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-rwxr-xr-xMaster/texmf-dist/asymptote/GUI/CubicBezier.py101
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diff --git a/Master/texmf-dist/asymptote/GUI/CubicBezier.py b/Master/texmf-dist/asymptote/GUI/CubicBezier.py
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+++ b/Master/texmf-dist/asymptote/GUI/CubicBezier.py
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+#!/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()