def __init__(self, pqr, init_dist):
self.active = [bool(x) for x in init_dist]
self.cox_mat = helpers.make_symmetry_matrix(pqr)
self.dfa = automata.get_automaton(self.cox_mat)
self.mirrors = self.get_mirrors(self.cox_mat)
self.init_v = helpers.get_init_point(self.mirrors, init_dist)
self.reflections = self.get_reflections(self.mirrors, init_dist)
self.fundamental_faces = []
def __init__(self, pqr, init_dist):
if helpers.get_geometry_type(pqr) != 0:
raise ValueError("The triple (p, q, r) must satisfy 1/p+1/q+1/r=1")
self.active = [bool(x) for x in init_dist]
self.cox_mat = helpers.make_symmetry_matrix(pqr)
self.dfa = get_automaton(self.cox_mat)
self.mirrors = self.get_mirrors(self.cox_mat)
self.init_v = helpers.get_init_point(self.mirrors, init_dist)
self.reflections = self.get_reflections(self.mirrors, init_dist)
self.fundamental_faces = []
def __init__(self, coxeter_matrix, mirrors, init_dist, extra_relations=()):
"""
parameters
----------
:coxeter_matrix: Coxeter matrix of the symmetry group of this polytope.
:mirrors: normal vectors of the mirrors.
:init_dist: distances between the initial vertex and the mirrors.
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"
"""
self.coxeter_matrix = coxeter_matrix
# reflection transformations about the mirrors
self.reflections = tuple(helpers.reflection_matrix(v) for v in mirrors)
# the initial vertex
self.init_v = helpers.get_init_point(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(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 = []
def __init__(self, coxeter_matrix, mirrors, init_dist, extra_relations):
"""
params:
`coxeter_matrix`: Coxeter matrix of the symmetry group.
`mirrors`: normal vectors of the mirrors.
`init_dist`: the distances between the initial point and the mirrors.
`extra_relations`: extra relations to be imposed on the generators.
"""
self.coxeter_matrix = coxeter_matrix
self.reflections = tuple(helpers.reflection_matrix(v) for v in mirrors)
self.init_v = helpers.get_init_point(mirrors, init_dist)
self.active = tuple(bool(x) for x in init_dist)
# generators of the symmetry group
self.symmetry_gens = tuple(range(len(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 += 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 = []