1 files changed, 101 insertions, 0 deletions
diff --git a/Master/texmf-dist/asymptote/GUI/CubicBezier.py b/Master/texmf-dist/asymptote/GUI/CubicBezier.py
new file mode 100755
index 00000000000..6455b700a79
--- /dev/null
+++ b/Master/texmf-dist/asymptote/GUI/CubicBezier.py
@@ -0,0 +1,101 @@
+#!/usr/bin/env python
+###########################################################################
+#
+# Convert a Bezier curve to a polyline
+#
+# Once Tk supports "RawCurves" this will not be needed.
+#
+#
+# Author: Orest Shardt
+# Created: June 29, 2007
+#
+###########################################################################
+import math
+
+def norm(vector):
+  """Return the norm of a vector"""
+  return math.sqrt(vector[0]**2+vector[1]**2)
+
+def splitLine(end0,end1,t):
+  """Split a line at the distance t, with t in (0,1)"""
+  return (end0[0]+t*(end1[0]-end0[0]),end0[1]+t*(end1[1]-end0[1]))
+
+def splitBezier(node0,control0,control1,node1,t):
+  """Find the nodes and control points for the segments of a Bezier curve split at t"""
+  a = splitLine(node0,control0,t)
+  b = splitLine(control0,control1,t)
+  c = splitLine(control1,node1,t)
+  d = splitLine(a,b,t)
+  e = splitLine(b,c,t)
+  f = splitLine(d,e,t)#this is the point on the curve at t
+  return ([node0,a,d,f],[f,e,c,node1])
+
+def BezierWidth(node0,control0,control1,node1):
+  """Compute the distance of the control points from the node-node axis"""
+  deltax = node1[0] - node0[0]
+  deltay = node1[1] - node0[1]
+  length = norm((deltax,deltay))
+  if length == 0:
+    y1 = control0[1]-node0[1]
+    y2 = control1[1]-node0[1]
+  else:
+    cosine = deltax/length
+    sine = deltay/length
+    y1 = cosine*(control0[1]-node0[1])-sine*(control0[0]-node0[0])
+    y2 = cosine*(control1[1]-node0[1])-sine*(control1[0]-node0[0])
+  if y1*y2 >= 0:
+    #same sign
+    return max(abs(y1),abs(y2))
+  else:
+    #opposite sign
+    return abs(y1)+abs(y2)
+
+#If the above algorithm fails, this one will work, but it is far from elegant
+#def computeIntermediates(steps,node0,control0,control1,node1):
+  #pointList = []
+  #for a in range(0,100,100/steps)+[100]:
+   #t = a/100.0
+   #t1 = 1-t
+   #x = node0[0]*t1**3+3*control0[0]*t*t1**2+3*control1[0]*t**2*t1+node1[0]*t**3
+   #y = node0[1]*t1**3+3*control0[1]*t*t1**2+3*control1[1]*t**2*t1+node1[1]*t**3
+   #pointList.append((x,y))
+  #return pointList
+#def makeBezier(steps,node0,control0,control1,node1):
+ #if len(node0)!=2 or len(control0)!=2 or len(control1)!=2 or len(node1)!=2:
+  #return -1
+ #else:
+  #return [node0]+computeIntermediates(steps,node0,control0,control1,node1)+[node1]
+
+def makeBezierIntermediates(node0,control0,control1,node1,epsilon):
+  """Find the points, excluding node0, to be used as the line segment endpoints"""
+  if(BezierWidth(node0,control0,control1,node1) <= epsilon):
+    return [node1]
+  else:
+    splitUp = splitBezier(node0,control0,control1,node1,0.5)
+    return makeBezierIntermediates(*splitUp[0]+[epsilon])+makeBezierIntermediates(*splitUp[1]+[epsilon])
+
+def makeBezier(node0,control0,control1,node1,epsilon=1):
+  """Return the vertices to be used in the polyline representation of a Bezier curve"""
+  return [node0]+makeBezierIntermediates(node0,control0,control1,node1,epsilon)
+
+if __name__ == '__main__':
+  pointList = makeBezier((-80,0),(-150,40),(150,120),(80,0),0.5)
+  from timeit import Timer
+  t = Timer('makeBezier((-80,0),(-40,-40),(40,120),(80,0),1)','from __main__ import makeBezier')
+  print pointList
+  print len(pointList)
+  iterations = 1000
+  time = t.timeit(iterations)
+  print "%d iterations took %f seconds (%f ms for each)."%(iterations,time,1000.0*time/iterations)
+  points = []
+  for point in pointList:
+    points.append(point[0])
+    points.append(-point[1])
+  from Tkinter import *
+  root = Tk()
+  canv = Canvas(root,scrollregion=(-100,-100,100,100))
+  canv.pack()
+  canv.create_line(points)
+  for point in pointList:
+   canv.create_oval(point[0],-point[1],point[0],-point[1],fill='red',outline='red')
+  root.mainloop()