def __init__(this, *args, **kwargs):
t1 = Rot(axis = vec(0, 0, 1), angle = GeomTypes.turn(0.2))
t2 = Rot(axis = vec(0, 0, 1), angle = GeomTypes.turn(0.4))
t3 = Rot(axis = vec(0, 0, 1), angle = GeomTypes.turn(0.6))
t4 = Rot(axis = vec(0, 0, 1), angle = GeomTypes.turn(0.8))
h0 = HalfTurn(vec(0, 1, tau))
Heptagons.EqlHeptagonShape.__init__(this,
directIsometries = [
GeomTypes.E, t1, t2, t3, t4,
h0, h0*t1, h0*t2, h0*t3, h0*t4,
t1*h0, t1*h0*t1, t1*h0*t2, t1*h0*t3, t1*h0*t4,
t2*h0, t2*h0*t1, t2*h0*t2, t2*h0*t3, t2*h0*t4,
t3*h0, t3*h0*t1, t3*h0*t2, t3*h0*t3, t3*h0*t4,
t4*h0, t4*h0*t1, t4*h0*t2, t4*h0*t3, t4*h0*t4
],
# abuse the opposite isometry (even though this is not an opposite
# isometry really) But for historical reasons I used a half turn
# here to prevent edges to be drawn twice.
#oppositeIsometry = GeomTypes.I,
oppositeIsometry = GeomTypes.Hx,
name = 'EglHeptA5xI_GD'
)
this.initArrs()
this.setH(H0)
this.setViewSettings(edgeR = 0.01, vertexR = 0.02)
def __init__(this, *args, **kwargs):
t1 = Rot(axis=vec(0, 0, 1), angle=GeomTypes.turn(0.2))
t2 = Rot(axis=vec(0, 0, 1), angle=GeomTypes.turn(0.4))
t3 = Rot(axis=vec(0, 0, 1), angle=GeomTypes.turn(0.6))
t4 = Rot(axis=vec(0, 0, 1), angle=GeomTypes.turn(0.8))
h0 = HalfTurn(vec(0, 1, tau))
Heptagons.EqlHeptagonShape.__init__(
this,
directIsometries=[
GeomTypes.E, t1, t2, t3, t4, h0, h0 * t1, h0 * t2, h0 * t3,
h0 * t4, t1 * h0, t1 * h0 * t1, t1 * h0 * t2, t1 * h0 * t3,
t1 * h0 * t4, t2 * h0, t2 * h0 * t1, t2 * h0 * t2,
t2 * h0 * t3, t2 * h0 * t4, t3 * h0, t3 * h0 * t1,
t3 * h0 * t2, t3 * h0 * t3, t3 * h0 * t4, t4 * h0,
t4 * h0 * t1, t4 * h0 * t2, t4 * h0 * t3, t4 * h0 * t4
],
# abuse the opposite isometry (even though this is not an opposite
# isometry really) But for historical reasons I used a half turn
# here to prevent edges to be drawn twice.
#oppositeIsometry = GeomTypes.I,
oppositeIsometry=GeomTypes.Hx,
name='EglHeptA5xI_GD')
this.initArrs()
this.setH(H0)
this.setViewSettings(edgeR=0.01, vertexR=0.02)
def __init__(this, *args, **kwargs):
this.atanHV2 = Geom3D.Rad2Deg * math.atan(1/V2)
Heptagons.EqlHeptagonShape.__init__(this,
directIsometries = [
GeomTypes.E,
Rot(angle = GeomTypes.turn(0.25), axis = GeomTypes.uz),
Rot(angle = GeomTypes.turn(0.50), axis = GeomTypes.uz),
Rot(angle = GeomTypes.turn(0.75), axis = GeomTypes.uz)
],
# abuse the opposite isometry (even though this is not an opposite
# isometry really) But for historical reasons I used a half turn
# here to prevent edges to be drawn twice.
#oppositeIsometry = GeomTypes.I,
oppositeIsometry = halfTurn,
name = 'EglHeptS4xI'
)
this.initArrs()
this.setH(1.0)
this.setViewSettings(edgeR = 0.02, vertexR = 0.04)
def setV(this):
# input this.h
St = this.h / (2*math.sqrt(2*Cq)*this.h - Cq)
#
# 2
# __..--'-_
# 1 -'' . _"- 3
# \ _-'
# \ _-'
# \-'
# 0
#
# z y
# ^ 7\
# |/
# ---> x
#
#
# The kite above is a 5th of the top face of dodecahedron
# standing on 1 face, 2 is a vertex, 1 and 3, centres of two edges
# and 0 a face centre.
#
Vs = [
vec(0.0, 0.0, this.h), # 0
Rl,
vec(0.0, St, St/2),
vec(-Rl[0], Rl[1], Rl[2]) # 3
]
# add heptagons
H = HalfTurn(Vs[3])
this.errorStr = ''
if this.heptPosAlt:
Ns = Vs
heptN = Heptagons.Kite2Hept(Vs[3], Vs[0], Vs[1], Vs[2])
if heptN == None:
this.errorStr = 'No valid equilateral heptagon for this position'
return
Mr = Rot(axis = GeomTypes.Vec3(Vs[2]), angle = GeomTypes.turn(0.2))
# p is a corner of the pentagon inside the pentagram
# p is rotated 1/5th turn to form a triangle
# together with 2 corners of the pentagram:
# 5 of these triangles will cover the pentagram.
# this is easier than finding the centre of the pentagram.
v3 = heptN[0][3]
v4 = heptN[0][4]
p = v3 + (v4 - v3)/tau
v = Mr*p
if this.triangleAlt:
vt = heptN[0][6]
xtraEdgeIndex = 15
else:
vt = heptN[0][5]
xtraEdgeIndex = 14
#print v
# A part that will form the regular pentagrams (with overlaps).
RegularTrianglePartV = [
heptN[0][3],
heptN[0][4],
vec(v[0], v[1], v[2]),
]
RegularTrianglePartN = Vs[2]
# vt is the vertex that will be projected by a half turn on the
# third vertex of the isosceles triangle.
IsoscelesTriangleV = [
heptN[0][5],
heptN[0][6],
vt
]
else:
heptN = Heptagons.Kite2Hept(Vs[1], Vs[2], Vs[3], Vs[0])
if heptN == None:
this.errorStr = 'No valid equilateral heptagon for this position'
return
if this.triangleAlt:
vt = heptN[0][1]
xtraEdgeIndex = 14
else:
vt = heptN[0][2]
xtraEdgeIndex = 15
# One third of regular pentagon.
RegularTrianglePartV = [
heptN[0][3],
heptN[0][4],
vec(0, 0, heptN[0][3][2]),
]
RegularTrianglePartN = RegularTrianglePartV[2]
# vt is the vertex that will be projected by a half turn on the
# third vertex of the isosceles triangle.
IsoscelesTriangleV = [
heptN[0][1],
heptN[0][2],
vt
]
if heptN == None:
this.errorStr = 'No valid equilateral heptagon for this position'
return
else:
this.errorStr = ''
# rotate vt by a half turn, IsoscelesTriangleV NOT auto updated.
vt = H * vt
IsoscelesTriangleV[2] = vt
Vs.extend(heptN[0]) # V4 - V10
Vs.extend(RegularTrianglePartV) # V11 - V13
Vs.extend(IsoscelesTriangleV) # V14 - V16
#for V in Vs: print V
Ns = [heptN[1] for i in range(11)]
Ns.extend([RegularTrianglePartN for i in range(3)])
IsoscelesTriangleN = Geom3D.Triangle(
IsoscelesTriangleV[0],
IsoscelesTriangleV[1],
IsoscelesTriangleV[2]
).normal()
Ns.extend([IsoscelesTriangleN for i in range(3)])
this.xtraEs = []
if this.addXtraEdge:
this.xtraEs = [xtraEdgeIndex, 16]
#this.showBaseOnly = True
this.setBaseVertexProperties(Vs = Vs, Ns = Ns)
Fs = []
Es = []
colIds = []
if this.showKite:
Fs.extend(this.kiteFs)
Es.extend(this.kiteEs)
colIds.extend(this.kiteColIds)
if this.showHepta:
Fs.extend(this.heptFs)
Es.extend(this.heptEs)
colIds.extend(this.heptColIds)
if this.showXtra:
Fs.extend(this.xtraFs)
Es.extend(this.xtraEs)
colIds.extend(this.xtraColIds)
this.setBaseEdgeProperties(Es = Es)
this.setBaseFaceProperties(Fs = Fs, colors = (this.theColors, colIds))
this.Vs = Vs
x = v1[0] - v0[0]
y = v1[1] - v0[1]
z = v1[2] - v0[2]
return (math.sqrt(x * x + y * y + z * z))
V2 = math.sqrt(2)
V3 = math.sqrt(3)
V5 = math.sqrt(5)
tau = (1.0 + V5) / 2
tau2 = tau + 1
dtau = 1.0 / tau
isomA5 = isometry.A5()
o5axis = GeomTypes.Vec([1, 0, tau])
o5fld = Rot(axis=o5axis, angle=GeomTypes.turn(1.0 / 5))
_o5fld = Rot(axis=o5axis, angle=GeomTypes.turn(-1.0 / 5))
isomO5 = isometry.C5(setup={'axis': o5axis})
o3axis = GeomTypes.Vec([0, dtau, tau])
o3fld = Rot(axis=o3axis, angle=GeomTypes.tTurn)
isomO3 = isometry.C3(setup={'axis': o3axis})
# get the col faces array by using a similar shape here, so it is calculated
# only once
colStabilisers = [
isometry.A4(setup={
'o2axis0': [1.0, 0.0, 0.0],
'o2axis1': [0.0, 0.0, 1.0],
}),
isometry.A4(setup={
def Vlen(v0, v1):
x = v1[0] - v0[0]
y = v1[1] - v0[1]
z = v1[2] - v0[2]
return (math.sqrt(x*x + y*y + z*z))
V2 = math.sqrt(2)
V3 = math.sqrt(3)
V5 = math.sqrt(5)
tau = (1.0 + V5)/2
tau2 = tau + 1
dtau = 1.0/tau
isomA5 = isometry.A5()
o5axis = GeomTypes.Vec([1, 0, tau])
o5fld = Rot(axis = o5axis, angle = GeomTypes.turn(1.0/5))
_o5fld = Rot(axis = o5axis, angle = GeomTypes.turn(-1.0/5))
isomO5 = isometry.C5(setup = {'axis': o5axis})
o3axis = GeomTypes.Vec([0, dtau, tau])
o3fld = Rot(axis = o3axis, angle = GeomTypes.tTurn)
isomO3 = isometry.C3(setup = {'axis': o3axis})
# get the col faces array by using a similar shape here, so it is calculated
# only once
colStabilisers = [
isometry.A4(setup = {
'o2axis0': [1.0, 0.0, 0.0],
'o2axis1': [0.0, 0.0, 1.0],
}),
isometry.A4(setup = {
def setV(this):
# input this.h
St = this.h / (Dtau2 * V3 * this.h - 3)
#print 's', St
#
# 0
# __..--'-_
# 3 -'' . _"- 1
# \ _-'
# \ _-'
# \-'
# 2
#
# z y
# ^ 7\
# |/
# ---> x
#
#
# The kite above is a 5th of the top face of dodecahedron
# standing on 1 face, 2 is a vertex, 1 and 3, centres of two edges
# and 0 a face centre.
#
Vs = [
vec(0.0, 0.0, this.h), # 0
Rl,
vec(0.0, -Dtau2 * St, St),
vec(-Rl[0], Rl[1], Rl[2]) # 3
]
# add heptagons
H = HalfTurn(Vs[3])
this.errorStr = ''
if not this.heptPosAlt:
Ns = Vs
heptN = Heptagons.Kite2Hept(Vs[3], Vs[0], Vs[1], Vs[2])
if heptN == None:
this.errorStr = 'No valid equilateral heptagon for this position'
return
Mr = Rot(axis=GeomTypes.Vec3(Vs[2]), angle=GeomTypes.turn(0.2))
# p is a corner of the pentagon inside the pentagram
# p is rotated 1/5th turn to form a triangle
# together with 2 corners of the pentagram:
# 5 of these triangles will cover the pentagram.
# this is easier than finding the centre of the pentagram.
v3 = heptN[0][3]
v4 = heptN[0][4]
p = v3 + (v4 - v3) / tau
v = Mr * p
if this.triangleAlt:
vt = heptN[0][6]
xtraEdgeIndex = 15
else:
vt = heptN[0][5]
xtraEdgeIndex = 14
# A part that will form the regular pentagrams (with overlaps).
RegularTrianglePartV = [
heptN[0][3],
heptN[0][4],
vec(v[0], v[1], v[2]),
]
RegularTrianglePartN = Vs[2]
# vt is the vertex that will be projected by a half turn on the
# third vertex of the isosceles triangle.
IsoscelesTriangleV = [heptN[0][5], heptN[0][6], vt]
else:
heptN = Heptagons.Kite2Hept(Vs[1], Vs[2], Vs[3], Vs[0])
if heptN == None:
this.errorStr = 'No valid equilateral heptagon for this position'
return
if this.triangleAlt:
vt = heptN[0][1]
xtraEdgeIndex = 14
else:
vt = heptN[0][2]
xtraEdgeIndex = 15
# One third of regular triangle.
RegularTrianglePartV = [
heptN[0][3],
heptN[0][4],
vec(0, 0, heptN[0][3][2]),
]
RegularTrianglePartN = RegularTrianglePartV[2]
# vt is the vertex that will be projected by a half turn on the
# third vertex of the isosceles triangle.
IsoscelesTriangleV = [heptN[0][1], heptN[0][2], vt]
if heptN == None:
this.errorStr = 'No valid equilateral heptagon for this position'
return
else:
this.errorStr = ''
vt = H * vt
# rotate vt by a half turn, IsoscelesTriangleV NOT auto updated.
IsoscelesTriangleV[2] = vt
Vs.extend(heptN[0]) # V4 - V10, the heptagon
Vs.extend(RegularTrianglePartV) # V11 - V13
Vs.extend(IsoscelesTriangleV) # V14 - V16
#for V in Vs: print V
#h = heptN[1]
#Ns = [[-h[0], -h[1], -h[2]] for i in range(11)]
Ns = [heptN[1] for i in range(11)]
Ns.extend([RegularTrianglePartN for i in range(3)])
IsoscelesTriangleN = Geom3D.Triangle(IsoscelesTriangleV[0],
IsoscelesTriangleV[1],
IsoscelesTriangleV[2]).normal()
Ns.extend([IsoscelesTriangleN for i in range(3)])
this.xtraEs = []
if this.addXtraEdge:
this.xtraEs = [xtraEdgeIndex, 16]
#this.showBaseOnly = True
this.setBaseVertexProperties(Vs=Vs, Ns=Ns)
Fs = []
Es = []
colIds = []
if this.showKite:
Fs.extend(this.kiteFs)
Es.extend(this.kiteEs)
colIds.extend(this.kiteColIds)
if this.showHepta:
Fs.extend(this.heptFs)
Es.extend(this.heptEs)
colIds.extend(this.heptColIds)
if this.showXtra:
Fs.extend(this.xtraFs)
Es.extend(this.xtraEs)
colIds.extend(this.xtraColIds)
this.setBaseEdgeProperties(Es=Es)
this.setBaseFaceProperties(Fs=Fs, colors=(this.theColors, colIds))
this.Vs = Vs
