def render_vertices_3d(self, **kwds):
"""
Return the 3d rendering of the vertices.
EXAMPLES::
sage: p = polytopes.cross_polytope(3)
sage: proj = p.projection()
sage: verts = proj.render_vertices_3d()
sage: verts.bounding_box()
((-1.0, -1.0, -1.0), (1.0, 1.0, 1.0))
"""
return point3d(self.coordinates_of(self.points), **kwds)
def render_vertices_3d(self, **kwds):
"""
Return the 3d rendering of the vertices.
EXAMPLES::
sage: p = polytopes.cross_polytope(3)
sage: proj = p.projection()
sage: verts = proj.render_vertices_3d()
sage: verts.bounding_box()
((-1.0, -1.0, -1.0), (1.0, 1.0, 1.0))
"""
return point3d(self.coordinates_of(self.points), **kwds)
def triangulation_render_3d(triangulation, **kwds):
r"""
Return a graphical representation of a 3-d triangulation.
INPUT:
- ``triangulation`` -- a :class:`Triangulation`.
- ``**kwds`` -- keywords that are passed on to the graphics primitives.
OUTPUT:
A 3-d graphics object.
EXAMPLES::
sage: p = [[0,-1,-1],[0,0,1],[0,1,0], [1,-1,-1],[1,0,1],[1,1,0]]
sage: points = PointConfiguration(p)
sage: triang = points.triangulate()
sage: triang.plot(axes=False) # indirect doctest
Graphics3d Object
"""
from sage.plot.plot3d.all import point3d, line3d, arrow3d, polygon3d
points = [point.reduced_affine() for point in triangulation.point_configuration()]
coord = [[p[0], p[1], p[2]] for p in points]
plot_points = sum([point3d(p, size=15, **kwds) for p in coord])
tmp_lines = []
for t in triangulation:
if len(t) >= 2:
tmp_lines.append([t[0], t[1]])
if len(t) >= 3:
tmp_lines.append([t[0], t[2]])
tmp_lines.append([t[1], t[2]])
if len(t) >= 4:
tmp_lines.append([t[0], t[3]])
tmp_lines.append([t[1], t[3]])
tmp_lines.append([t[2], t[3]])
all_lines = []
interior_lines = []
for l in tmp_lines:
if l not in all_lines:
all_lines.append(l)
else:
interior_lines.append(l)
exterior_lines = [l for l in all_lines if not l in interior_lines]
from sage.plot.plot3d.texture import Texture
line_int = Texture(color="darkblue", ambient=1, diffuse=0)
line_ext = Texture(color="green", ambient=1, diffuse=0)
triang_int = Texture(opacity=0.3, specular=0, shininess=0, diffuse=0, ambient=1, color="yellow")
triang_ext = Texture(opacity=0.6, specular=0, shininess=0, diffuse=0, ambient=1, color="green")
plot_interior_lines = sum(
[line3d([coord[l[0]], coord[l[1]]], thickness=2, texture=line_int, **kwds) for l in interior_lines]
)
plot_exterior_lines = sum(
[line3d([coord[l[0]], coord[l[1]]], thickness=3, texture=line_ext, **kwds) for l in exterior_lines]
)
tmp_triangs = []
for t in triangulation:
if len(t) >= 3:
tmp_triangs.append([t[0], t[1], t[2]])
if len(t) >= 4:
tmp_triangs.append([t[0], t[1], t[3]])
tmp_triangs.append([t[0], t[2], t[3]])
tmp_triangs.append([t[1], t[2], t[3]])
all_triangs = []
interior_triangs = []
for l in tmp_triangs:
if l not in all_triangs:
all_triangs.append(l)
else:
interior_triangs.append(l)
exterior_triangs = [l for l in all_triangs if not l in interior_triangs]
plot_interior_triangs = sum(
[polygon3d([coord[t[0]], coord[t[1]], coord[t[2]]], texture=triang_int, **kwds) for t in interior_triangs]
)
plot_exterior_triangs = sum(
[polygon3d([coord[t[0]], coord[t[1]], coord[t[2]]], texture=triang_ext, **kwds) for t in exterior_triangs]
)
return plot_points + plot_interior_lines + plot_exterior_lines + plot_interior_triangs + plot_exterior_triangs
def triangulation_render_3d(triangulation, **kwds):
r"""
Return a graphical representation of a 3-d triangulation.
INPUT:
- ``triangulation`` -- a :class:`Triangulation`.
- ``**kwds`` -- keywords that are passed on to the graphics primitives.
OUTPUT:
A 3-d graphics object.
EXAMPLES::
sage: p = [[0,-1,-1],[0,0,1],[0,1,0], [1,-1,-1],[1,0,1],[1,1,0]]
sage: points = PointConfiguration(p)
sage: triang = points.triangulate()
sage: triang.plot(axes=False) # indirect doctest
Graphics3d Object
"""
from sage.plot.plot3d.all import point3d, line3d, polygon3d
points = [
point.reduced_affine()
for point in triangulation.point_configuration()
]
coord = [[p[0], p[1], p[2]] for p in points]
plot_points = sum([point3d(p, size=15, **kwds) for p in coord])
tmp_lines = []
for t in triangulation:
if len(t) >= 2:
tmp_lines.append([t[0], t[1]])
if len(t) >= 3:
tmp_lines.append([t[0], t[2]])
tmp_lines.append([t[1], t[2]])
if len(t) >= 4:
tmp_lines.append([t[0], t[3]])
tmp_lines.append([t[1], t[3]])
tmp_lines.append([t[2], t[3]])
all_lines = []
interior_lines = []
for l in tmp_lines:
if l not in all_lines:
all_lines.append(l)
else:
interior_lines.append(l)
exterior_lines = [l for l in all_lines if not l in interior_lines]
from sage.plot.plot3d.texture import Texture
line_int = Texture(color='darkblue', ambient=1, diffuse=0)
line_ext = Texture(color='green', ambient=1, diffuse=0)
triang_int = Texture(opacity=0.3,
specular=0,
shininess=0,
diffuse=0,
ambient=1,
color='yellow')
triang_ext = Texture(opacity=0.6,
specular=0,
shininess=0,
diffuse=0,
ambient=1,
color='green')
plot_interior_lines = sum([
line3d([coord[l[0]], coord[l[1]]],
thickness=2,
texture=line_int,
**kwds) for l in interior_lines
])
plot_exterior_lines = sum([
line3d([coord[l[0]], coord[l[1]]],
thickness=3,
texture=line_ext,
**kwds) for l in exterior_lines
])
tmp_triangs = []
for t in triangulation:
if len(t) >= 3:
tmp_triangs.append([t[0], t[1], t[2]])
if len(t) >= 4:
tmp_triangs.append([t[0], t[1], t[3]])
tmp_triangs.append([t[0], t[2], t[3]])
tmp_triangs.append([t[1], t[2], t[3]])
all_triangs = []
interior_triangs = []
for l in tmp_triangs:
if l not in all_triangs:
all_triangs.append(l)
else:
interior_triangs.append(l)
exterior_triangs = [l for l in all_triangs if not l in interior_triangs]
plot_interior_triangs = \
sum([ polygon3d([coord[t[0]], coord[t[1]], coord[t[2]]],
texture = triang_int, **kwds)
for t in interior_triangs ])
plot_exterior_triangs = \
sum([ polygon3d([coord[t[0]], coord[t[1]], coord[t[2]]],
texture = triang_ext, **kwds)
for t in exterior_triangs ])
return \
plot_points + \
plot_interior_lines + plot_exterior_lines + \
plot_interior_triangs + plot_exterior_triangs