Add various new initial curves

problems/initial-curve.py

@@ -4,6 +4,98 @@ import math
 #
 # Note: This method does not have to return unit vectors.  Any non-zero vectors
 # will do; they are normalized after reading anyway.
+
+#
+#
+# Kurve
+#
+#def f(x):
+#    return [math.sin(0.5*math.pi*x[0]), math.cos(0.5*math.pi*x[0]), math.sin(10*math.pi*x[0])]
+
+#
+#
+#Spirale
+#
+#def f(x):
+#	a=0.05
+#	n=3
+#	phi=2*n*math.pi*x[0]
+#	radius= a*math.sqrt(phi)
+#	normsquared = radius*radius
+#	return [(2*radius*math.cos(phi))/(normsquared +1), (2*radius*math.sin(phi)) / (normsquared +1), (1-normsquared) / (normsquared +1)]
+
+# 
+#
+#Doppelspirale
+#
+#def f(x):
+#	a=0.05
+#	n=3
+#	phi = 4*n*math.pi*math.sqrt((1-2*x[0])*(1-2*x[0]))
+#	radius = a*math.sqrt(phi)
+#	radiusBeiViertel = a*math.sqrt(2*n*math.pi)
+#
+#	if 0<= x[0]< 0.25:
+#		line= radiusBeiViertel-x[0]+0.25
+#		normsquared = line*line
+#		return [2*line / (normsquared +1), 0, (1-normsquared) / (normsquared +1)]
+#	elif 0.25<= x[0]< 0.5:
+#		normsquared = radius*radius
+#		return [(2*radius*math.cos(phi))/(normsquared +1), (2*radius*math.sin(phi)) / (normsquared +1), (1-normsquared) / (normsquared +1)]
+#	elif 0.5<= x[0] < 0.75:
+#		normsquared = radius*radius
+#		return [-(2*radius*math.cos(phi))/(normsquared +1), -(2*radius*math.sin(phi)) / (normsquared +1), (1-normsquared) / (normsquared +1)]
+#	else:
+#		line=-radiusBeiViertel-x[0]+0.75
+#		normsquared = line*line
+#		return [2*line / (normsquared +1), 0, (1-normsquared) / (normsquared +1)]
+
+
+#
+#
+# Kreis
+#def f(x):
+#	phi= 2*math.pi*x[0]
+#	radius=0.5
+#	normsquared = radius*radius
+#	return [(2*radius*math.cos(phi))/(normsquared +1), (2*radius*math.sin(phi)) / (normsquared +1), (1-normsquared) / (normsquared +1)]
+
+# Kreis (flach)
+#def f(x):
+#	phi= 2*math.pi*x[0]
+#	radius=0.5
+#	return [radius*math.cos(phi), radius*math.sin(phi)]
+
+# Ellipse
+#def f(x):
+#	phi= 2*math.pi*x[0]
+#	radius1=0.5
+#	radius2=0.05
+#	normsquared = radius1*radius1+(radius2*radius2*-radius1*radius1)*math.sin(phi)*math.sin(phi)
+#	return [(2*radius1*math.cos(phi))/(normsquared +1), (2*radius2*math.sin(phi)) / (normsquared +1), (1-normsquared) / (normsquared +1)]
+
+
+#
+#geschlossene Doppelspirale 
+#
 def f(x):
-    return [math.sin(0.5*math.pi*x[0]), math.cos(0.5*math.pi*x[0]), math.sin(10*math.pi*x[0])]
+	a=0.1
+	n=2
+	b=0.05
+	z= (x[0]-2*b+0.5)*0.5*1/(1-2*b)
+	phi1 = 4*n*math.pi*math.sqrt((1-2*z)*(1-2*z))
+	phi2= (2*n+1)*math.pi*math.sqrt((1-2*x[0])*(1-2*x[0]))
+	radius1 = a*math.sqrt(phi1)
+	radius2 = a*math.sqrt(phi2)
+
+	if 0<= x[0]< b:
+		line= 4*a*(math.sqrt(2*n*math.pi)-math.sqrt((2*n+1)*math.pi))*x[0]+ a*math.sqrt((2*n+1)*math.pi)
+		normsquared = line*line
+		return [2*line / (normsquared +1), 0, (1-normsquared) / (normsquared +1)]
+	elif b<= x[0]< 0.5:
+		normsquared = radius1*radius1
+		return [(2*radius1*math.cos(phi1))/(normsquared +1), (2*radius1*math.sin(phi1)) / (normsquared +1), (1-normsquared) / (normsquared +1)]
+	else:
+		normsquared = radius2*radius2
+		return [-(2*radius2*math.cos(phi2))/(normsquared +1), -(2*radius2*math.sin(phi2)) / (normsquared +1), (1-normsquared) / (normsquared +1)]