initial commit

apps/curve_subdivision.py

@@ -0,0 +1,85 @@
+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')