Plotting

This notebook can be downloaded here.

# The import will work if the package was installed using pip.
import pyrigi.frameworkDB as frameworks
import pyrigi.graphDB as graphs
from pyrigi import Graph, Framework

Methods Graph.plot() and Framework.plot() offer various plotting options. The default behaviour is the following:

G = Graph([(0,1), (1,2), (2,3), (0,3)])
G.plot()

F = Framework(G, {0: (0,0), 1: (1,1), 2: (3,1), 3: (2,0)})
F.plot()

Graph layouts

By default, a placement is generated using spring_layout().

G = graphs.ThreePrism()
G.plot()

Other options use random_layout(), circular_layout() or planar_layout():

G.plot(layout="random")
G.plot(layout="circular")
G.plot(layout="planar")

One can also specify a placement of the vertices explicitly:

G.plot(placement={0: (0, 0), 1: (0, 2), 2: (2, 1), 3: (6, 0), 4: (6, 2), 5: (4, 1)})

Canvas options

The size of the canvas can be specified.

S = frameworks.Square()
S.plot(canvas_width=2)

S.plot(canvas_height=2)

S.plot(canvas_width=2, canvas_height=2)

Also the aspect ratio:

S.plot(aspect_ratio=0.4)

Formatting

There are various options to format a plot.

Vertex color/size or label color/size can be changed.

G = Graph([[0,1]])
formatting = {
    "placement": {0: [0,0], 1: [1,0]},
    "canvas_height": 1,
}
G.plot(vertex_labels=False, vertex_color='green', **formatting)
G.plot(vertex_size=1500, font_size=30, font_color='#FFFFFF', **formatting)

There are various styles of vertices and edges.

formatting["vertex_labels"] = False
G.plot(vertex_shape='s', edge_style='-', **formatting)
G.plot(vertex_shape='o', edge_style='--', **formatting)
G.plot(vertex_shape='^', edge_style='-.', **formatting)
G.plot(vertex_shape='>', edge_style=':', **formatting)
G.plot(vertex_shape='v', edge_style='solid', **formatting)
G.plot(vertex_shape='<', edge_style='dashed', **formatting)
G.plot(vertex_shape='d', edge_style='dashdot', **formatting)
G.plot(vertex_shape='p', edge_style='dotted', **formatting)
G.plot(vertex_shape='h', edge_width=3, **formatting)
G.plot(vertex_shape='8', edge_width=5, **formatting)

Edge coloring

The color of all edges can be changed.

P = graphs.Path(6)
formatting = {
    "placement": {v: [v, 0] for v in P.vertex_list()},
    "canvas_height": 2,
    "edge_width": 5,
}
P.plot(edge_color='red', **formatting)

If a partition of the edges is specified, then each part is colored differently.

P.plot(edge_color=[[[0, 1], [2, 3]], [[1, 2]], [[5, 4], [4, 3]]], **formatting)

If the partition is incomplete, the missing edges are black.

P.plot(edge_color=[[[0, 1], [2, 3]], [[5, 4], [4, 3]]], **formatting)

Visually distinct colors are generated using the package distinctipy.

P30 = graphs.Path(30)
P30.plot(
    vertex_size=15,
    vertex_labels=False,
    edge_color=[[e] for e in P30.edge_list()],
    edge_width=3
)

Another possibility is to provide a dictionary assigning to a color a list of edges. Missing edges are again black.

P.plot(
    edge_color={
        "yellow": [[0, 1], [2, 3]],
        "#ABCDEF": [[5, 4], [4, 3]]
    },
    **formatting
)

Framework plotting

Currently, only plots of frameworks in the plane are implemented.

F = frameworks.Complete(9)
F.plot()

The same formatting options as for graphs are available for frameworks.

F = frameworks.Complete(9)
F.plot(
    vertex_labels=False,
    vertex_color='#A2B4C6',
    edge_style='dashed',
    edge_width=2,
    edge_color={"pink": [[0,1],[3,6]], "lightgreen": [[2, 3], [3, 5]]}
)

Infinitesimal Flexes

It is possible to include infinitesimal flexes in the plot. With the keyword inf_flex=n, we can pick the n-th nontrivial infinitesimal flex from a basis of the rigidity matrix’s kernel. There are several keywords that allow us to alter the style of the drawn arrows.

G = Graph([[0, 1], [0, 2], [1, 2], [2, 3], [2, 4], [3, 4]])
p = {0: [6, 8], 1: [6, -14], 2: [0, 0], 3: [-4, 4], 4: [-4, -4]}
F = Framework(G, p)
F.plot(
    inf_flex=0,
    flex_width=4,
    flex_length=0.25,
    flex_color="darkgrey",
    flex_style="-",
    flex_arrowsize=15
)

It is also possible to provide a specific infinitesimal flex with the following chain of commands:

F = frameworks.ThreePrism(realization="flexible")
flex = F.nontrivial_inf_flexes()[0]
F.plot(inf_flex=flex)

It is important to use the same order of the vertices of F as Graph.vertex_list() when providing the infinitesimal flex as a Matrix. To circumvent that, we also support adding an infinitesimal flex as a dict[Vertex, Vector]:

F = frameworks.Square()
flex = {0: (1, -1), 1: (1, 1), 2: (-1, 1), 3: (-1, -1)}
F.plot(inf_flex=flex)