def UHPSidePairingsOfSpecificIdealPolygon(self, genus, numberOfPunctures):
g, p = genus, numberOfPunctures
if g == 0 and p < 3:
pass
elif g == 1 and p == 0:
pass
else:
f = self.UHPSpecificCombinatorialSidePairing(g, p)
NumOfSides = (4 * g) + (2 * (p - 1))
SidePairings = {}
for k in range(NumOfSides):
if k == f(NumOfSides - 1):
SidePairings[k] = numpy.matrix(
[[NumOfSides - 1, (NumOfSides - 1) * (-k)], [0, 1]]
) #numpy.matrix([[NumOfSides-1,0],[0,1]])*numpy.matrix([[1,-k],[0,1]])
elif k == NumOfSides - 1:
SidePairings[k] = (SidePairings[f(k)])**(-1)
else:
#TranslationMatrix = numpy.matrix([[1,f(k)-k],[0,1]])
#Elliptic180 = Mobius_CP.MobiusTransitivity().MobiusMatrixz1z2z3Tow1w2w3(f(k)+(1/2)+1j,f(k),f(k)+1,f(k)+(1/2)+1j,f(k)+1,f(k))#Mobius_CP.MobiusFromParameters().MobMatrixFromParams([f(k)+(1/2)+1j,f(k)+(1/2)-1j],-1)
SidePairings[k] = Mobius_CP.MobiusTransitivity(
).MobiusMatrixz1z2z3Tow1w2w3(
k + (1 / 2) + 1j, k, k + 1,
f(k) + (1 / 2) + 1j,
f(k) + 1, f(k)) #Elliptic180*TranslationMatrix
return SidePairings
def effectOf_pushButtonCPMTOrbitsRandomCircle(self):
MobiusTrans = Mobius_CP.MobiusAssocToMatrix(
self.lineEditCPMTOrbitsComplexNumberalpha.text(),
self.lineEditCPMTOrbitsComplexNumberbeta.text(),
self.lineEditCPMTOrbitsComplexNumbergamma.text(),
self.lineEditCPMTOrbitsComplexNumberdelta.text())
P = numpy.complex(numpy.random.random(), numpy.random.random())
Q = numpy.complex(numpy.random.random(), numpy.random.random())
R = numpy.complex(numpy.random.random(), numpy.random.random())
numberOfPointsInOrbit = int(self.spinBoxCPMTOrbits.cleanText())
OrbitP = MobiusTrans.Mob_trans_iterable(P, numberOfPointsInOrbit)
OrbitQ = MobiusTrans.Mob_trans_iterable(Q, numberOfPointsInOrbit)
OrbitR = MobiusTrans.Mob_trans_iterable(R, numberOfPointsInOrbit)
pointsForPlotP = Steiner_grids_CP.coordsOfComplex().coords(OrbitP)
pointsForPlotQ = Steiner_grids_CP.coordsOfComplex().coords(OrbitQ)
pointsForPlotR = Steiner_grids_CP.coordsOfComplex().coords(OrbitR)
centersAndRadii = [
(Steiner_grids_CP.commonCircles().commonCirclesFunction(
OrbitP[k], OrbitQ[k]))(OrbitR[k])
for k in range(0, numberOfPointsInOrbit, 1)
]
t = numpy.linspace(0, 2 * numpy.pi, 500)
for k in range(0, numberOfPointsInOrbit, 1):
self.mplWidgetIn_pageCP.canvas.axis.plot(
((centersAndRadii[k])[0])[0] +
(centersAndRadii[k])[1] * numpy.cos(t),
((centersAndRadii[k])[0])[1] +
(centersAndRadii[k])[1] * numpy.sin(t), 'b-')
line, = self.mplWidgetIn_pageCP.canvas.axis.plot(
((centersAndRadii[0])[0])[0] +
(centersAndRadii[0])[1] * numpy.cos(t),
((centersAndRadii[0])[0])[1] +
(centersAndRadii[0])[1] * numpy.sin(t),
'r-',
linewidth=3)
def update(k):
# Update the line and the axes (with a new xlabel). Return a tuple of
# "artists" that have to be redrawn for this frame.
line.set_xdata(((centersAndRadii[k])[0])[0] +
(centersAndRadii[k])[1] * numpy.cos(t))
line.set_ydata(((centersAndRadii[k])[0])[1] +
(centersAndRadii[k])[1] * numpy.sin(t))
return line,
anim = FuncAnimation(
self.mplWidgetIn_pageCP.canvas.fig,
update,
#init_func=init,
frames=numberOfPointsInOrbit,
interval=250,
blit=True)
self.mplWidgetIn_pageCP.canvas.draw()
def effectOf_pushButtonCPMTOrbitsSinglePoint(self):
MobiusTrans = Mobius_CP.MobiusAssocToMatrix(
self.lineEditCPMTOrbitsComplexNumberalpha.text(),
self.lineEditCPMTOrbitsComplexNumberbeta.text(),
self.lineEditCPMTOrbitsComplexNumbergamma.text(),
self.lineEditCPMTOrbitsComplexNumberdelta.text())
z_0 = numpy.complex(self.lineEditCPMTOrbitsComplexNumberz_0.text())
numberOfPointsInOrbit = int(self.spinBoxCPMTOrbits.cleanText())
Orbit = MobiusTrans.Mob_trans_iterable(z_0, numberOfPointsInOrbit)
pointsForPlot = Steiner_grids_CP.coordsOfComplex().coords(Orbit)
for k in range(0, numberOfPointsInOrbit, 1):
self.mplWidgetIn_pageCP.canvas.axis.plot(
(pointsForPlot[0])[k], (pointsForPlot[1])[k], 'ob')
line, = self.mplWidgetIn_pageCP.canvas.axis.plot((pointsForPlot[0])[0],
(pointsForPlot[1])[0],
marker='o',
color='r')
def update(i):
# Update the line and the axes (with a new xlabel). Return a tuple of
# "artists" that have to be redrawn for this frame.
line.set_xdata((pointsForPlot[0])[i])
line.set_ydata((pointsForPlot[1])[i])
return line,
# x = numpy.arange(0, 20, 0.1)
# self.mplWidgetIn_pageCP.canvas.axis.scatter(x, x + numpy.random.normal(0, 3.0, len(x)))
# line, = self.mplWidgetIn_pageCP.canvas.axis.plot(x, x - 5, 'r-', linewidth=2)
#
# def update(i):
# # Update the line and the axes (with a new xlabel). Return a tuple of
# # "artists" that have to be redrawn for this frame.
# line.set_ydata(x - 5 + i)
# return line,
# initialPlot, = self.mplWidgetIn_pageCP.canvas.axis.plot((pointsForPlot[0])[0],(pointsForPlot[1])[0],'or', animated = True)
#
## def init():
## initialPlot.set_data([],[])
## return initialPlot,
#
# def animate(k):
# x = (pointsForPlot[0])[k]
# y = (pointsForPlot[1])[k]
# print(x,y)
# initialPlot.set_data(x,y)
# return initialPlot,
#
anim = FuncAnimation(
self.mplWidgetIn_pageCP.canvas.fig,
update,
#init_func=init,
frames=numberOfPointsInOrbit,
interval=500,
blit=True)
self.mplWidgetIn_pageCP.canvas.draw()
def UHPCheckIfTheGroupIsFuchsianForSpecificSidePairing(
self, genus, numberOfPunctures):
g, p = genus, numberOfPunctures
if g == 0 and p < 3:
pass
elif g == 1 and p == 0:
pass
else:
sidePairings = self.UHPSidePairingsOfSpecificIdealPolygon(g, p)
orbits = self.UHPVertexOrbitsUnderSpecificCombinatorialSidePairing(
g, p)
for orbit in orbits:
transformation = sidePairings[orbit[0]]
j = 1
while j < len(orbit):
transformation = sidePairings[orbit[j]] * transformation
j = j + 1
print(Mobius_CP.MobiusAssocToMatrix().isParEllHypLox(
transformation[0, 0], transformation[0, 1],
transformation[1, 0], transformation[1, 1]))
def PDSidePairingsOfSpecificIdealPolygon(
self, genus, numberOfPunctures,
orders): #orders is supposed to be the list of orders of orb pts
g, p = genus, numberOfPunctures
o = len(orders)
if g == 0 and p < 3:
pass
elif g == 1 and p == 0:
pass
else:
f = self.PDSpecificCombinatorialSidePairing(g, p, o)
midpoints = self.PDSidesOfSpecificIdealPolygon(g, p,
orders)["midpoints"]
NumOfSides = (4 * g) + (2 * (p - 1)) + (2 * o)
SidePairings = {}
for k in range((4 * g) + (2 * (p - 1))):
SidePairings[k] = [
Mobius_CP.MobiusTransitivity().MobiusMatrixz1z2z3Tow1w2w3(
numpy.cos(2 * (
(f(k) + 1) % NumOfSides) * numpy.pi / NumOfSides) +
numpy.sin(2 * (
(f(k) + 1) % NumOfSides) * numpy.pi / NumOfSides) *
(1j),
numpy.cos(2 * (
(f(k)) % NumOfSides) * numpy.pi / NumOfSides) +
numpy.sin(2 * (
(f(k)) % NumOfSides) * numpy.pi / NumOfSides) *
(1j), midpoints[f(k)],
numpy.cos(2 * k * numpy.pi / NumOfSides) +
numpy.sin(2 * k * numpy.pi / NumOfSides) * (1j),
numpy.cos(2 * (k + 1) * numpy.pi / NumOfSides) +
numpy.sin(2 * (k + 1) * numpy.pi / NumOfSides) * (1j),
midpoints[k])
]
#print(Mobius_CP.MobiusAssocToMatrix().isParEllHypLox(SidePairings[k][0,0],SidePairings[k][0,1],SidePairings[k][1,0],SidePairings[k][1,1]))
MobTransUHPtoPD = {}
for l in range((4 * g) + (2 * (p - 1)), NumOfSides, 2):
a = numpy.cos(2 * l * numpy.pi / NumOfSides) + numpy.sin(
2 * l * numpy.pi / NumOfSides) * (1j)
b = numpy.cos(2 * (l + 1) * numpy.pi / NumOfSides) + numpy.sin(
2 * (l + 1) * numpy.pi / NumOfSides) * (1j)
c = numpy.cos(2 * (l + 2) * numpy.pi / NumOfSides) + numpy.sin(
2 * (l + 2) * numpy.pi / NumOfSides) * (1j)
MobTransUHPtoPD[l] = Mobius_CP.MobiusTransitivity(
).MobiusTransz1z2z3Tow1w2w3(-1, 0, 1, a, b, c)
for k in range((4 * g) + (2 * (p - 1)), NumOfSides):
if k % 2 == 0:
order = orders[int((k - ((4 * g) + (2 * (p - 1)))) / 2)]
theta = (2 * numpy.pi) / order
w = numpy.cos(2 * k * numpy.pi / NumOfSides) + numpy.sin(
2 * k * numpy.pi / NumOfSides) * (1j)
z = MobTransUHPtoPD[k](-numpy.tan(numpy.pi - (theta / 4)) *
(1j))
x = numpy.cos(2 *
(k + 2) * numpy.pi / NumOfSides) + numpy.sin(
2 *
(k + 2) * numpy.pi / NumOfSides) * (1j)
SidePairings[k] = [
Mobius_CP.MobiusTransitivity().
MobiusMatrixz1z2z3Tow1w2w3(x, midpoints[f(k)], z, w,
midpoints[k], z)
]
if k % 2 == 1:
order = orders[int(
(k - 1 - ((4 * g) + (2 * (p - 1)))) / 2)]
theta = (2 * numpy.pi) / order
x = numpy.cos(2 *
(k - 1) * numpy.pi / NumOfSides) + numpy.sin(
2 *
(k - 1) * numpy.pi / NumOfSides) * (1j)
w = MobTransUHPtoPD[k - 1](-numpy.tan(numpy.pi -
(theta / 4)) * (1j))
z = numpy.cos(2 *
(k + 1) * numpy.pi / NumOfSides) + numpy.sin(
2 *
(k + 1) * numpy.pi / NumOfSides) * (1j)
SidePairings[k] = [
Mobius_CP.MobiusTransitivity().
MobiusMatrixz1z2z3Tow1w2w3(w, midpoints[f(k)], x, w,
midpoints[k], z)
]
return SidePairings
def PDSidesOfSpecificIdealPolygon(
self, genus, numberOfPunctures,
orders): #orders is supposed to be the list of orders of orb pts
# NOTE: TRY TO IMPROVE THE WAY THE SIDES ARE COLORED
g, p = genus, numberOfPunctures
o = len(orders)
#print(orders)
if g == 0 and p < 3:
pass
elif g == 1 and p == 0:
pass
else:
NumOfSides = (4 * g) + (2 * (p - 1)) + (2 * o)
midpoints = {}
triplesOfPtsOnCurves = {}
for k in range((4 * g) + (2 * (p - 1))):
w = numpy.cos(2 * k * numpy.pi / NumOfSides) + numpy.sin(
2 * k * numpy.pi / NumOfSides) * (1j)
z = numpy.cos(2 * (k + 1) * numpy.pi / NumOfSides) + numpy.sin(
2 * (k + 1) * numpy.pi / NumOfSides) * (1j)
eCenter = w * (1 + (z - w) / (z + w))
thetaw = myarg0To2Pi(
w - eCenter) #numpy.angle(-(w-eCenter))+numpy.pi
thetaz = myarg0To2Pi(
z - eCenter) #numpy.angle(-(z-eCenter))+numpy.pi
def parametrized_curve(t):
parametrization = eCenter + (z - eCenter) * (numpy.cos(t) +
numpy.sin(t) *
(1j))
return parametrization
midpoints[k] = parametrized_curve(
(min(numpy.abs(thetaz - thetaw),
(2 * numpy.pi) - numpy.abs(thetaz - thetaw))) / 2)
triplesOfPtsOnCurves[k] = [[
z,
parametrized_curve(
(min(numpy.abs(thetaz - thetaw),
(2 * numpy.pi) - numpy.abs(thetaz - thetaw))) /
2), w
]]
MobTransUHPtoPD = {}
for l in range((4 * g) + (2 * (p - 1)), NumOfSides, 2):
a = numpy.cos(2 * l * numpy.pi / NumOfSides) + numpy.sin(
2 * l * numpy.pi / NumOfSides) * (1j)
b = numpy.cos(2 * (l + 1) * numpy.pi / NumOfSides) + numpy.sin(
2 * (l + 1) * numpy.pi / NumOfSides) * (1j)
c = numpy.cos(2 * (l + 2) * numpy.pi / NumOfSides) + numpy.sin(
2 * (l + 2) * numpy.pi / NumOfSides) * (1j)
MobTransUHPtoPD[l] = Mobius_CP.MobiusTransitivity(
).MobiusTransz1z2z3Tow1w2w3(-1, 0, 1, a, b, c)
for k in range((4 * g) + (2 * (p - 1)), NumOfSides):
if k % 2 == 0:
order = orders[int((k - ((4 * g) + (2 * (p - 1)))) / 2)]
theta = (2 * numpy.pi) / order
w = numpy.cos(2 * k * numpy.pi / NumOfSides) + numpy.sin(
2 * k * numpy.pi / NumOfSides) * (1j)
z = MobTransUHPtoPD[k](-numpy.tan(numpy.pi - (theta / 4)) *
(1j))
inv = z / (z.real**2 + z.imag**2)
if k % 2 == 1:
order = orders[int(
(k - 1 - ((4 * g) + (2 * (p - 1)))) / 2)]
theta = (2 * numpy.pi) / order
w = MobTransUHPtoPD[k - 1](-numpy.tan(numpy.pi -
(theta / 4)) * (1j))
z = numpy.cos(2 *
(k + 1) * numpy.pi / NumOfSides) + numpy.sin(
2 *
(k + 1) * numpy.pi / NumOfSides) * (1j)
inv = w / (w.real**2 + w.imag**2)
eCenter = e_circumcenter_and_radius(
w, z, inv)[0][0] + e_circumcenter_and_radius(
w, z, inv)[0][1] * (1j)
thetaw = myarg0To2Pi(
w - eCenter) #numpy.angle(-(w-eCenter))+numpy.pi
thetaz = myarg0To2Pi(
z - eCenter) #numpy.angle(-(z-eCenter))+numpy.pi
def parametrized_curve(t):
parametrization = eCenter + (z - eCenter) * (numpy.cos(t) +
numpy.sin(t) *
(1j))
return parametrization
midpoints[k] = parametrized_curve(
(min(numpy.abs(thetaz - thetaw),
(2 * numpy.pi) - numpy.abs(thetaz - thetaw))) / 2)
triplesOfPtsOnCurves[k] = [[
z,
parametrized_curve(
(min(numpy.abs(thetaz - thetaw),
(2 * numpy.pi) - numpy.abs(thetaz - thetaw))) /
2), w
]]
#basicColors = [(200, 200, 255)]#["m", "c", "r", "k", "g", "y", "b"]#["m", "c", "r", "k", "g", "y", "b", "w"]
basicColors = [(255, 0, 0),
(0, 230, 0), (0, 0, 255), (255, 153, 0),
(204, 0, 204), "m", "b", "k", "g", "r"]
curvesColors = {}
# l = len(basicColors)
# for k in range(4*(g-1)-2):
# if k % l == 0 or k % l == 4 :
# curvesColors[k] = basicColors[int(k/2)%len(basicColors)]
# curvesColors[k+2] = basicColors[int(k/2)%len(basicColors)]
# if k % l == 3 or k % l == 7 :
# curvesColors[k] = basicColors[int((k-1)/2)%len(basicColors)]
# curvesColors[k+2] = basicColors[int((k-1)/2)%len(basicColors)]
f = self.PDSpecificCombinatorialSidePairing(g, p, o)
for k in range(NumOfSides): #range(4*(g-1)+1,4*(g-1)+1+p):
curvesColors[k] = basicColors[k % len(basicColors)]
curvesColors[f(k)] = basicColors[k % len(basicColors)]
result = {
"triplesOfPtsOnCurves": triplesOfPtsOnCurves,
"midpoints": midpoints,
"curvesColors": curvesColors
}
#print(curves)
return result