def draw(coxeter_diagram,
trunc_type,
description="polychora",
extra_relations=(),
**kwargs):
coxeter_matrix = helpers.make_symmetry_matrix(
[x.numerator for x in coxeter_diagram])
mirrors = helpers.get_mirrors(coxeter_diagram)
P = Polychora(coxeter_matrix, mirrors, trunc_type, extra_relations)
P.build_geometry()
write_to_pov(P, **kwargs)
print("rendering {} with {} vertices, {} edges, {} faces".format(
description, P.num_vertices, P.num_edges, P.num_faces))
process = subprocess.Popen(POV_COMMAND.format(description),
shell=True,
stderr=subprocess.PIPE,
stdin=subprocess.PIPE,
stdout=subprocess.PIPE)
_, err = process.communicate()
if process.returncode:
print(type(err), err)
raise IOError("POVRay error: " + err.decode("ascii"))
def anim(coxeter_diagram,
trunc_type,
description="polyhedra",
snub=False,
extra_relations=()):
"""Call POV-Ray to render the frames and FFmpeg to generate the movie.
"""
coxeter_matrix = helpers.fill_matrix(
[x.numerator for x in coxeter_diagram])
mirrors = helpers.get_mirrors(coxeter_diagram)
if snub:
P = Snub(coxeter_matrix, mirrors, trunc_type)
else:
P = Polyhedra(coxeter_matrix, mirrors, trunc_type, extra_relations)
P.build_geometry()
write_to_pov(P)
process = subprocess.Popen(POV_COMMAND.format(description),
shell=True,
stderr=subprocess.PIPE,
stdin=subprocess.PIPE,
stdout=subprocess.PIPE)
_, err = process.communicate()
if process.returncode:
print(type(err), err)
raise IOError("POVRay error: " + err.decode("ascii"))
subprocess.call(FFMPEG_COMMAND.format(description, description),
shell=True)
def main():
coxeter_diagram = (5, 2, 2, 3, 2, 3)
coxeter_matrix = helpers.fill_matrix(coxeter_diagram)
mirrors = helpers.get_mirrors(coxeter_diagram)
P = Polychora(coxeter_matrix, mirrors, (1, 0, 0, 0))
P.build_geometry()
write_to_pov(P)
subprocess.call(POV_COMMAND, shell=True)
def render_star_polyhedra(coxeter_diagram,
trunc_type,
extra_relations=(),
render_file="star-polyhedra.pov",
output=None):
coxeter_matrix = helpers.fill_matrix([x.numerator for x in coxeter_diagram])
mirrors = helpers.get_mirrors(coxeter_diagram)
P = models.Polyhedra(coxeter_matrix, mirrors, trunc_type, extra_relations)
_render_model(P, render_file, output)
def __init__(self):
coxeter_diagram = (3, 2, 2, 3, 3, 2)
coxeter_matrix = helpers.fill_matrix(coxeter_diagram)
mirrors = helpers.get_mirrors(coxeter_diagram)
super().__init__(coxeter_matrix, mirrors, (1, 1, 1, 1), extra_relations=())
self.symmetry_gens = tuple(range(6))
self.symmetry_rels = ((0,) * 3, (2,) * 3, (4,) * 3,
(0, 2) * 2, (0, 4) * 2, (3, 4) * 2,
(0, 1), (2, 3), (4, 5))
self.rotations = ((0,), (2,), (4,), (0, 2), (0, 4), (3, 4))
def render_polychora(coxeter_diagram,
trunc_type,
render_file,
output=None):
"""
The main entrance for rendering 4d polychora.
"""
coxeter_matrix = helpers.fill_matrix(coxeter_diagram)
mirrors = helpers.get_mirrors(coxeter_diagram)
P = models.Polychora(coxeter_matrix, mirrors, trunc_type)
_render_model(P, render_file, output)
def render_polyhedra(coxeter_diagram,
trunc_type,
render_file="polyhedra.pov",
output=None,
snub=False):
"""
The main entrance for rendering 3d polyhedra.
"""
coxeter_matrix = helpers.fill_matrix(coxeter_diagram)
mirrors = helpers.get_mirrors(coxeter_diagram)
if snub:
P = models.Snub(coxeter_matrix, mirrors, trunc_type)
else:
P = models.Polyhedra(coxeter_matrix, mirrors, trunc_type)
_render_model(P, render_file, output)
def anim(coxeter_diagram,
trunc_type,
description="polychora-rotation4d",
glass_tex="NBglass",
face_index=0,
vertex_color="SkyBlue",
edge_color="Orange",
extra_relations=()):
"""Call POV-Ray to render the frames and FFmpeg to generate the movie.
"""
coxeter_matrix = helpers.fill_matrix([x.numerator for x in coxeter_diagram])
mirrors = helpers.get_mirrors(coxeter_diagram)
P = Polychora(coxeter_matrix, mirrors, trunc_type, extra_relations)
P.build_geometry()
write_to_pov(P, glass_tex, face_index, vertex_color, edge_color)
subprocess.call(POV_COMMAND.format(description), shell=True)
subprocess.call(FFMPEG_COMMAND.format(description, description), shell=True)
def __init__(self, coxeter_diagram, init_dist, extra_relations=()):
"""
parameters
----------
:coxeter_diagram: Coxeter diagram for this polytope.
:init_dist: distances between the initial vertex and the mirrors.
:extra_relations: a presentation of a star polytope can be obtained by
imposing more relations on the generators. For example "(ρ0ρ1ρ2ρ1)^n = 1"
for some integer n, where n is the number of sides of a hole.
See Coxeter's article
"Regular skew polyhedra in three and four dimensions,
and their topological analogues"
"""
# Coxeter matrix of the symmetry group
self.coxeter_matrix = helpers.get_coxeter_matrix(coxeter_diagram)
self.mirrors = helpers.get_mirrors(coxeter_diagram)
# reflection transformations about the mirrors
self.reflections = tuple(helpers.reflection_matrix(v) for v in self.mirrors)
# the initial vertex
self.init_v = helpers.get_init_point(self.mirrors, init_dist)
# a mirror is active if and only if the initial vertex is off it
self.active = tuple(bool(x) for x in init_dist)
# generators of the symmetry group
self.symmetry_gens = tuple(range(len(self.coxeter_matrix)))
# relations between the generators
self.symmetry_rels = tuple((i, j) * self.coxeter_matrix[i][j]
for i, j in combinations(self.symmetry_gens, 2))
self.symmetry_rels += tuple(extra_relations)
# to be calculated later
self.vtable = None
self.num_vertices = None
self.vertex_coords = []
self.num_edges = None
self.edge_indices = []
self.edge_coords = []
self.num_faces = None
self.face_indices = []
self.face_coords = []
def __init__(self, upper_triangle, init_dist):
# the Coxeter matrix
self.coxeter_matrix = helpers.get_coxeter_matrix(upper_triangle)
# the reflecting mirrors
self._mirrors = helpers.get_mirrors(upper_triangle)
# reflection transformations about the mirrors
self._reflections = tuple(
helpers.reflection_matrix(v) for v in self._mirrors)
# coordinates of the initial vertex
self.init_v = helpers.get_init_point(self._mirrors, init_dist)
# a bool list holds if a mirror is active or not.
self.active = tuple(bool(x) for x in init_dist)
dim = len(self.coxeter_matrix)
# generators of the Coxeter group
self.symmetry_gens = tuple(range(dim))
# relations between the generators
self.symmetry_rels = tuple(
(i, j) * self.coxeter_matrix[i][j]
for i, j in combinations(self.symmetry_gens, 2))
# to be calculated later
self._vtable = None
self.num_vertices = None
self.vertex_coords = []
self.num_edges = None
self.edge_indices = []
self.edge_coords = []
self.num_faces = None
self.face_indices = []
self.face_coords = []
