def render_3d(projection, **kwds):
"""
Return 3d rendering of a polyhedron projected into
3-dimensional ambient space.
NOTE:
This method, ``render_3d``, is used in the ``show()``
method of a polyhedron if it is in 3 dimensions.
EXAMPLES::
sage: p1 = Polyhedron(vertices=[[1,1,1]], rays=[[1,1,1]])
sage: p2 = Polyhedron(vertices=[[2,0,0], [0,2,0], [0,0,2]])
sage: p3 = Polyhedron(vertices=[[1,0,0], [0,1,0], [0,0,1]], rays=[[-1,-1,-1]])
sage: p1.projection().show() + p2.projection().show() + p3.projection().show()
It correctly handles various degenerate cases::
sage: Polyhedron(lines=[[1,0,0],[0,1,0],[0,0,1]]).show() # whole space
sage: Polyhedron(vertices=[[1,1,1]], rays=[[1,0,0]], lines=[[0,1,0],[0,0,1]]).show() # half space
sage: Polyhedron(vertices=[[1,1,1]], lines=[[0,1,0],[0,0,1]]).show() # R^2 in R^3
sage: Polyhedron(rays=[[0,1,0],[0,0,1]], lines=[[1,0,0]]).show() # quadrant wedge in R^2
sage: Polyhedron(rays=[[0,1,0]], lines=[[1,0,0]]).show() # upper half plane in R^3
sage: Polyhedron(lines=[[1,0,0]]).show() # R^1 in R^2
sage: Polyhedron(rays=[[0,1,0]]).show() # Half-line in R^3
sage: Polyhedron(vertices=[[1,1,1]]).show() # point in R^3
"""
if is_Polyhedron(projection):
projection = Projection(projection)
return \
projection.render_vertices_3d(width=3, color='green', **kwds) +\
projection.render_wireframe_3d(width=3, color='green', **kwds) + \
projection.render_solid_3d(**kwds)
def render_2d(projection, **kwds):
"""
Return 2d rendering of the projection of a polyhedron into
2-dimensional ambient space.
EXAMPLES::
sage: p1 = Polyhedron(vertices=[[1,1]], rays=[[1,1]])
sage: q1 = p1.projection()
sage: p2 = Polyhedron(vertices=[[1,0], [0,1], [0,0]])
sage: q2 = p2.projection()
sage: p3 = Polyhedron(vertices=[[1,2]])
sage: q3 = p3.projection()
sage: p4 = Polyhedron(vertices=[[2,0]], rays=[[1,-1]], lines=[[1,1]])
sage: q4 = p4.projection()
sage: q1.show() + q2.show() + q3.show() + q4.show()
sage: from sage.geometry.polyhedron.plot import render_2d
sage: q = render_2d(p1.projection())
sage: q._Graphics__objects
[Point set defined by 1 point(s),
Arrow from (1.0,1.0) to (2.0,2.0),
Polygon defined by 3 points]
"""
if is_Polyhedron(projection):
projection = Projection(projection)
return \
projection.render_points_2d(zorder=2, pointsize=10, **kwds) + \
projection.render_outline_2d(zorder=1, **kwds) + \
projection.render_fill_2d(zorder=0, rgbcolor=(0,1,0), **kwds)
def render_3d(projection, point_opts={}, line_opts={}, polygon_opts={}):
"""
Return 3d rendering of a polyhedron projected into
3-dimensional ambient space.
NOTE:
This method, ``render_3d``, is used in the ``show()``
method of a polyhedron if it is in 3 dimensions.
EXAMPLES::
sage: p1 = Polyhedron(vertices=[[1,1,1]], rays=[[1,1,1]])
sage: p2 = Polyhedron(vertices=[[2,0,0], [0,2,0], [0,0,2]])
sage: p3 = Polyhedron(vertices=[[1,0,0], [0,1,0], [0,0,1]], rays=[[-1,-1,-1]])
sage: p1.projection().show() + p2.projection().show() + p3.projection().show()
It correctly handles various degenerate cases::
sage: Polyhedron(lines=[[1,0,0],[0,1,0],[0,0,1]]).show() # whole space
sage: Polyhedron(vertices=[[1,1,1]], rays=[[1,0,0]], lines=[[0,1,0],[0,0,1]]).show() # half space
sage: Polyhedron(vertices=[[1,1,1]], lines=[[0,1,0],[0,0,1]]).show() # R^2 in R^3
sage: Polyhedron(rays=[[0,1,0],[0,0,1]], lines=[[1,0,0]]).show() # quadrant wedge in R^2
sage: Polyhedron(rays=[[0,1,0]], lines=[[1,0,0]]).show() # upper half plane in R^3
sage: Polyhedron(lines=[[1,0,0]]).show() # R^1 in R^2
sage: Polyhedron(rays=[[0,1,0]]).show() # Half-line in R^3
sage: Polyhedron(vertices=[[1,1,1]]).show() # point in R^3
"""
if is_Polyhedron(projection):
projection = Projection(projection)
from sage.plot.plot3d.base import Graphics3d
plt = Graphics3d()
if isinstance(point_opts, dict):
point_opts.setdefault('width', 3)
plt += projection.render_vertices_3d(**point_opts)
if isinstance(line_opts, dict):
line_opts.setdefault('width', 3)
plt += projection.render_wireframe_3d(**line_opts)
if isinstance(polygon_opts, dict):
plt += projection.render_solid_3d(**polygon_opts)
return plt
def render_3d(projection, point_opts={}, line_opts={}, polygon_opts={}):
"""
Return 3d rendering of a polyhedron projected into
3-dimensional ambient space.
NOTE:
This method, ``render_3d``, is used in the ``show()``
method of a polyhedron if it is in 3 dimensions.
EXAMPLES::
sage: p1 = Polyhedron(vertices=[[1,1,1]], rays=[[1,1,1]])
sage: p2 = Polyhedron(vertices=[[2,0,0], [0,2,0], [0,0,2]])
sage: p3 = Polyhedron(vertices=[[1,0,0], [0,1,0], [0,0,1]], rays=[[-1,-1,-1]])
sage: p1.projection().show() + p2.projection().show() + p3.projection().show()
It correctly handles various degenerate cases::
sage: Polyhedron(lines=[[1,0,0],[0,1,0],[0,0,1]]).show() # whole space
sage: Polyhedron(vertices=[[1,1,1]], rays=[[1,0,0]], lines=[[0,1,0],[0,0,1]]).show() # half space
sage: Polyhedron(vertices=[[1,1,1]], lines=[[0,1,0],[0,0,1]]).show() # R^2 in R^3
sage: Polyhedron(rays=[[0,1,0],[0,0,1]], lines=[[1,0,0]]).show() # quadrant wedge in R^2
sage: Polyhedron(rays=[[0,1,0]], lines=[[1,0,0]]).show() # upper half plane in R^3
sage: Polyhedron(lines=[[1,0,0]]).show() # R^1 in R^2
sage: Polyhedron(rays=[[0,1,0]]).show() # Half-line in R^3
sage: Polyhedron(vertices=[[1,1,1]]).show() # point in R^3
"""
if is_Polyhedron(projection):
projection = Projection(projection)
from sage.plot.plot3d.base import Graphics3d
plt = Graphics3d()
if isinstance(point_opts, dict):
point_opts.setdefault('width', 3)
plt += projection.render_vertices_3d(**point_opts)
if isinstance(line_opts, dict):
line_opts.setdefault('width', 3)
plt += projection.render_wireframe_3d(**line_opts)
if isinstance(polygon_opts, dict):
plt += projection.render_solid_3d(**polygon_opts)
return plt
def render_2d(projection, point_opts={}, line_opts={}, polygon_opts={}):
"""
Return 2d rendering of the projection of a polyhedron into
2-dimensional ambient space.
EXAMPLES::
sage: p1 = Polyhedron(vertices=[[1,1]], rays=[[1,1]])
sage: q1 = p1.projection()
sage: p2 = Polyhedron(vertices=[[1,0], [0,1], [0,0]])
sage: q2 = p2.projection()
sage: p3 = Polyhedron(vertices=[[1,2]])
sage: q3 = p3.projection()
sage: p4 = Polyhedron(vertices=[[2,0]], rays=[[1,-1]], lines=[[1,1]])
sage: q4 = p4.projection()
sage: q1.show() + q2.show() + q3.show() + q4.show()
sage: from sage.geometry.polyhedron.plot import render_2d
sage: q = render_2d(p1.projection())
sage: q._objects
[Point set defined by 1 point(s),
Arrow from (1.0,1.0) to (2.0,2.0),
Polygon defined by 3 points]
"""
if is_Polyhedron(projection):
projection = Projection(projection)
from sage.plot.graphics import Graphics
plt = Graphics()
if isinstance(point_opts, dict):
point_opts.setdefault('zorder', 2)
point_opts.setdefault('pointsize', 10)
plt += projection.render_points_2d(**point_opts)
if isinstance(line_opts, dict):
line_opts.setdefault('zorder', 1)
plt += projection.render_outline_2d(**line_opts)
if isinstance(polygon_opts, dict):
polygon_opts.setdefault('zorder', 0)
plt += projection.render_fill_2d(**polygon_opts)
return plt
def render_2d(projection, point_opts={}, line_opts={}, polygon_opts={}):
"""
Return 2d rendering of the projection of a polyhedron into
2-dimensional ambient space.
EXAMPLES::
sage: p1 = Polyhedron(vertices=[[1,1]], rays=[[1,1]])
sage: q1 = p1.projection()
sage: p2 = Polyhedron(vertices=[[1,0], [0,1], [0,0]])
sage: q2 = p2.projection()
sage: p3 = Polyhedron(vertices=[[1,2]])
sage: q3 = p3.projection()
sage: p4 = Polyhedron(vertices=[[2,0]], rays=[[1,-1]], lines=[[1,1]])
sage: q4 = p4.projection()
sage: q1.show() + q2.show() + q3.show() + q4.show()
sage: from sage.geometry.polyhedron.plot import render_2d
sage: q = render_2d(p1.projection())
sage: q._objects
[Point set defined by 1 point(s),
Arrow from (1.0,1.0) to (2.0,2.0),
Polygon defined by 3 points]
"""
if is_Polyhedron(projection):
projection = Projection(projection)
from sage.plot.graphics import Graphics
plt = Graphics()
if isinstance(point_opts, dict):
point_opts.setdefault('zorder', 2)
point_opts.setdefault('pointsize', 10)
plt += projection.render_points_2d(**point_opts)
if isinstance(line_opts, dict):
line_opts.setdefault('zorder', 1)
plt += projection.render_outline_2d(**line_opts)
if isinstance(polygon_opts, dict):
polygon_opts.setdefault('zorder', 0)
plt += projection.render_fill_2d(**polygon_opts)
return plt
