154 lines
3.7 KiB
Python
154 lines
3.7 KiB
Python
from numba import jit, c16
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from numba.experimental import jitclass
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from cmath import sqrt
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from math import tanh, atanh, pi
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from lines import cLineIntersection, cBetween
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def deg2rad(rA): return rA/180*pi
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def rad2degd(rA): return rA*180/pi
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@jit(cache=True)
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def cap(rN):
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if rN < 0:
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return 0
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return rN
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@jit(cache=True)
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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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@jit(cache=True)
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def c_tr(cN):
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return cN.real, cN.imag
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@jit(cache=True)
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def cNorm(cN):
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return ZeroCheck(cN)/abs(ZeroCheck(cN))
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@jit(cache=True)
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def cDot(cA, cB):
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return (cA * cB.conjugate()).real
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@jit(cache=True)
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def cDist(cA, cB):
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return abs(cA-cB)
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@jit(cache=True)
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def MobiusInt(cA,cB,cC,cD): # Bruh
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try:
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return Klein2Poincare(cLineIntersection(Poincare2Klein(cA),Poincare2Klein(cB),Poincare2Klein(cC),Poincare2Klein(cD)))
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except:
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return 0j
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@jit(cache=True)
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def MobiusBetween(cA,cB,cN):
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return cBetween(Poincare2Klein(cA),Poincare2Klein(cB),Poincare2Klein(cN))
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@jit(cache=True)
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def MobiusAdd(cA, cB):
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return (cA + cB) / (1 + cA.conjugate() * cB)
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@jit(cache=True)
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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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@jit(cache=True)
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def MobiusAddGyr(cA, cB):
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return MobiusAdd(cA, cB), MobiusGyr(cA, cB)
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@jit(cache=True)
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def MobiusScalar(cA, rT):
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m = abs(cA)
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return tanh(rT * atanh(m)) * cA / m
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@jit(cache=True)
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def MobiusCoadd(cA,cB):
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return MobiusAdd(cA, (MobiusGyr(cA,-cB) * cB))
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@jit(cache=True)
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def MobiusCosub(cA,cB):
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return MobiusAdd(cA, -(MobiusGyr(cA,cB) * cB))
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@jit(cache=True)
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def MobiusLine(cA,cB,rT):
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return MobiusAdd(
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cA,
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MobiusScalar(
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MobiusAdd(-cA,cB),
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rT))
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@jit(cache=True)
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def MobiusDist(cA,cB):
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return abs(MobiusAdd(-cB,cA))
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@jit(cache=True)
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def Poincare2Klein(cN):
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return 2*cN / (1 + cDot(cN,cN))
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@jit(cache=True)
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def Klein2Poincare(cN):
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return (1-sqrt(1-cDot(cN,cN)))*cN/cDot(cN,cN)
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gyrosig = [
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('cPos', c16),
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('cRot', c16)
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]
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@jitclass(gyrosig)
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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 __iadd__(self, gA):
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cAdd, cGyr = MobiusAddGyr(self.cPos, gA.cPos)
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self.cPos = cAdd
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self.cRot = self.cRot * gA.cRot * cGyr
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def __isub__(self, gA):
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ngA = -gA
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cAdd, cGyr = MobiusAddGyr(self.cPos, ngA.cPos)
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self.cPos = cAdd
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self.cRot = self.cRot * ngA.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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def dist(self,gA):
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return abs((-self+gA).cPos)
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