quadratics, axi render command

axi/drawing.py

@@ -3,7 +3,8 @@ from __future__ import division
 from math import sin, cos, radians
 
 from .paths import (
-    simplify_paths, sort_paths, join_paths, crop_paths, convex_hull)
+    simplify_paths, sort_paths, join_paths, crop_paths, convex_hull,
+    expand_quadratics)
 
 try:
     import cairo
@@ -19,10 +20,11 @@ class Drawing(object):
     def loads(cls, data):
         paths = []
         for line in data.split('\n'):
-            points = line.strip().split()
-            points = [map(float, x.split(',')) for x in points]
-            if points:
-                paths.append(points)
+            path = line.strip().split()
+            path = [map(float, x.split(',')) for x in path]
+            path = expand_quadratics(path)
+            if path:
+                paths.append(path)
         return cls(paths)
 
     @classmethod

axi/main.py

@@ -12,6 +12,15 @@ def main():
         return
     command, args = args[0], args[1:]
     command = command.lower()
+    if command == 'render':
+        d = axi.Drawing.load(args[0])
+        d = d.rotate_and_scale_to_fit(12, 8.5, step=90)
+        path = args[1] if len(args) > 1 else 'out.png'
+        im = d.render(
+            scale=109 * 1, line_width=0.25/25.4)
+            # show_axi_bounds=False, use_axi_bounds=False)
+        im.write_to_png(path)
+        return
     device = axi.Device()
     if command == 'zero':
         device.zero_position()

axi/paths.py

@@ -119,3 +119,35 @@ def convex_hull(points):
     if isinstance(hull, geometry.Point):
         return list(hull.coords)
     raise Exception('unhandled convex hull geometry')
+
+def quadratic_path(x0, y0, x1, y1, x2, y2):
+    n = int(hypot(x1 - x0, y1 - y0) + hypot(x2 - x1, y2 - y1))
+    n = max(n, 4)
+    points = []
+    m = 1 / float(n - 1)
+    for i in range(n):
+        t = i * m
+        u = 1 - t
+        a = u * u
+        b = 2 * u * t
+        c = t * t
+        x = a * x0 + b * x1 + c * x2
+        y = a * y0 + b * y1 + c * y2
+        points.append((x, y))
+    return points
+
+def expand_quadratics(path):
+    result = []
+    previous = (0, 0)
+    for point in path:
+        if len(point) == 2:
+            result.append(point)
+            previous = point
+        elif len(point) == 4:
+            x0, y0 = previous
+            x1, y1, x2, y2 = point
+            result.extend(quadratic_path(x0, y0, x1, y1, x2, y2))
+            previous = (x2, y2)
+        else:
+            raise Exception('invalid point: %r' % point)
+    return result