added "examples" folder

examples/compute-many-points-quickly-using-numpy-arrays.py

@@ -0,0 +1,56 @@
+"""The goal of this gist is to show how to compute many points on a path 
+quickly using NumPy arrays.  I.e. there's a much faster way than using, say
+[some_path.point(t) for t in many_tvals].  The example below assumes the 
+`Path` object is composed entirely of `CubicBezier` objects, but this can
+easily be generalized to paths containing `Line` and `QuadraticBezier` objects
+also.  
+Note: The relevant matrix transformation for quadratics can be found in the
+svgpathtools.bezier module."""
+
+import numpy as np
+from svgpathtools import *
+
+
+class HigherOrderBezier:
+    def __init__(self, bpoints):
+        self.bpts = bpoints
+
+    def bpoints(self):
+        return self.bpts
+
+    def point(self, t):
+        return bezier_point(self.bpoints(), t)
+
+    def __repr__(self):
+        return str(self.bpts)
+
+
+def random_bezier(degree):
+    if degree <= 3:
+        return bpoints2bezier(polynomial2bezier(np.random.rand(degree + 1)))
+    else:
+        return HigherOrderBezier(np.random.rand(degree + 1))
+
+
+def points_in_each_seg_slow(path, tvals):
+    return [seg.poly()(tvals) for seg in path]
+
+
+def points_in_each_seg(path, tvals):
+    """Compute seg.point(t) for each seg in path and each t in tvals."""
+    A = np.matrix([[-1,  3, -3,  1], # transforms cubic bez to standard poly
+                   [ 3, -6,  3,  0],
+                   [-3,  3,  0,  0],
+                   [ 1,  0,  0,  0]])
+    B = [seg.bpoints() for seg in path]
+    return np.dot(B, np.dot(A, np.power(tvals, [[3],[2],[1],[0]])))
+
+
+if __name__ == '__main__':
+    num_segs = 1000
+    testpath = Path(*[random_bezier(3) for dummy in range(num_segs)])
+    tvals = np.linspace(0, 1, 10)
+
+    pts = points_in_each_seg(testpath, tvals)
+    pts_check = points_in_each_seg_slow(testpath, tvals)
+    print np.max(pts - pts_check)

examples/determine-if-svg-path-is-contained-in-other-path-example.py

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+"""
+An example of how to determine if an svg path is contained in another 
+svg path in Python.
+
+Note: for discontinuous paths you can use the svgpathtools 
+Path.continuous_subpaths() method to split a paths into a list of its 
+continuous subpaths.
+"""
+
+from svgpathtools import *
+
+def path1_is_contained_in_path2(path1, path2):
+    assert path2.isclosed()  # This question isn't well-defined otherwise
+    if path2.intersect(path1):
+        return False
+
+    # find a point that's definitely outside path2
+    xmin, xmax, ymin, ymax = path2.bbox()
+    B = (xmin + 1) + 1j*(ymax + 1)
+
+    A = path1.start  # pick an arbitrary point in path1
+    AB_line = Path(Line(A, B))
+    number_of_intersections = len(AB_line.intersect(path2))
+    if number_of_intersections % 2:  # if number of intersections is odd
+        return True
+    else:
+        return False
+
+
+# Test examples
+closed_path = Path(Line(0,5), Line(5,5+5j), Line(5+5j, 0))
+path_that_is_contained = Path(Line(1+1j, 2+2j))
+print(path1_is_contained_in_path2(path_that_is_contained, closed_path))
+
+path_thats_not_contained = Path(Line(10+10j, 20+20j))
+print(path1_is_contained_in_path2(path_thats_not_contained, closed_path))
+
+path_that_intersects = Path(Line(2+1j, 10+10j))
+print(path1_is_contained_in_path2(path_that_intersects, closed_path))

examples/distance-between-two-svg-paths-example.py

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+from svgpathtools import *
+
+# create some example paths
+path1 = CubicBezier(1,2+3j,3-5j,4+1j)
+path2 = path1.rotated(60).translated(3)
+
+# find minimizer
+from scipy.optimize import fminbound
+def dist(t):
+	return path1.radialrange(path2.point(t))[0][0]
+T2 = fminbound(dist, 0, 1)
+
+# Let's do a visual check
+pt2 = path2.point(T2)
+T1 = path1.radialrange(pt2)[0][1]
+pt1 = path1.point(T1)
+disvg([path1, path2, Line(pt1, pt2)], 'grb', nodes=[pt1, pt2])