Trac #33596: PolyhedralComplex.plot(explosion_factor=1)

URL: https://trac.sagemath.org/33596
Reported by: mkoeppe
Ticket author(s): Matthias Koeppe, Yuan Zhou
Reviewer(s): Yuan Zhou, Matthias Koeppe

src/sage/geometry/polyhedral_complex.py

@@ -723,17 +723,81 @@ def plot(self, **kwds):
  """
  Return a plot of the polyhedral complex, if it is of dim at most 3.
 
+ INPUT:
+
+ - ``explosion_factor`` -- (default: 0) if positive, separate the cells of
+ the complex by extra space. In this case, the following keyword arguments
+ can be passed to :func:`exploded_plot`:
+
+ - ``center`` -- (default: ``None``, denoting the origin) the center of explosion
+ - ``sticky_vertices`` -- (default: ``False``) boolean or dict.
+ Whether to draw line segments between shared vertices of the given polyhedra.
+ A dict gives options for :func:`sage.plot.line`.
+ - ``sticky_center`` -- (default: ``True``) boolean or dict. When ``center`` is
+ a vertex of some of the polyhedra, whether to draw line segments connecting the
+ ``center`` to the shifted copies of these vertices.
+ A dict gives options for :func:`sage.plot.line`.
+
+ - ``color`` -- (default: ``None``) if ``"rainbow"``, assign a different color
+ to every maximal cell; otherwise, passed on to
+ :meth:`~sage.geometry.polyhedron.base.Polyhedron_base.plot`.
+
+ - other keyword arguments are passed on to
+ :meth:`~sage.geometry.polyhedron.base.Polyhedron_base.plot`.
+
  EXAMPLES::
 
  sage: p1 = Polyhedron(vertices=[(1, 1), (0, 0), (1, 2)])
  sage: p2 = Polyhedron(vertices=[(1, 2), (0, 0), (0, 2)])
- sage: pc = PolyhedralComplex([p1, p2])
- sage: pc.plot() # optional - sage.plot
- Graphics object consisting of 10 graphics primitives
+ sage: p3 = Polyhedron(vertices=[(0, 0), (0, 2), (-1, 1)])
+ sage: pc1 = PolyhedralComplex([p1, p2, p3, -p1, -p2, -p3])
+ sage: bb = dict(xmin=-2, xmax=2, ymin=-3, ymax=3, axes=False)
+ sage: g0 = pc1.plot(color='rainbow', **bb) # optional - sage.plot
+ sage: g1 = pc1.plot(explosion_factor=0.5, **bb) # optional - sage.plot
+ sage: g2 = pc1.plot(explosion_factor=1, color='rainbow', alpha=0.5, **bb) # optional - sage.plot
+ sage: graphics_array([g0, g1, g2]).show(axes=False) # not tested
+
+ sage: pc2 = PolyhedralComplex([polytopes.hypercube(3)])
+ sage: pc3 = pc2.subdivide(new_vertices=[(0, 0, 0)])
+ sage: g3 = pc3.plot(explosion_factor=1, color='rainbow', # optional - sage.plot
+ ....: alpha=0.5, axes=False, online=True)
+ sage: pc4 = pc2.subdivide(make_simplicial=True)
+ sage: g4 = pc4.plot(explosion_factor=1, center=(1, -1, 1), fill='blue', # optional - sage.plot
+ ....: wireframe='white', point={'color':'red', 'size':10},
+ ....: alpha=0.6, online=True)
+ sage: pc5 = PolyhedralComplex([
+ ....: Polyhedron(rays=[[1,0,0], [0,1,0], [0,0,-1]]),
+ ....: Polyhedron(rays=[[1,0,0], [0,-1,0], [0,0,-1]]),
+ ....: Polyhedron(rays=[[1,0,0], [0,-1,0], [0,0,1]]),
+ ....: Polyhedron(rays=[[-1,0,0], [0,-1,0], [0,0,-1]]),
+ ....: Polyhedron(rays=[[-1,0,0], [0,-1,0], [0,0,1]]),
+ ....: Polyhedron(rays=[[-1,0,0], [0,1,0], [0,0,-1]]),
+ ....: Polyhedron(rays=[[-1,0,0], [0,1,0], [0,0,1]])])
+ sage: g5 = pc5.plot(explosion_factor=0.3, color='rainbow', alpha=0.8, # optional - sage.plot
+ ....: point={'size': 20}, axes=False, online=True)
+
  """
  if self.dimension() > 3:
  raise ValueError("cannot plot in high dimension")
- return sum(cell.plot(**kwds) for cell in self.maximal_cell_iterator())
+ if kwds.get('explosion_factor', 0):
+ return exploded_plot(self.maximal_cell_iterator(), **kwds)
+
+ from sage.plot.colors import rainbow
+ from sage.plot.graphics import Graphics
+
+ color = kwds.get('color')
+ polyhedra = self.maximal_cell_iterator()
+ if color == 'rainbow':
+ polyhedra = list(polyhedra)
+ cell_colors_dict = dict(zip(polyhedra,
+ rainbow(len(polyhedra))))
+ g = Graphics()
+ for cell in polyhedra:
+ options = copy(kwds)
+ if color == 'rainbow':
+ options['color'] = cell_colors_dict[cell]
+ g += cell.plot(**options)
+ return g
 
  def is_pure(self):
  """
@@ -2433,3 +2497,110 @@ def cells_list_to_cells_dict(cells_list):
  else:
  cells_dict[d] = set([cell])
  return cells_dict
+
+
+def exploded_plot(polyhedra, *,
+ center=None, explosion_factor=1, sticky_vertices=False,
+ sticky_center=True, point=None, **kwds):
+ r"""
+ Return a plot of several ``polyhedra`` in one figure with extra space between them.
+
+ INPUT:
+
+ - ``polyhedra`` -- an iterable of :class:`~sage.geometry.polyhedron.base.Polyhedron_base` objects
+
+ - ``center`` -- (default: ``None``, denoting the origin) the center of explosion
+
+ - ``explosion_factor`` -- (default: 1) a nonnegative number; translate polyhedra by this
+ factor of the distance from ``center`` to their center
+
+ - ``sticky_vertices`` -- (default: ``False``) boolean or dict. Whether to draw line segments between shared
+ vertices of the given polyhedra. A dict gives options for :func:`sage.plot.line`.
+
+ - ``sticky_center`` -- (default: ``True``) boolean or dict. When ``center`` is a vertex of some
+ of the polyhedra, whether to draw line segments connecting the ``center`` to the shifted copies
+ of these vertices. A dict gives options for :func:`sage.plot.line`.
+
+ - ``color`` -- (default: ``None``) if ``"rainbow"``, assign a different color to every maximal cell and
+ every vertex; otherwise, passed on to :meth:`~sage.geometry.polyhedron.base.Polyhedron_base.plot`.
+
+ - other keyword arguments are passed on to :meth:`~sage.geometry.polyhedron.base.Polyhedron_base.plot`.
+
+ EXAMPLES::
+
+ sage: from sage.geometry.polyhedral_complex import exploded_plot
+ sage: p1 = Polyhedron(vertices=[(1, 1), (0, 0), (1, 2)])
+ sage: p2 = Polyhedron(vertices=[(1, 2), (0, 0), (0, 2)])
+ sage: p3 = Polyhedron(vertices=[(0, 0), (1, 1), (2, 0)])
+ sage: exploded_plot([p1, p2, p3]) # optional - sage.plot
+ Graphics object consisting of 20 graphics primitives
+ sage: exploded_plot([p1, p2, p3], center=(1, 1)) # optional - sage.plot
+ Graphics object consisting of 19 graphics primitives
+ sage: exploded_plot([p1, p2, p3], center=(1, 1), sticky_vertices=True) # optional - sage.plot
+ Graphics object consisting of 23 graphics primitives
+ """
+ from sage.plot.colors import rainbow
+ from sage.plot.graphics import Graphics
+ from sage.plot.line import line
+ from sage.plot.point import point as plot_point
+ import itertools
+
+ polyhedra = list(polyhedra)
+ g = Graphics()
+ if not polyhedra:
+ return g
+ dim = polyhedra[0].ambient_dimension()
+ if center is None:
+ from sage.rings.rational_field import QQ
+ center = vector(QQ, dim)
+ else:
+ center = vector(center)
+ translations = [explosion_factor * ((p.center()
+ + sum(r.vector() for r in p.rays()))
+ - center)
+ for p in polyhedra]
+ vertex_translations_dict = {}
+ for P, t in zip(polyhedra, translations):
+ for v in P.vertices():
+ v = v.vector()
+ v.set_immutable()
+ vertex_translations_dict[v] = vertex_translations_dict.get(v, [])
+ vertex_translations_dict[v].append(v + t)
+
+ color = kwds.get('color')
+ if color == 'rainbow':
+ cell_colors_dict = dict(zip(polyhedra,
+ rainbow(len(polyhedra))))
+ for p, t in zip(polyhedra, translations):
+ options = copy(kwds)
+ if color == 'rainbow':
+ options['color'] = cell_colors_dict[p]
+ g += (p + t).plot(point=False, **options)
+
+ if sticky_vertices or sticky_center:
+ if sticky_vertices is True:
+ sticky_vertices = dict(color='gray')
+ if sticky_center is True:
+ sticky_center = dict(color='gray')
+ for vertex, vertex_translations in vertex_translations_dict.items():
+ if vertex == center:
+ if sticky_center:
+ for vt in vertex_translations:
+ g += line((center, vt), **sticky_center)
+ else:
+ if sticky_vertices:
+ for vt1, vt2 in itertools.combinations(vertex_translations, 2):
+ g += line((vt1, vt2), **sticky_vertices)
+ if point is None:
+ # default from sage.geometry.polyhedron.plot
+ point = dict(size=10)
+ if point is not False:
+ if color == 'rainbow':
+ vertex_colors_dict = dict(zip(vertex_translations_dict.keys(),
+ rainbow(len(vertex_translations_dict.keys()))))
+ for vertex, vertex_translations in vertex_translations_dict.items():
+ options = copy(point)
+ if color == 'rainbow':
+ options['color'] = vertex_colors_dict[vertex]
+ g += plot_point(vertex_translations, **options)
+ return g