design/selfinter1.py

   1 #!/usr/bin/env python
   2 import sys;sys.path.insert(0, "..")
   3 from math import *
   4 #sys.path.insert(0, os.path.expanduser("~/python/pyx-trunk"))
   5 from pyx import *
   6 # File for invalid parametrisations of Bezier curves
   7 # Some examples
   8
   9 def Dx_m(Dy):
  10     return (-1-2*Dy-sqrt((1+2*Dy)**2+3))/3.0
  11
  12 def Dx_p(Dy):
  13     return (-1-2*Dy+sqrt((1+2*Dy)**2+3))/3.0
  14
  15 def pass00(Dy):
  16     return 1.0/(3.0*(Dy+1))
  17
  18 def pass10(Dy):
  19     return (1.0+Dy**3)/(3.0*(Dy+1))
  20
  21 def acurve(Dx, Dy, trafo_reverse=False):
  22     p = path.curve(0,0, 0,1, Dx,1+Dy, 1,0)
  23     if trafo_reverse:
  24         # calculate the trafo to put p2=(1,-1):
  25         # (for the right branch only)
  26         x2, y2 = Dx, Dy+1
  27         tr1 = trafo.scale(1, -1.0/y2)
  28         pp = tr1.apply_pt(x2, y2)
  29         tr2 = trafo.trafo(matrix=((1, (pp[0]-1)), (0, 1)))
  30         p = p.transformed(tr2*tr1)
  31     c = canvas.canvas()
  32     c.stroke(p, [deco.shownormpath()])
  33     #c.text(-0.2, -10*unit.x_pt, r"\noindent$\Delta x=%g $\par\noindent$\Delta y=%g$"%(Dx,Dy),
  34     #       [text.parbox(4), text.size.footnotesize])
  35     return c
  36
  37 dx = 3
  38 dy = -3
  39
  40 Dy = -2.5
  41 e = 0.1
  42 # test the left branch:
  43 cc = acurve(pass00(Dy), Dy) # passes through startpoint
  44 #cc = acurve(Dx_m(Dy)-e, Dy)
  45 c  = acurve(Dx_m(Dy)  , Dy); cc.insert(c, [trafo.translate(1*dx, 0)])
  46 c  = acurve(Dx_m(Dy)+e, Dy); cc.insert(c, [trafo.translate(2*dx, 0)])
  47
  48 # test the right branch:
  49 #cc = acurve(Dx_p(Dy)-e, Dy, True)
  50 #c  = acurve(Dx_p(Dy)  , Dy, True); cc.insert(c, [trafo.translate(1*dx, 0)])
  51 ##c  = acurve(Dx_p(Dy)+e, Dy, True); cc.insert(c, [trafo.translate(2*dx, 0)])
  52 #c  = acurve(pass10(Dy), Dy, True); cc.insert(c, [trafo.translate(2*dx, 0)]) # passes through endpoint
  53
  54 cc.writePDFfile()
  55