def printTrisAngles(this):
# TODO: fix this function. Which angles to take (ie which faces) depends
# on the triangle alternative.
tris = this.triFs[this.edgeAlternative]
# for non 1 loose
# for i in range(0, len(tris) - 2, 2):
d = 2
# for 1 loose:
d = 1
for i in range(2):
norm0 = Geom3D.Triangle(
this.baseShape.Vs[tris[i][0]],
this.baseShape.Vs[tris[i][1]],
this.baseShape.Vs[tris[i][2]],
).normal(True)
print 'norm0 %d: ', norm0
norm1 = Geom3D.Triangle(
this.baseShape.Vs[tris[i + d][0]],
this.baseShape.Vs[tris[i + d][1]],
this.baseShape.Vs[tris[i + d][2]],
).normal(True)
print 'norm1 %d: ', norm1
inprod = norm0 * norm1
print 'Tris angle %d: %.6f degrees' % (i, math.acos(inprod) *
Geom3D.Rad2Deg)
print '------------' # TODO move out
def setV(this):
# input this.h
St = this.h / (4*this.h - 1)
if this.heptPosAlt:
#
# z
# ^
# |
# ---> y
# /
# V_
# x
#
# There are vertices with more than one index, because the normals
# will differ.
#
# '-,
# / '-,
# / -.2
# | 5 -' \ 1, 11
# / 3.-' 0 '-
# | / 4 8 __'-10
# / ,-' __--""
# /,=---"" 7
# 6 9
#
# For tetrahedral position: 1, 3, and 5 are on the vertices of a
# cube and 2, 4, 6, are on the face centres of that cube
#
Vs = [
vec( St, St, -St), # 0
vec( 0.0, 1.0, 0.0),
vec( this.h, this.h, this.h),
vec( 1.0, 0.0, 0.0), # 3
vec( St, St, -St), # 4
vec( 1.0, 0.0, 0.0),
vec( this.h, -this.h, -this.h),
vec( 0.0, 0.0, -1.0), # 7
vec( St, St, -St), # 8
vec( 0.0, 0.0, -1.0),
vec(-this.h, this.h, -this.h),
vec( 0.0, 1.0, 0.0) # 11
]
# Normals are set below, after calculating the heptagons
#this.Ns = this.NsAlt
else:
#
# z
# ^
# |
# ---> y
# /
# V_
# x
#
# There are vertices with more than one index, because the normals
# will differ.
#
# 6
# 9 /
# '-, 7 V_
# / '-,
# / -.0, 4, 8
# | 10 -' \ 3, 5
# /11,1.-' '-
# | / 2 __'-
# / ,-' __--""
# /,=---""
#
#
# For tetrahedral position: 1, 3, and 5 are on the vertices of a
# cube and 2, 4, 6, are on the face centres of that cube
#
Vs = [
vec( this.h, this.h, this.h), # 0
vec( 1.0, 0.0, 0.0),
vec( St, St, -St),
vec( 0.0, 1.0, 0.0), # 3
vec( this.h, this.h, this.h), # 4
vec( 0.0, 1.0, 0.0),
vec(-St, St, St),
vec( 0.0, 0.0, 1.0), # 7
vec( this.h, this.h, this.h), # 8
vec( 0.0, 0.0, 1.0),
vec( St, -St, St),
vec( 1.0, 0.0, 0.0) # 11
]
# Normals are set below, after calculating the heptagons
#this.Ns = this.NsPref
# add heptagons
heptN = Heptagons.Kite2Hept(Vs[3], Vs[2], Vs[1], Vs[0])
if heptN == None:
this.errorStr = 'No valid equilateral heptagon for this position'
return
else:
this.errorStr = ''
Vs.extend(heptN[0]) # V12 - V18
Ns = range(33)
for i in range(4):
Ns[i] = heptN[1]
for i in range(12, 19):
Ns[i] = heptN[1]
heptN = Heptagons.Kite2Hept(Vs[7], Vs[6], Vs[5], Vs[4])
Vs.extend(heptN[0]) # V19 - V25
for i in range(4, 8):
Ns[i] = heptN[1]
for i in range(19, 26):
Ns[i] = heptN[1]
heptN = Heptagons.Kite2Hept(Vs[11], Vs[10], Vs[9], Vs[8])
Vs.extend(heptN[0]) # V26 - V32
for i in range(8, 12):
Ns[i] = heptN[1]
for i in range(26, 33):
Ns[i] = heptN[1]
# add equilateral triangles:
Vs.extend([Vs[15], Vs[22], Vs[29]]) # V33 - V35
# add isosceles triangles:
this.xtraEs = []
if this.triangleAlt:
Vs.extend([Vs[13], Vs[14], Vs[32]]) # V36 - V38
Vs.extend([Vs[20], Vs[21], Vs[18]]) # V39 - V41
Vs.extend([Vs[27], Vs[28], Vs[25]]) # V42 - V44
if this.addXtraEdge:
this.xtraEs = [36, 38, 39, 41, 42, 44]
else:
Vs.extend([Vs[13], Vs[14], Vs[14]]) # V36 - V38
Vs.extend([Vs[20], Vs[21], Vs[21]]) # V39 - V41
Vs.extend([Vs[27], Vs[28], Vs[28]]) # V42 - V44
if this.heptPosAlt:
v = Vs[38]
Vs[38] = vec(-v[0], v[1], -v[2]) # Hy * V9
v = Vs[41]
Vs[41] = vec( v[0], -v[1], -v[2]) # Hx * V23
else:
v = Vs[38]
Vs[38] = vec( v[0], -v[1], -v[2]) # Hx * V9
v = Vs[41]
Vs[41] = vec(-v[0], v[1], -v[2]) # Hy * V23
v = Vs[44]
Vs[44] = vec(-v[0], -v[1], v[2]) # Hz * V16
if this.addXtraEdge:
this.xtraEs = [37, 38, 40, 41, 43, 44]
# normal of equilateral triangle
for i in range(3):
Ns.append(Vs[0])
# normal of isosceles triangles
for i in range(3):
o = 36 + 3*i
IsoscelesTriangleN = Geom3D.Triangle(
Vs[o],
Vs[o+1],
Vs[o+2]
).normal()
Ns.extend([IsoscelesTriangleN, IsoscelesTriangleN, IsoscelesTriangleN])
this.xtraFs = [
[33, 34, 35],
[36, 37, 38],
[39, 40, 41],
[42, 43, 44]
]
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))
def setV(this):
# input this.h
St = this.h / (2*this.h - 1)
if this.heptPosAlt:
#
# z
# ^
# |
# ---> y
# /
# V_
# x
#
# .------------.
# ,' 2 _____1,'|
# ,' ,' ,'11|
# .-----3.----0' | |
# | 5| 4|8 | |
# | | | ,' |
# | +-----+' 10-
# | 6 7|9 ,'
# | |,'
# '------------'
#
Vs = [
vec(St, St, St), # 0
vec(0.0, 1.0, 1.0),
vec(0.0, 0.0, this.h),
vec(1.0, 0.0, 1.0), # 3
vec(St, St, St), # 4
vec(1.0, 0.0, 1.0),
vec(this.h, 0.0, 0.0),
vec(1.0, 1.0, 0.0), # 7
vec(St, St, St), # 8
vec(1.0, 1.0, 0.0),
vec(0.0, this.h, 0.0),
vec(0.0, 1.0, 1.0) # 11
]
else:
#
# z
# ^
# |
# ---> y
# /
# V_
# x
#
# .------------.
# ,' 0 _____3,'|
# ,' ,' ,'|9|
# .-----1.----2' | |
# | 7| 6|10| |
# | | | ,' |
# | +-----+' 8 -
# | 4 5|11,'
# | |,'
# '------------'
#
Vs = [
vec(0.0, 0.0, this.h), # 0
vec(1.0, 0.0, 1.0),
vec(St, St, St),
vec(0.0, 1.0, 1.0), # 3
vec(this.h, 0.0, 0.0), # 4
vec(1.0, 1.0, 0.0),
vec(St, St, St),
vec(1.0, 0.0, 1.0), # 7
vec(0.0, this.h, 0.0), # 8
vec(0.0, 1.0, 1.0),
vec(St, St, St),
vec(1.0, 1.0, 0.0), # 11
]
# add heptagons
heptN = Heptagons.Kite2Hept(Vs[3], Vs[2], Vs[1], Vs[0])
if heptN == None:
this.errorStr = 'No valid equilateral heptagon for this position'
return
else:
this.errorStr = ''
Vs.extend(heptN[0]) # V12 - V18
Ns = range(33)
for i in range(4):
Ns[i] = heptN[1]
for i in range(12, 19):
Ns[i] = heptN[1]
heptN = Heptagons.Kite2Hept(Vs[7], Vs[6], Vs[5], Vs[4])
Vs.extend(heptN[0]) # V19 - V25
for i in range(4, 8):
Ns[i] = heptN[1]
for i in range(19, 26):
Ns[i] = heptN[1]
heptN = Heptagons.Kite2Hept(Vs[11], Vs[10], Vs[9], Vs[8])
Vs.extend(heptN[0]) # V26 - V32
for i in range(8, 12):
Ns[i] = heptN[1]
for i in range(26, 33):
Ns[i] = heptN[1]
xtraEs = []
# add extra faces:
if this.heptPosAlt:
# Eql triangle
Vs.extend([Vs[15], Vs[22], Vs[29]]) # V33 - V35
# Isosceles triangles
if this.triangleAlt:
Vs.extend([Vs[13], Vs[14], Vs[32]]) # V36 - V38
Vs.extend([Vs[20], Vs[21], Vs[18]]) # V39 - V41
Vs.extend([Vs[27], Vs[28], Vs[25]]) # V42 - V44
else:
v = Vs[14]
Vs.extend([Vs[13], Vs[14], vec(-v[0], v[1], v[2])]) # V36 - V38
v = Vs[21]
Vs.extend([Vs[20], Vs[21], vec( v[0], -v[1], v[2])]) # V39 - V41
v = Vs[28]
Vs.extend([Vs[27], Vs[28], vec( v[0], v[1], -v[2])]) # V42 - V44
for i in range(3):
Ns.append(Vs[0]) # N33 - N35
# normals for the isosceles triangles:
# N36 - N38, N39 - N41 and N42 - N44
for i in range(3):
o = 36 + 3*i
IsoscelesTriangleN = Geom3D.Triangle(
Vs[o],
Vs[o+1],
Vs[o+2]
).normal()
Ns.extend([IsoscelesTriangleN, IsoscelesTriangleN, IsoscelesTriangleN])
xtraFs = [
# Eql triangle
[33, 34, 35],
# Isosceles triangles
[36, 37, 38],
[39, 40, 41],
[42, 43, 44],
]
this.xtraColIds = [2 for i in range(4)]
if this.addXtraEdge:
if this.triangleAlt:
xtraEs = [36, 38, 39, 41, 42, 44]
else:
xtraEs = [37, 38, 40, 41, 43, 44]
else:
# The Squares, divided into rectangular isosceles triangles,
# because of the sym-op
Vs.extend([Vs[15], Vs[16], vec(0, 0, Vs[15][2])]) # V33 - V35
Vs.extend([Vs[22], Vs[23], vec(Vs[22][0], 0, 0)]) # V36 - V38
Vs.extend([Vs[29], Vs[30], vec(0, Vs[29][1], 0)]) # V39 - V41
# add isosceles triangles:
if this.triangleAlt:
v = Vs[13]
Vs.extend([Vs[13], Vs[14], vec(v[0], -v[1], v[2])]) # V42 - V44
v = Vs[20]
Vs.extend([Vs[20], Vs[21], vec(v[0], v[1], -v[2])]) # V45 - V47
v = Vs[27]
Vs.extend([Vs[27], Vs[28], vec(-v[0], v[1], v[2])]) # V48 - V50
else:
Vs.extend([Vs[13], Vs[14], Vs[24]]) # V42 - V44
Vs.extend([Vs[20], Vs[21], Vs[31]]) # V45 - V47
Vs.extend([Vs[27], Vs[28], Vs[17]]) # V48 - V50
# normals for the equilateral triangles:
for i in range(3):
Ns.append(Vs[0]) # N33 - N35
for i in range(3):
Ns.append(Vs[4]) # N36 - N38
for i in range(3):
Ns.append(Vs[8]) # N39 - N41
# normals for the isosceles triangles:
# N42 - N44, N45 - N47 and N48 - N50
for i in range(3):
o = 42 + 3*i
IsoscelesTriangleN = Geom3D.Triangle(
Vs[o],
Vs[o+1],
Vs[o+2]
).normal()
Ns.extend([IsoscelesTriangleN, IsoscelesTriangleN, IsoscelesTriangleN])
xtraFs = [
# square parts:
[33, 34, 35],
[36, 37, 38],
[39, 40, 41],
# isosceles triangles:
[42, 43, 44],
[45, 46, 47],
[48, 49, 50]
]
this.xtraColIds = [2 for i in range(6)]
if this.addXtraEdge:
if this.triangleAlt:
xtraEs = [42, 44, 45, 47, 48, 50]
else:
xtraEs = [43, 44, 46, 47, 49, 50]
#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(xtraFs)
Es.extend(xtraEs)
colIds.extend(this.xtraColIds)
this.setBaseEdgeProperties(Es = Es)
this.setBaseFaceProperties(Fs = Fs, colors = (this.theColors, colIds))
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
def setV(this):
# input this.h
St = this.h / (4 - tau2 - (4 * this.h / tau2))
# z
# ^
# |
# ---> y
# /
# V_
# x
# 2
# __..--'-_
# 1 -'' . _"- 3
# \ _-'
# \ _-'
# \-'
# 0
#
# 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
vec(-tau2/2, -w, tau2),
vec(2.0*St, 0.0, -tau2*St),
vec(-tau2/2, w, tau2) # 3
]
# add heptagons
Ns = Vs
if this.heptPosAlt:
heptN = Heptagons.Kite2Hept(Vs[3], Vs[0], Vs[1], Vs[2])
if heptN == None: return
Mr = Rot(angle = GeomTypes.tTurn, axis = Vs[2])
v = Mr*heptN[0][4]
if this.triangleAlt:
vt = heptN[0][6]
xtraEdgeIndex = 15
else:
vt = heptN[0][5]
xtraEdgeIndex = 14
#print v
# One third of regular triangle.
RegularTrianglePartV = [
heptN[0][3],
heptN[0][4],
vec(v[0], v[1], v[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: 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]),
]
# 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 = ''
H = HalfTurn(Vs[3])
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)]
RegularTrianglePartN = RegularTrianglePartV[2]
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