def mobiusband(gmap=None):
from math import pi, cos, sin
from numpy import array
nbsq = 16
if gmap is None: gmap = GMap(2)
gmap, msquares = toposquares(nbsq, gmap)
for i in xrange(nbsq - 1):
gmap.sew_dart(msquares[i][5], msquares[i + 1][0])
gmap.sew_dart(msquares[nbsq - 1][4], msquares[0][0])
dalpha = 2 * pi / nbsq
radius1, radius2 = 10, 5
length = 1
alpha = 0
ralpha = pi / 8
for sqid in xrange(nbsq):
dart1, dart2 = msquares[sqid][0], msquares[sqid][1]
centralpos = array([0, radius1 * cos(alpha), radius2 * sin(alpha)])
#u,v = [1,0,0], [0,cos(alpha),sin(alpha)]
#deltapos = [length*cos(alpha), length*sin(alpha)]
position1 = centralpos + [
length * cos(ralpha), length * sin(ralpha) * cos(alpha),
length * sin(ralpha) * sin(alpha)
]
gmap.set_position(dart1, position1)
position2 = centralpos + [
length * cos(pi + ralpha), length * sin(pi + ralpha) * cos(alpha),
length * sin(pi + ralpha) * sin(alpha)
]
gmap.set_position(dart2, position2)
alpha += dalpha
ralpha += dalpha / 2
return gmap, sum(msquares, [])
def gmap_from_triangular_mesh(points, triangles, center=False):
gmap = GMap()
triangle_edges = np.sort(
np.concatenate(
[np.transpose([v, list(v[1:]) + [v[0]]]) for v in triangles]))
edges = array_unique(triangle_edges)
triangle_edges = (vq(triangle_edges, edges)[0]).reshape(
(len(triangles), 3))
triangle_edge_vertices = np.concatenate(
[np.transpose([v, list(v[1:]) + [v[0]]]) for v in triangles])
triangle_edge_orientation = (triangle_edge_vertices[:, 1] >
triangle_edge_vertices[:, 0]).reshape(
(len(triangles), 3))
triangle_darts = {}
for fid, t in enumerate(triangles):
gmap, tri = topopolygon(3, gmap)
triangle_darts[fid] = tri
for eid, e in enumerate(edges):
fids_to_sew, darts_to_sew = np.where(triangle_edges == eid)
orientations_to_sew = triangle_edge_orientation[(fids_to_sew,
darts_to_sew)]
if len(orientations_to_sew) > 1:
gmap.sew_dart(
2,
triangle_darts[fids_to_sew[0]][2 * darts_to_sew[0] +
(1 - orientations_to_sew[0])],
triangle_darts[fids_to_sew[1]][2 * darts_to_sew[1] +
(1 - orientations_to_sew[1])])
mesh_center = np.mean(points, axis=0) if center else np.zeros(3)
for fid, t in enumerate(triangles):
for i, p in enumerate(t):
gmap.set_position(triangle_darts[fid][2 * i],
points[p] - mesh_center)
return gmap
def crossshape():
gmap = GMap(3)
gmap, cube1 = cube(gmap=gmap)
gmap, cube2 = cube(gmap=gmap, center=[10, 0, 0])
gmap.sew_dart(cube1[8], cube2[8 * 3 + 1])
gmap, cube3 = cube(gmap=gmap, center=[0, 10, 0])
gmap.sew_dart(cube1[8 * 2], cube3[8 * 4 + 1])
gmap, cube4 = cube(gmap=gmap, center=[0, 0, 10])
gmap.sew_dart(cube1[0], cube4[8 * 5 + 1])
gmap, cube5 = cube(gmap=gmap, center=[-10, 0, 0])
gmap.sew_dart(cube1[8 * 3], cube5[8 + 1])
gmap, cube6 = cube(gmap=gmap, center=[0, -10, 0])
gmap.sew_dart(cube1[8 * 4], cube6[8 * 2 + 1])
gmap, cube7 = cube(gmap=gmap, center=[0, 0, -10])
gmap.sew_dart(cube1[8 * 5], cube7[1])
return gmap, sum([cube1, cube2, cube3, cube4, cube5, cube6, cube7], [])
