def star_tesselation(self):
t = getattr(self,'_star_tesselation',None)
if t is None:
co_nt = NTracer(self.dimension)
lines = []
planes = [Plane(co_nt,co_nt.Vector(islice(part.position,co_nt.dimension))) for part in self.parts]
las = self.line_apothem_square()
for pgroup in combinations(planes,co_nt.dimension-1):
try:
line = plane_line_intersection(co_nt,pgroup)
except ValueError:
pass
else:
if line:
for lineb in lines:
if almost_equal(line.p0,lineb.p0) and almost_equal(line.v,lineb.v):
lineb.planes |= line.planes
break
else:
outer_dist = line.dist_square(co_nt.Vector()) - las
if outer_dist < 0.1:
line.outer = outer_dist > -0.1
lines.append(line)
pmap = {}
for line in lines:
pmap[line] = {}
graph = FuzzyGraph()
maxr = self.circumradius_square() + 0.1
for l1,l2 in combinations(lines,2):
inter = line_intersection(co_nt,l1,l2)
if inter and inter[0].square() < maxr:
n = graph.add(inter[0],l1.planes | l2.planes,l1.outer or l2.outer)
pmap[l1][n] = inter[1]
pmap[l2][n] = inter[2]
for line,poss in list(pmap.items()):
if len(poss) == 0: continue
if len(poss) == 1:
graph.remove(poss[0])
continue
poss = sorted(list(poss.items()),key=(lambda x: x[1]))
if line.outer:
for i in range(len(poss)-1):
join(poss[i][0],poss[i+1][0])
elif len(poss) == 2:
join(poss[0][0],poss[1][0])
elif len(poss) > 3:
for i in range(2,len(poss)-2):
graph.remove(poss[i][0])
join(poss[0][0],poss[1][0])
join(poss[-1][0],poss[-2][0])
t = []
self._star_tesselation = t
for n in islice(graph.nodes,0,len(graph.nodes)-co_nt.dimension):
for cycle in n.find_cycles(co_nt.dimension):
t.append([nt.Vector(tuple(x.pos) + (0,) * (nt.dimension-co_nt.dimension)) for x in cycle] + [nt.Vector()])
n.detach()
return t
def compose(part,order,schlafli):
if schlafli.numerator * (math.pi - part.dihedral_s) >= math.pi * 2 * schlafli.denominator:
exit("Component #{0} ({1}) is invalid because the angles of the parts add up to 360\u00b0 or\nmore and thus can't be folded inward".format(order,schlafli))
higher = PolyTope(
order+1,
schlafli,
higher_dihedral_supplement(schlafli,part.dihedral_s),
part.apothem)
potentials = higher.add_face(Instance(part,nt.Vector.axis(order,higher.apothem)))
while potentials:
potentials = higher.propogate_faces(potentials)
return higher
jitter = nt.Vector((0,0,0) + (0.0001,) * (nt.dimension-3))
def process_movement():
global x_move, y_move, w_move
if x_move or y_move or w_move:
h = math.sqrt(x_move*x_move + y_move*y_move + w_move*w_move)
a2 = camera.axes[0]*(x_move/h) + camera.axes[1]*(-y_move/h)
if w_move: a2 += camera.axes[3] * (w_move / h)
camera.transform(nt.Matrix.rotation(
camera.axes[2],
a2,
h * ROT_SENSITIVITY))
camera.normalize()
camera.origin = camera.axes[2] * cam_distance + jitter
scene.set_camera(camera)
