) | |
| stroke_widths.append(3.0) | |
| stroke_widths.append(1.5) | |
| prec = 1.0 | |
| queue = [cubic] | |
| num_quadratics = 0 | |
| while len(queue) > 0: | |
| c = queue[-1] | |
| queue = queue[:-1] | |
| # Criteria for conversion | |
| # http://caffeineowl.com/graphics/2d/vectorial/cubic2quad01.html | |
| p = c.end - 3 * c.control2 + 3 * c.control1 - c.start | |
| d = math.sqrt(p.real * p.real + p.imag * p.imag) * math.sqrt(3.0) / 36 | |
| t = math.pow(1.0 / d, 1.0 / 3.0) | |
| if t < 1.0: | |
| c0, c1 = split_cubic(c, 0.5) | |
| queue.append(c0) | |
| queue.append(c1) | |
| else: | |
| quadratic = cubic_to_quadratic(c) | |
| print(quadratic) | |
| add_quadratic(quadratic) | |
| num_quadratics += 1 | |
| print('num_quadratics:', num_quadratics) | |
| svgpathtools.wsvg(paths, | |
| colors = colors, | |
| stroke_widths = stroke_widths, | |
| nodes = dots, | |
| node_colors = ncols, | |
| node_radii = nradii, | |
| filename = filename) | |
| convert_and_write_svg(svgpathtools.CubicBezier(100+200j, 426+50j, 50+50j, 300+200j), | |
| 'results/curve_subdivision/subdiv_curve0.svg') | |
| convert_and_write_svg(svgpathtools.CubicBezier(100+200j, 427+50j, 50+50j, 300+200j), | |
| 'results/curve_subdivision/subdiv_curve1.svg') | |