72 lines
1.8 KiB
Python
72 lines
1.8 KiB
Python
def ZeroCheck(cN):
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if cN == complex(0,0):
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return complex(1,0)
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else:
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return cN
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def c_tr(cN):
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return cN.real, cN.imag
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def cNorm(cN):
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return ZeroCheck(cN)/abs(ZeroCheck(cN))
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def cDot(cA, cB):
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return (cA * cB.conjugate()).real
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def cDist(cA, cB):
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return abs(cA-cB)
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def MobiusAdd(cA, cB):
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return (cA + cB) / (1 + cA.conjugate() * cB)
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def MobiusGyr(cA, cB):
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return (1 + cA * cB.conjugate()) / (1 + cA.conjugate() * cB)
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def MobiusAddGyr(cA, cB):
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return MobiusAdd(cA, cB), MobiusGyr(cA, cB)
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def Poincare2Klein(cN):
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return 2*cN / (1 + cDot(cN,cN))
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class GyroVector:
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def __init__(self, cPos, cRot):
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self.cPos = complex(cPos)
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self.cRot = complex(cRot)
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self.normalize()
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def __add__(gA, gB):
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#cAdd, cGyr = MobiusAddGyr(gA.cPos, gB.cPos / gA.cRot)
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cAdd, cGyr = MobiusAddGyr(gA.cPos, gB.cPos)
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return GyroVector(cAdd, gA.cRot * gB.cRot * cGyr)
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def __neg__(self):
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return GyroVector(-(self.cRot * self.cPos), 1/self.cRot)
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def __sub__(gA, gB):
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return gA + (-gB)
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def copy(self):
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return GyroVector(self.cPos,self.cRot)
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def normalize(self):
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if abs(self.cPos) > 1:
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self.cPos = cNorm(self.cPos)
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self.cRot = cNorm(self.cRot)
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def rotate(self,cRot):
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self.cRot *= cRot
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def transform(self, cA):
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#cAdd, cGyr = MobiusAddGyr(self.cPos, cA / ZeroCheck(self.cRot))
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cAdd, cGyr = MobiusAddGyr(self.cPos, cA / self.cRot)
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self.cPos = cAdd
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self.cRot = self.cRot * cGyr
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def transformed(self, cA):
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#cAdd, cGyr = MobiusAddGyr(self.cPos, cA / ZeroCheck(self.cRot))
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#return GyroVector(cAdd, self.cRot * cGyr)
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return gA.copy().transform(cA)
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def nrtransformed(self, cA):
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return MobiusAdd(self.cPos, cA / self.cRot)
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