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flextegrity.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sun Mar 8 11:40:54 2020
@author: Kirby Urner
Oct 13, 2024: write new tests, rewrite test6, simplify constants
Oct 06, 2024: test16 for 7-frame animated GIF
Oct 05, 2024: test15 for 9-frame animated GIF
Sept-Oct,2024: keep adding new tests (scenarios) to make povs
Sept 21, 2024: added PD, RT, implemented faces as polygons
Sept 19, 2021: altered to work with new qray.py
wherein Qvector.xyz is a property
"""
import math
from math import sqrt as rt2
from qrays import Qvector, Vector
import sympy as sy
# from sympy import sqrt as rt2
PHI = (1 + rt2(5))/2
ORIGIN = Qvector((0,0,0,0))
A = Qvector((1,0,0,0))
B = Qvector((0,1,0,0))
C = Qvector((0,0,1,0))
D = Qvector((0,0,0,1))
# from Wikipedia (Quadray Coordinates)
E,F,G,H = B+C+D, A+C+D, A+B+D, A+B+C
I,J,K,L,M,N = A+B, A+C, A+D, B+C, B+D, C+D
O,P,Q,R,S,T = I+J, I+K, I+L, I+M, N+J, N+K
U,V,W,X,Y,Z = N+L, N+M, J+L, L+M, M+K, K+J
sfactor = 20/(5 * rt2(2) * PHI**2) # VE/icosa vol ratio
# OPPOSITE DIAGONALS
# ZY WX
# RV OS
# TU PQ
control = (Z - T).length()
midface = (Z + Y)
gold = 0.5 * PHI * midface/midface.length()
Zi = gold + J/J.length() * control/2
Yi = gold + M/M.length() * control/2
midface = (W + X)
gold = 0.5 * PHI * midface/midface.length()
Wi = gold + J/J.length() * control/2
Xi = gold + M/M.length() * control/2
midface = (R + V)
gold = 0.5 * PHI * midface/midface.length()
Ri = gold + I/I.length() * control/2
Vi = gold + N/N.length() * control/2
midface = (O + S)
gold = 0.5 * PHI * midface/midface.length()
Oi = gold + I/I.length() * control/2
Si = gold + N/N.length() * control/2
midface = (T + U)
gold = 0.5 * PHI * midface/midface.length()
Ti = gold + K/K.length() * control/2
Ui = gold + L/L.length() * control/2
midface = (P + Q)
gold = 0.5 * PHI * midface/midface.length()
Pi = gold + K/K.length() * control/2
Qi = gold + L/L.length() * control/2
class Polyhedron:
"""
Designed to be subclassed, not used directly
"""
def scale(self, scalefactor):
if hasattr(self, "volume"):
new_volume = self.volume * scalefactor ** 3
newverts = {}
for v in self.vertexes:
newverts[v] = self.vertexes[v] * scalefactor
newme = type(self)()
newme.volume = new_volume # new volume
newme.vertexes = newverts # substitutes new guts
newme.edges = newme._distill() # update edges to use new verts
return newme
__mul__ = __rmul__ = scale
def translate(self, vector):
newverts = {}
for v in self.vertexes:
newverts[v] = self.vertexes[v] + vector
newme = type(self)()
newme.vertexes = newverts # substitutes new tent stakes
if hasattr(self, "center"): # shift center before suppress!
newme.center = self.center + vector
if hasattr(self, "suppress"):
newme.suppress = self.suppress
if newme.suppress:
newme.faces = newme._suppress()
newme.edges = newme._distill() # update edges to use new verts
return newme
__add__ = __radd__ = translate
def _distill(self):
edges = []
unique = set()
for f in self.faces:
for pair in zip(f , f[1:] + (f[0],)):
unique.add( tuple(sorted(pair)) )
for edge in unique:
edges.append( Edge(self.vertexes[edge[0]],
self.vertexes[edge[1]]) )
return edges
class Edge:
"""
Edges are defined by two Vectors (above) and express as cylinder via draw().
"""
def __init__(self, v0, v1):
self.v0 = v0 # actual coordinates, not a letter label
self.v1 = v1
def __repr__(self):
return 'Edge from %s to %s' % (self.v0, self.v1)
#=== DRAW ROUTINES ===
def draw_vert(v, c, r, t, *, texture = False):
v = v.xyz
x,y,z = v.x, v.y, v.z
data = "< %s, %s, %s >" % (x,y,z), r, c
if not texture:
template = ("sphere { %s, %s texture "
"{ pigment { color %s } } no_shadow }")
else:
template = ("sphere { %s, %s texture "
"{ %s } no_shadow }")
print(template % data, file=t)
def draw_face(p, f, c, t, *, texture = False):
"""
POLYGON:
polygon
{
Number_Of_Points, <Point_1> <Point_2>... <Point_n>
[OBJECT_MODIFIER...]
}
Parameters
----------
f : tuple of tuples
vertexes around a face
f : tuple of strings
labels of verts around a face
c : string
color info
t : file object
Returns
-------
None.
"""
data = ""
num_points = len(f)
for v in f:
coords = p.vertexes[v].xyz
x,y,z = coords.x, coords.y, coords.z
data += "< %s, %s, %s > " % (x, y, z)
if not texture:
template = ("polygon { %s, %s texture "
"{ pigment { color %s } } no_shadow }")
print(template % (num_points, data, c), file=t)
else:
template = ("polygon { %s, %s texture "
"{ %s } no_shadow }")
print(template % (num_points, data, c), file=t)
def draw_edge(e, c, r, t, *, texture=False):
v = e.v0.xyz
v0 = "< %s, %s, %s >" % (v.x, v.y, v.z)
v = e.v1.xyz
v1 = "< %s, %s, %s >" % (v.x, v.y, v.z)
data = (v0, v1, r, c)
if not texture:
template = ("cylinder { %s, %s, %s texture "
"{pigment { color %s } } no_shadow }")
else:
template = ("cylinder { %s, %s, %s texture "
"{ %s } no_shadow }")
print(template % data, file=t)
def draw_poly(p, the_file, v=True, f=False, e=True, *, texture=False):
ec = p.edge_color
er = p.edge_radius
vc = p.vert_color
vr = p.vert_radius
fc = p.face_color
if v:
alt_color = "rgb <{}, {}, {}>".format(1, 0, 0) # red
alt_radius = 0.05
for label, v in p.vertexes.items():
if label == None: # replace None with exceptional v e.g. 'z'
draw_vert(v, alt_color, alt_radius, the_file, texture=texture)
else:
draw_vert(v, vc, vr, the_file, texture=texture)
if f:
for f in p.faces:
draw_face(p, f, fc, the_file, texture=texture)
if e:
for e in p.edges:
draw_edge(e, ec, er, the_file, texture=texture)
class Tetrahedron(Polyhedron):
"""
Tetrahedron
"""
def __init__(self):
# POV-Ray
self.edge_color = "rgb <{}, {}, {}>".format(1, 173/255, 0) # orange
self.edge_radius= 0.03
self.vert_color = "rgb <{}, {}, {}>".format(1, 173/255, 0) # orange
self.vert_radius= 0.03
self.face_color = self.edge_color # often not used
verts = dict(a = Qvector((1,0,0,0)), #A
b = Qvector((0,1,0,0)), #B
c = Qvector((0,0,1,0)), #C
d = Qvector((0,0,0,1))) #D
self.name = "Tetrahedron"
self.volume = 1 # per Concentric Hierarchy
self.center = ORIGIN
# 4 vertices
self.vertexes = verts
# 4 faces
self.faces = (('a','b','c'),('a','c','d'),
('a','d','b'),('b','d','c'))
self.edges = self._distill()
class InvTetrahedron(Polyhedron):
"""
Inverse Tetrahedron
"""
def __init__(self):
# POV-Ray
self.edge_color = "rgb <{}, {}, {}>".format(67/255, 70/255, 75/255) # black
self.edge_radius= 0.03
self.vert_color = self.edge_color
self.vert_radius= 0.03
self.face_color = "rgb <0, 0, 0>" # not used
self.face_color = self.edge_color # often not used
verts = dict(e = -Qvector((1,0,0,0)), #E
f = -Qvector((0,1,0,0)), #F
g = -Qvector((0,0,1,0)), #G
h = -Qvector((0,0,0,1))) #H
self.name = "InvTetrahedron"
self.volume = 1 # per Concentric Hierarchy
self.center = ORIGIN
# 4 vertices
self.vertexes = verts
# 4 faces
self.faces = (('e','f','g'),('e','g','h'),
('e','h','f'),('f','h','g'))
self.edges = self._distill()
class Cube (Polyhedron):
"""
Cube
"""
def __init__(self):
# POV-Ray
self.edge_color = "rgb <0, 1, 0>"
self.edge_radius= 0.03
self.vert_color = "rgb <0, 1, 0>"
self.vert_radius= 0.03
self.face_color = self.edge_color
verts = {}
for vert_label in "abcdefgh":
# keep the uppercase A-Z universe (namespace) unobstructed
verts[vert_label] = eval(vert_label.upper())
self.name = "Cube"
self.volume = 3 # per Concentric Hierarchy
self.center = ORIGIN
# 8 vertices
self.vertexes = verts
# 6 faces
self.faces = (('a','f','c','h'),('h','c','e','b'),
('b','e','d','g'),('g','d','f','a'),
('c','f','d','e'),('a','h','b','g'))
self.edges = self._distill()
class Cuboid (Polyhedron):
"""
Cuboid with height, width, depth = sqrt(1), sqrt(2), sqrt(4)
"""
def __init__(self):
# POV-Ray
self.edge_color = "rgb <255/255, 20/255, 147/255>"
self.edge_radius= 0.03
self.vert_color = "rgb <255/255, 20/255, 147/255>"
self.vert_radius= 0.03
self.face_color = "rgb <255/255, 20/255, 147/255>"
verts = {}
verts['A'] = Vector(( 1, 0.5, math.sqrt(2)/2))
verts['B'] = Vector(( 1, -0.5, math.sqrt(2)/2))
verts['C'] = Vector(( 1, -0.5, -math.sqrt(2)/2))
verts['D'] = Vector(( 1, 0.5, -math.sqrt(2)/2))
verts['E'] = Vector((-1, 0.5, math.sqrt(2)/2))
verts['F'] = Vector((-1, -0.5, math.sqrt(2)/2))
verts['G'] = Vector((-1, -0.5, -math.sqrt(2)/2))
verts['H'] = Vector((-1, 0.5, -math.sqrt(2)/2))
self.name = "Cuboid"
self.volume = 8 # per Concentric Hierarchy
self.center = ORIGIN
# 8 vertices
self.vertexes = verts
# 6 faces
self.faces = (('A','B','C','D'),('E','F','G','H'),
('A','E','F','B'),('D','H','G','C'),
('A','E','H','D'),('B','F','G','C'))
self.edges = self._distill()
class Octahedron (Polyhedron):
"""
Octahedron
"""
def __init__(self):
# POV-Ray
self.edge_color = "rgb <1, 0, 0>"
self.edge_radius= 0.03
self.vert_color = "rgb <1, 0, 0>"
self.vert_radius= 0.03
self.face_color = "rgb <1, 0, 0>"
verts = {}
for vert_label in "ijklmn":
# keep the uppercase A-Z universe unobstructed
verts[vert_label] = eval(vert_label.upper())
self.name = "Octahedron"
self.volume = 4 # per Concentric Hierarchy (84S + 20S)
self.center = ORIGIN
# 6 vertices
self.vertexes = verts
# 8 faces
self.faces = (('j','k','i'),('j','i','l'),('j','l','n'),('j','n','k'),
('m','k','i'),('m','i','l'),('m','l','n'),('m','n','k'))
self.edges = self._distill()
class RD (Polyhedron):
"""
Rhombic Dodecahedron
"""
def __init__(self):
self.edge_color = "rgb <0, 0, 1>"
self.edge_radius= 0.03
self.vert_color = "rgb <0, 0, 1>"
self.vert_radius= 0.03
self.face_color = self.edge_color
verts = {}
for vert_label in "abcdefghijklmn":
# keep the uppercase A-Z universe unobstructed
verts[vert_label] = eval(vert_label.upper())
self.name = "RD"
self.volume = 6 # per Concentric Hierarchy
self.center = ORIGIN
# 14 vertices
self.vertexes = verts
# 12 faces
# I,J,K,L,M,N = A+B, A+C, A+D, B+C, B+D, C+D
self.faces = (('j','f','k','a'),('j','f','n','c'),('j','c','l','h'),('j','h','i','a'),
('m','d','k','g'),('m','d','n','e'),('m','e','l','b'),('m','b','i','g'),
('k','d','n','f'),('n','c','l','e'),('l','h','i','b'),('i','a','k','g'))
self.edges = self._distill()
class Icosahedron (Polyhedron):
def __init__(self):
# 20 vertices
self.edge_color = "rgb <0, 1, 1>"
self.edge_radius= 0.03
self.vert_color = "rgb <0, 1, 1>"
self.vert_radius= 0.03
self.face_color = self.edge_color
self.vertexes = dict(o = Oi,
p = Pi,
q = Qi,
r = Ri,
s = Si,
t = Ti,
u = Ui,
v = Vi,
w = Wi,
x = Xi,
y = Yi,
z = Zi)
self.name = "Icosahedron"
self.volume = 5 * rt2(2) * PHI**2
self.center = ORIGIN
# 20 faces
# OPPOSITE DIAGONALS of cubocta
# ZY WX
# RV OS
# TU PQ
self.faces = (('o','w','s'),('o','z','s'),
('z','p','y'),('z','t','y'),
('t','v','u'),('t','s','u'),
('w','q','x'),('w','u','x'),
('p','o','q'),('p','r','q'),
('r','y','v'),('r','x','v'),
('z','s','t'),('t','y','v'),
('y','p','r'),('r','q','x'),
('x','u','v'),('u','s','w'),
('w','q','o'),('o','z','p'))
self.edges = self._distill()
class PD (Polyhedron):
# Pentagonal Dodecahedron
def __init__(self):
# Sienna Brown rgb(160,82,45)
self.edge_color = "rgb <%s, %s, %s>" % (160/255, 82/255, 45/255)
self.edge_radius= 0.03
self.vert_color = self.edge_color
self.vert_radius= 0.03
self.face_color = self.edge_color
# 20 vertexes
# V + F = E + 2; 20 + 12 = 30 + 2
L = ((Wi + Qi + Oi)/3 - (Pi + Oi + Qi)/3).length()
sk = (1/L) * (1/PHI)
self.vertexes = dict(osw = sk * (Oi + Wi + Si)/3,
osz = sk * (Oi + Zi + Si)/3,
pyz = sk * (Zi + Pi + Yi)/3,
tyz = sk * (Zi + Ti + Yi)/3,
tuv = sk * (Ti + Vi + Ui)/3,
stu = sk * (Ti + Si + Ui)/3,
qwx = sk * (Wi + Qi + Xi)/3,
uwx = sk * (Wi + Ui + Xi)/3,
opq = sk * (Pi + Oi + Qi)/3,
pqr = sk * (Pi + Ri + Qi)/3,
rvy = sk * (Ri + Yi + Vi)/3,
rvx = sk * (Ri + Xi + Vi)/3,
stz = sk * (Zi + Si + Ti)/3,
tvy = sk * (Ti + Yi + Vi)/3,
pry = sk * (Yi + Pi + Ri)/3,
qrx = sk * (Ri + Qi + Xi)/3,
uvx = sk * (Xi + Ui + Vi)/3,
suw = sk * (Ui + Si + Wi)/3,
oqw = sk * (Wi + Qi + Oi)/3,
opz = sk * (Oi + Zi + Pi)/3)
self.name = "PD"
self.volume = 3 * rt2(2) * (PHI**2 + 1)
self.center = ORIGIN
# 12 faces
self.faces = (('oqw', 'opq', 'opz', 'osz', 'osw'), # o
('opq', 'pqr', 'pry', 'pyz', 'opz'), # p
('opq', 'pqr', 'qrx', 'qwx', 'oqw'), # q
('qrx', 'pqr', 'pry', 'rvy', 'rvx'), # r
('stu', 'suw', 'osw', 'osz', 'stz'), # s
('stu', 'stz', 'tyz', 'tvy', 'tuv'), # t
('suw', 'uwx', 'uvx', 'tuv', 'stu'), # u
('tvy', 'tuv', 'uvx', 'rvx', 'rvy'), # v
('osw', 'oqw', 'qwx', 'uwx', 'suw'), # w
('uwx', 'qwx', 'qrx', 'rvx', 'uvx'), # x
('pyz', 'pry', 'rvy', 'tvy', 'tyz'), # y
('osz', 'opz', 'pyz', 'tyz', 'stz'), # z
)
self.edges = self._distill()
class RT (Polyhedron):
# Rhombic Triacontahedron
def __init__(self):
# Purple Heart rgb(105,53,156)
self.edge_color = "rgb <%s, %s, %s>" % (105/255, 53/255, 156/255)
self.edge_radius= 0.03
self.vert_color = self.edge_color
self.vert_radius= 0.03
self.face_color = self.edge_color
# 32 vertexes
# V + F = E + 2; 32 + 30 = 60 + 2
L = ((Wi + Qi + Oi)/3 - (Pi + Oi + Qi)/3).length()
sk = (1/L) * (1/PHI)
self.vertexes = dict(osw = sk * (Oi + Wi + Si)/3,
osz = sk * (Oi + Zi + Si)/3,
pyz = sk * (Zi + Pi + Yi)/3,
tyz = sk * (Zi + Ti + Yi)/3,
tuv = sk * (Ti + Vi + Ui)/3,
stu = sk * (Ti + Si + Ui)/3,
qwx = sk * (Wi + Qi + Xi)/3,
uwx = sk * (Wi + Ui + Xi)/3,
opq = sk * (Pi + Oi + Qi)/3,
pqr = sk * (Pi + Ri + Qi)/3,
rvy = sk * (Ri + Yi + Vi)/3,
rvx = sk * (Ri + Xi + Vi)/3,
stz = sk * (Zi + Si + Ti)/3,
tvy = sk * (Ti + Yi + Vi)/3,
pry = sk * (Yi + Pi + Ri)/3,
qrx = sk * (Ri + Qi + Xi)/3,
uvx = sk * (Xi + Ui + Vi)/3,
suw = sk * (Ui + Si + Wi)/3,
oqw = sk * (Wi + Qi + Oi)/3,
opz = sk * (Oi + Zi + Pi)/3)
self.vertexes.update(dict(
o = Oi,
p = Pi,
q = Qi,
r = Ri,
s = Si,
t = Ti,
u = Ui,
v = Vi,
w = Wi,
x = Xi,
y = Yi,
z = Zi))
self.name = "RT"
self.volume = 20 * rt2(9./8)
self.center = ORIGIN
# 30 faces
self.faces = (('s', 'stz', 'z', 'osz'),
('s', 'osz', 'o', 'osw'),
('s', 'suw', 'w', 'osw'),
('s', 'suw', 'u', 'stu'),
('s', 'stu', 't', 'stz'),
('r', 'qrx', 'q', 'pqr'),
('r', 'pry', 'p', 'pqr'),
('r', 'pry', 'y', 'rvy'),
('r', 'rvx', 'v', 'rvy'),
('r', 'qrx', 'x', 'rvx'),
('v', 'tuv', 't', 'tvy'),
('t', 'tyz', 'y', 'tvy'),
('y', 'tyz', 'z', 'pyz'),
('z', 'pyz', 'p', 'opz'),
('p', 'opz', 'o', 'opq'),
('o', 'oqw', 'q', 'opq'),
('q', 'oqw', 'w', 'qwx'),
('w', 'uwx', 'x', 'qwx'),
('x', 'uwx', 'u', 'uvx'),
('u', 'tuv', 'v', 'uvx'),
('v', 'tvy', 'y', 'rvy'),
('y', 'pry', 'p', 'pyz'),
('p', 'pqr', 'q', 'opq'),
('q', 'qwx', 'x', 'qrx'),
('x', 'uvx', 'v', 'rvx'),
('t', 'stz', 'z', 'tyz'),
('z', 'osz', 'o', 'opz'),
('o', 'osw', 'w', 'oqw'),
('w', 'suw', 'u', 'uwx'),
('u', 'stu', 't', 'tuv'),
)
self.edges = self._distill()
class Cuboctahedron (Polyhedron):
def __init__(self):
# 8 vertices
self.edge_color = "rgb <1, 1, 0>"
self.edge_radius= 0.03
self.vert_color = "rgb <1, 1, 0>"
self.vert_radius= 0.03
self.face_color = self.edge_color
self.vertexes = dict(o = O,
p = P,
q = Q,
r = R,
s = S,
t = T,
u = U,
v = V,
w = W,
x = X,
y = Y,
z = Z)
self.name = "Cuboctahedron"
self.volume = 20
self.center = ORIGIN
# 6 faces
self.faces = (('o','w','s','z'),('z','p','y','t'),
('t','v','u','s'),('w','q','x','u'),
('o','p','r','q'),('r','y','v','x'),
('z','s','t'),('t','y','v'),
('y','p','r'),('r','q','x'),
('x','u','v'),('u','s','w'),
('w','q','o'),('o','z','p'))
self.edges = self._distill()
class Struts(Polyhedron):
def __init__(self, c=None, ico=None, suppress=False):
self.edge_color = "rgb <1, 0, 0>"
self.edge_radius= 0.02
self.vert_color = "rgb <1, 0, 0>"
self.vert_radius= 0.02
self.face_color = "rgb <0, 0, 0>"
self.suppress = suppress
if not c and not ico:
c = Cube()
ico = Icosahedron()
self.vertexes = dict(
# cube mid-edges
af = (c.vertexes['a'] + c.vertexes['f'])/2,
ag = (c.vertexes['a'] + c.vertexes['g'])/2,
ah = (c.vertexes['a'] + c.vertexes['h'])/2,
be = (c.vertexes['b'] + c.vertexes['e'])/2,
bh = (c.vertexes['b'] + c.vertexes['h'])/2,
bg = (c.vertexes['b'] + c.vertexes['g'])/2,
ce = (c.vertexes['c'] + c.vertexes['e'])/2,
cf = (c.vertexes['c'] + c.vertexes['f'])/2,
ch = (c.vertexes['c'] + c.vertexes['h'])/2,
de = (c.vertexes['d'] + c.vertexes['e'])/2,
df = (c.vertexes['d'] + c.vertexes['f'])/2,
dg = (c.vertexes['d'] + c.vertexes['g'])/2,
# icosa mid-edges
# OPPOSITE DIAGONALS of cubocta
# ZY WX
# RV OS
# TU PQ
os = (ico.vertexes['o'] + ico.vertexes['s'])/2,
pq = (ico.vertexes['p'] + ico.vertexes['q'])/2,
rv = (ico.vertexes['r'] + ico.vertexes['v'])/2,
tu = (ico.vertexes['t'] + ico.vertexes['u'])/2,
wx = (ico.vertexes['w'] + ico.vertexes['x'])/2,
yz = (ico.vertexes['y'] + ico.vertexes['z'])/2
)
self.name = 'struts'
self.center = ico.center
self.faces = (('os', 'af'), ('os', 'ch'),
('rv', 'be'), ('rv', 'dg'),
('tu', 'cf'), ('tu', 'de'),
('pq', 'ah'), ('pq', 'bg'),
('yz', 'ag'), ('yz', 'df'),
('wx', 'bh'), ('wx', 'ce'))
if self.suppress:
self.faces = self._suppress()
self.edges = self._distill()
def _suppress(self):
"""
A global IVM of integral Qray positions is expected for
the suppress feature to work. This could be an n-frequency
cuboctahedron or perhaps a layered tetrahedron of half-
octahedron of balls.
"""
global IVM
keep = []
# print("Suppressing disconnected edges")
for f in self.faces:
# print(f, self.center)
neighbor = self.center + eval(f[1][0].upper()) + eval(f[1][1].upper())
# print("Neighbor=", neighbor)
for layer in IVM:
if neighbor in IVM[layer]:
# print("Bing!")
keep.append(f)
break
else:
pass
# print("Not found")
return keep
from itertools import permutations
g = permutations((2,1,1,0))
unique = {p for p in g} # set comprehension
def twelve_around_one(p):
twelve = [ ]
for v in unique:
trans_vector = Qvector(v)
twelve.append(p + trans_vector)
return twelve
pov_header = \
"""
// Persistence of Vision Ray Tracer Scene Description File
// File: xyz.pov
// Vers: 3.6
// Desc: test file
// Date: Sat Sep 7 09:49:33 2019
// Auth: me
// ==== Standard POV-Ray Includes ====
#include "colors.inc" // Standard Color definitions
// include "textures.inc" // Standard Texture definitions
// include "functions.inc" // internal functions usable in user defined functions
// ==== Additional Includes ====
// Don't have all of the following included at once, it'll cost memory and time
// to parse!
// --- general include files ---
// include "chars.inc" // A complete library of character objects, by Ken Maeno
#include "skies.inc" // Ready defined sky spheres
// include "stars.inc" // Some star fields
// include "strings.inc" // macros for generating and manipulating text strings
// --- textures ---
// include "finish.inc" // Some basic finishes
// include "glass.inc" // Glass textures/interiors
// include "golds.inc" // Gold textures
#include "metals.inc" // Metallic pigments, finishes, and textures
#include "stones.inc" // Binding include-file for STONES1 and STONES2
// include "stones1.inc" // Great stone-textures created by Mike Miller
// include "stones2.inc" // More, done by Dan Farmer and Paul Novak
// include "woodmaps.inc" // Basic wooden colormaps
// include "woods.inc" // Great wooden textures created by Dan Farmer and Paul Novak
global_settings {assumed_gamma 1.0}
global_settings {ambient_light rgb<1, 1, 1> }
// perspective (default) camera
camera {
location <2.5, 0.1, 0.2>
rotate <35, 35, 10.0>
look_at <0.0, 0.0, 0.0>
right x*image_width/image_height
}
// create a regular point light source
light_source {
0*x // light's position (translated below)
color rgb <1,1,1> // light's color
translate <-20, 15, 10>
}
// create a regular point light source
light_source {
0*x // light's position (translated below)
color rgb <1,1,1> // light's color
translate <20, -15, -10>
}
sky_sphere { S_Cloud2 scale 2 translate -1}
background { color rgb <1.0, 1.0, 1.0> }
"""
def test1():
"""
minimalist, uses default Icosahedron and PD
no fidling with attributes, no rescaling.
"""
f = open("testing123.pov", "w")
f.write(pov_header)
ico = Icosahedron()
pd = PD()
draw_poly(ico, f)
draw_poly(pd, f)
f.close()
def test2():
"""
same as test1 but adding a Rhombic Triacontahedron
ico and pd are duals of each other, sized by default
to criss-cross at mid-edges thereby forming verts
of the correspondingly sized RT
"""
f = open("testing123.pov", "w")
f.write(pov_header)
ico = Icosahedron()
pd = PD()
rt = RT()
draw_poly(ico, f)
draw_poly(pd, f)
draw_poly(rt, f)
f.close()
def test3():
"""
Remember you can edit these by turning shapes on and off.
You have control over the filename if you wish to stop
overwriting the same testing123 over and over
"""
f = open("testing123.pov", "w")
f.write(pov_header)
# ico = Icosahedron()
rt = RT()
draw_poly(rt, f)
# draw_poly(ico, f)
f.close()
def test4():
"""
Taking default Icosahedron to have R=1 edges (vs D=1),
such scaling by sfactor gives IcosaWithin (IW), which,
when further scaled up by PHI, becomes faces flush
with 2F SuperCube. 4 * Cube() because everything's
doubled when R=1 vs 0.5.
"""
f = open("testing123.pov", "w")
f.write(pov_header)
octa = 2 * Octahedron()
ico = Icosahedron() * sfactor
rt = RT() * sfactor * PHI
cu = 4 * Cube()
draw_poly(ico, f)
draw_poly(octa, f)
draw_poly(cu, f)
draw_poly(rt, f)
f.close()
def test5():
"""
Same as above, but once RT is faces flush with
containing cube, enlarge is very slightly to
force its diamond faces to protrude and show
up clearly against the 2F cube faces background
"""
f = open("marble_polys.pov", "w")
f.write(pov_header)
rt = RT() * sfactor * PHI * 1.01 # push out faces a bit more
rt.face_color = "T_Stone18"
cu = 4 * Cube()
cu.face_color = "T_Stone17"
draw_poly(rt, f, v=False, e=False, f=True, texture=True)
draw_poly(cu, f, v=False, e=False, f=True, texture=True)
f.close()
def test6():
"""
Back to D=1. Shrink initial D edge Icosa by half then
scale up by sfactor, known to be edges of the icosa
inscribing in the corresponding Octa. Include the
2F Cube with faces-flush RT in addition to IW faces
flush with Octa.
"""
out = open("iw_rt_123.pov", "w")
out.write(pov_header)
# Icosa with edges sfactor = S/E
icosaWithin = Icosahedron() * 0.5 * sfactor # D=1 (volume 60S + 20s3)
octa = Octahedron() # corresponding octa edges D
rt = RT() * 0.5 * sfactor * PHI # blow up corresponding RT by PHI
cu_2F = Cube() * 2 # 2F Cube
draw_poly(icosaWithin, out)
draw_poly(octa, out)
draw_poly(cu_2F, out)
draw_poly(rt, out)
out.close()
def test7():
out = open("ico_pd.pov", "w")
out.write(pov_header)
#ico = Icosahedron()*2
#pd = PD()*2
rt = RT()*2
#draw_poly(ico, out)
#draw_poly(pd, out)
draw_poly(rt, out)
out.close()
def test8():
out = open("ball_rt.pov", "w")
out.write(pov_header)
draw_vert(ORIGIN, "T_Stone18", 0.5, out, texture=True)
rt = RT() * (1/PHI) # SuperRT scaled down to wrap uniradius ball
rt.edge_radius = 0.02
rt.vert_radius = 0.04
rt.vert_color = 'T_Copper_1A'
rt.edge_color = 'T_Chrome_1A'
draw_poly(rt, out, v=True, e=True, f=False, texture=True)
out.close()
def test9():
out = open("ball_rt_rd.pov", "w")
out.write(pov_header)
draw_vert(ORIGIN, "T_Stone18", 0.5, out, texture=True)
rt = RT() * (1/PHI) # SuperRT scaled down to wrap uniradius ball
rt.edge_radius = 0.02
rt.vert_radius = 0.04
rt.vert_color = 'T_Copper_1A'
rt.edge_color = 'T_Chrome_1A'
rt2 = RT() * (1/PHI) * 0.9994 * (3/2)**(1/3) # 7.5 RT_K
rt2.edge_radius = 0.02
rd = RD()
rd.edge_radius = 0.02
rd.vert_radius = 0.04
rd.vert_color = 'T_Copper_1A'
rd.edge_color = 'T_Silver_1A'
draw_poly(rd, out, v=True, e=True, f=False, texture=True)
draw_poly(rt, out, v=True, e=True, f=False, texture=True)
draw_poly(rt2, out, v=False, e=True, f=False)
out.close()
def test10():
out = open("ball_in_rt_t.pov", "w")
out.write(pov_header)
draw_vert(ORIGIN, "rgb <1, 0, 0>", 0.5, out)
rt = RT() * (1/(3*rt2(2)))**(1/3) # RT_T
rt.face_color = "T_Stone17"
draw_poly(rt, out, v=False, e=False, f=True, texture=True)
out.close()
def test11():
out = open("rt_spokes.pov", "w")
out.write(pov_header)
rt_t = RT() * (1/(3*rt2(2)))**(1/3) # RT_T
for face in rt_t.faces:
spoke = ORIGIN
for i in range(4):
spoke += rt_t.vertexes[face[i]]
spoke = spoke * 0.25
edge = Edge(ORIGIN, spoke)
draw_edge(edge, "rgb <0, 0, 1>", 0.02, out)
rt_t.edge_radius = 0.01
draw_poly(rt_t, out, v=False, e=True, f=False)
rt_e = RT() * (1/PHI) # RT_E
for face in rt_e.faces:
spoke = ORIGIN
for i in range(4):
spoke += rt_e.vertexes[face[i]]
spoke = spoke * 0.25
edge = Edge(ORIGIN, spoke)
draw_edge(edge, "rgb <1, 0, 0>", 0.01, out)
rt_t.face_color = "T_Stone17"
draw_poly(rt_t, out, v=False, e=False, f=True, texture=True)
out.close()
def test12():
out = open("stella_octangula.pov", "w")