design/invalid2.py

   1 #!/usr/bin/env python3
   2 import sys;sys.path.insert(0, "..")
   3 from math import *
   4 from pyx import *
   5 # File for invalid parametrisations of Bezier curves
   6 # Draws a sketch of the areas where invalid params are to be expected
   7
   8 def lhs(x, y, sign1):
   9     if sign1 > 0:
  10         return -3*y*(-x + abs(x))
  11     else:
  12         return -3*y*(-x - abs(x))
  13
  14 def rhs(x, y, sign2):
  15     if sign2 > 0:
  16         return (1-3*x) * (1-y + sqrt(1+y+y*y))
  17     else:
  18         return (1-3*x) * (1-y - sqrt(1+y+y*y))
  19
  20 def f(x, y):
  21     xsigns = [-1, 1]
  22     ysigns = [-1, 1]
  23     if 0 < x < 1:
  24         xsigns = [1]
  25     if y > -1:
  26         ysigns = [-1]
  27
  28     val = float("inf")
  29     for sign1 in xsigns:
  30         for sign2 in ysigns:
  31             val = min(val, abs(lhs(x,y,sign1) - rhs(x,y,sign2)))
  32     return val
  33
  34 xmin, xmax, xn = -2, 3, 250
  35 xvalues = [xmin + (xmax-xmin)*i/(xn-1) for i in range(xn)]
  36 ymin, ymax, yn = -3, 2, 250
  37 yvalues = [ymin + (ymax-ymin)*i/(yn-1) for i in range(yn)]
  38
  39 d = []
  40 for x in xvalues:
  41     for y in yvalues:
  42         d.append((x, y, log(f(x, y))))
  43
  44 g = graph.graphxy(width=10,
  45     x=graph.axis.lin(title=r"$\Delta x$", min=xmin, max=xmax),
  46     y=graph.axis.lin(title=r"$\Delta y$", min=ymin, max=ymax),
  47 )
  48 g.plot(graph.data.points(d, x=1, y=2, color=3, title=None),
  49        [graph.style.density(gradient=color.rgbgradient.Rainbow)])
  50 g.dolayout()
  51 g.plot(graph.data.function("x(y)=(-1-2*y-sqrt((1+2*y)**2+3))/3.0"), [graph.style.line([style.linestyle.dotted])])
  52 g.plot(graph.data.function("x(y)=(-1-2*y+sqrt((1+2*y)**2+3))/3.0", max=-1), [graph.style.line([style.linestyle.dotted])])
  53 g.writePDFfile()
  54