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#!/usr/bin/env python3
import sys;sys.path.insert(0, "..")
from math import *
from pyx import *
# File for invalid parametrisations of Bezier curves
# Draws a sketch of the areas where invalid params are to be expected
def lhs(x, y, sign1):
if sign1 > 0:
return -3*y*(-x + abs(x))
else:
return -3*y*(-x - abs(x))
def rhs(x, y, sign2):
if sign2 > 0:
return (1-3*x) * (1-y + sqrt(1+y+y*y))
else:
return (1-3*x) * (1-y - sqrt(1+y+y*y))
def f(x, y):
xsigns = [-1, 1]
ysigns = [-1, 1]
if 0 < x < 1:
xsigns = [1]
if y > -1:
ysigns = [-1]
val = float("inf")
for sign1 in xsigns:
for sign2 in ysigns:
val = min(val, abs(lhs(x,y,sign1) - rhs(x,y,sign2)))
return val
xmin, xmax, xn = -2, 3, 250
xvalues = [xmin + (xmax-xmin)*i/(xn-1) for i in range(xn)]
ymin, ymax, yn = -3, 2, 250
yvalues = [ymin + (ymax-ymin)*i/(yn-1) for i in range(yn)]
d = []
for x in xvalues:
for y in yvalues:
d.append((x, y, log(f(x, y))))
g = graph.graphxy(width=10,
x=graph.axis.lin(title=r"$\Delta x$", min=xmin, max=xmax),
y=graph.axis.lin(title=r"$\Delta y$", min=ymin, max=ymax),
)
g.plot(graph.data.points(d, x=1, y=2, color=3, title=None),
[graph.style.density(gradient=color.rgbgradient.Rainbow)])
g.dolayout()
g.plot(graph.data.function("x(y)=(-1-2*y-sqrt((1+2*y)**2+3))/3.0"), [graph.style.line([style.linestyle.dotted])])
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])])
g.writePDFfile()
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