Polylines

Polylines are made of vertices (points in 3D space) and edges linking them. They allow to embed a graph in \(\mathbb{R}^3\) and visualize it.

Edges are stored in a specific data container called edges as ordered pairs of vertex indices. They are not oriented and the smallest vertex index is always first. For example, \((1,3)\) is a valid edge index but \((3,1)\) is not. Edge orientation is performed automatically when instancing a Polyline from a RawMeshData (see Edition and Manual Creation)

Example of a polyline

Polyline

Bases: Mesh

A data structure for representing polylines.

Attributes:

Name	Type	Description
vertices	DataContainer	the container for all vertices
edges	DataContainer	the container for all edges
__str__		Representation of the object and its elements as a string.

id_edges property

Shortcut for range(len(self.edges))

id_vertices property

Shortcut for range(len(self.vertices))

Polyline Connectivity

Connectivity handler class. Allows connectivity queries on the object, like neighbours of a vertex, etc.

Connectivity is computed lazily only when needed in the code. For instance, the first call to mesh.connectivity.vertex_to_vertices will generate the vertex_to_vertices dictionnary, so that the next call will not perform any computation but a lookup in the array.

clear()

Resets connectivity. The next query in the code will regenerate internal arrays.

edge_id(V1, V2)

id of an edge. If self.edges[i] contains edges (A,B), then edge_id(A,B)=edge_id(B,A)=i If (A,B) is not a valid edge of the mesh, returns None

Parameters:

Name	Type	Description	Default
V1	int	first vertex of the edge	required
V2	int	second vertex of the edge	required

Returns:

Name	Type	Description
int	int	the id of edge (V1,V2), or None if the edge does not exist.

edge_to_vertices(E)

Returns the two vertex indices that are adjacent to edge `E

Parameters:

Name	Type	Description	Default
E	int	edge index	required

Returns:

Name	Type	Description
list	list	two vertex indices

other_edge_end(E, V)

Vertex at the opposite end of edge E from vertex V. Returns None if V is not adjacent to edge E

Parameters:

Name	Type	Description	Default
E	int	edge id	required
V	int	vertex id	required

Returns:

Name	Type	Description
int	int	the vertex W such that E is the edge (V,W). Returns None if V is not adjacent to edge E

vertex_to_edges(V)

Neighborhood of vertex V in terms of edges.

Parameters:

Name	Type	Description	Default
V	int	vertex id	required

Returns:

Name	Type	Description
list	list	list of edges E such that V belongs to E.

vertex_to_vertices(V)

Neighborhood of vertex V in terms of vertices.

Parameters:

Name	Type	Description	Default
V	int	vertex id	required

Returns:

Name	Type	Description
list	list	list of vertices W such that (V,W) is a valid edge in the polyline.