euclidean_polygonal_surfaces

The category of surfaces built by gluing Euclidean polygons.

See flatsurf.geometry.categories for a general description of the category framework in sage-flatsurf.

Normally, you won’t create this (or any other) category directly. The correct category is automatically determined for immutable surfaces.

EXAMPLES:

sage: from flatsurf import MutableOrientedSimilaritySurface
sage: C = MutableOrientedSimilaritySurface(QQ).category()

sage: from flatsurf.geometry.categories import EuclideanPolygonalSurfaces
sage: C.is_subcategory(EuclideanPolygonalSurfaces())
True

class flatsurf.geometry.categories.euclidean_polygonal_surfaces.EuclideanPolygonalSurfaces

The category of surfaces built by gluing Euclidean polygons (or more generally, polygons in two-dimensional real space).

EXAMPLES:

sage: from flatsurf.geometry.categories import EuclideanPolygonalSurfaces
sage: EuclideanPolygonalSurfaces()
Category of euclidean polygonal surfaces

class ParentMethods

Provides methods available to all surfaces that are built from polygons in the real plane.

If you want to add functionality for such surfaces you most likely want to put it here.

graphical_surface(*args, **kwargs)

Return a graphical representation of this surface.

This method can be used to further configure or augment a plot beyond the possibilities of plot().

The documentation of sage-flatsurf contains a section of example plots or consult the flatsurf.graphical.surface reference for all the details.

EXAMPLES:

sage: from flatsurf import translation_surfaces
sage: S = translation_surfaces.square_torus()
sage: S.graphical_surface()
Graphical representation of Translation Surface in H_1(0) built from a square

plot(**kwargs)

Return a plot of this surface.

The documentation of sage-flatsurf contains a section of example plots or consult the flatsurf.graphical.surface reference for all the details.

EXAMPLES:

sage: from flatsurf import translation_surfaces
sage: S = translation_surfaces.square_torus()
sage: S.plot()
Graphics object consisting of 10 graphics primitives

plot_polygon(label, graphical_surface=None, plot_polygon=True, plot_edges=True, plot_edge_labels=True, edge_labels=None, polygon_options={'axes': True}, edge_options=None, edge_label_options=None)

Returns a plot of the polygon with the provided label.

Note that this method plots the polygon in its coordinates as opposed to graphical coordinates that the :func:plot method uses. This makes it useful for visualizing the natural coordinates of the polygon.

INPUT:

• graphical_surface – (default None) If provided this function pulls graphical options from the graphical surface. If not provided, we use the default graphical surface.

• plot_polygon – (default True) If True, we plot the solid polygon.

• polygon_options – (default {"axes":True}) Options for the rendering of the polygon. These options will be passed to plot_polygon(). This should be either None or a dictionary.

• plot_edges – (default True) If True, we plot the edges of the polygon as segments.

• edge_options – (default None) Options for the rendering of the polygon edges. These options will be passed to plot_edge(). This should be either None or a dictionary.

• plot_edge_labels – (default True) If True, we plot labels on the edges.

• edge_label_options – (default None) Options for the rendering of the edge labels. These options will be passed to plot_edge_label(). This should be either None or a dictionary.

• edge_labels – (default None) If None and plot_edge_labels is True, we write the edge number on each edge. Otherwise edge_labels should be a list of strings of length equal to the number of edges of the polygon. The strings will be printed on each edge.

EXAMPLES:

sage: from flatsurf import similarity_surfaces
sage: s = similarity_surfaces.example()
sage: s.plot()
...Graphics object consisting of 13 graphics primitives

sage: s.plot_polygon(1)
...Graphics object consisting of 7 graphics primitives

sage: labels = []
sage: p = s.polygon(1)
sage: for e in range(len(p.vertices())):
....:     labels.append(str(p.edge(e)))
sage: s.plot_polygon(1, polygon_options=None, plot_edges=False, edge_labels=labels, edge_label_options={"color":"red"})
...Graphics object consisting of 4 graphics primitives

super_categories()

The categories such surfaces are also automatically contained in, namely the category of surfaces built from polygons.

EXAMPLES:

sage: from flatsurf.geometry.categories import EuclideanPolygonalSurfaces
sage: C = EuclideanPolygonalSurfaces()
sage: C.super_categories()
[Category of polygonal surfaces]