create.mesh.2.5D {fdaPDE}

Create a mesh.2.5D object from the nodes locations and the connectivity matrix

Description

Create a mesh.2.5D object from the nodes locations and the connectivity matrix

Usage

create.mesh.2.5D(
  nodes,
  triangles = NULL,
  order = 1,
  nodesattributes = NULL,
  segments = NULL,
  holes = NULL
)

Arguments

nodes

A #nodes-by-3 matrix containing the x, y, z coordinates of the mesh nodes.

triangles

A #triangles-by-3 (when order = 1) or #triangles-by-6 (when order = 2) matrix. It specifies the triangles giving the row's indices in nodes of the triangles' vertices and (when nodes = 2) also if the triangles' edges midpoints. The triangles' vertices and midpoints are ordered as described at
https://www.cs.cmu.edu/~quake/triangle.highorder.html.

order

Either '1' or '2'. It specifies wether each mesh triangle should be represented by 3 nodes (the triangle' vertices) or by 6 nodes (the triangle's vertices and midpoints). These are respectively used for linear (order = 1) and quadratic (order = 2) Finite Elements. Default is order = 1.

nodesattributes

A matrix with #nodes rows containing nodes' attributes. These are passed unchanged to the output. This has been added for consistency with the function create.mesh.2D.

segments

A #segments-by-2 matrix. Each row contains the row's indices in nodes of the vertices where the segment starts from and ends to. Segments are edges that are not splitted during the triangulation process. These are for instance used to define the boundaries of the domain. This has been added for consistency with the function create.mesh.2D.

holes

A #holes-by-3 matrix containing the x, y, z coordinates of a point internal to each hole of the mesh. These points are used to carve holes in the triangulation, when the domain has holes. This has been added for consistency with the function create.mesh.2D.

Value

An object of the class mesh.2.5D with the following output:

nodes

A #nodes-by-3 matrix containing the x, y, z coordinates of the mesh nodes.

nodesmarkers

A vector of length #nodes, with entries either '1' or '0'. An entry '1' indicates that the corresponding node is a boundary node; an entry '0' indicates that the corresponding node is not a boundary node.

nodesattributes

A matrix with #nodes rows containing nodes' attributes. These are passed unchanged from the input.

triangles

A #triangles-by-3 (when order = 1) or #triangles-by-6 (when order = 2) matrix. It specifies the triangles giving the indices in nodes of the triangles' vertices and (when nodes = 2) also if the triangles' edges midpoints. The triangles' vertices and midpoints are ordered as described at
https://www.cs.cmu.edu/~quake/triangle.highorder.html.

segmentsmarker

A vector of length #segments with entries either '1' or '0'. An entry '1' indicates that the corresponding element in segments is a boundary segment; an entry '0' indicates that the corresponding segment is not a boundary segment.

edges

A #edges-by-2 matrix containing all the edges of the triangles in the output triangulation. Each row contains the row's indices in nodes, indicating the nodes where the edge starts from and ends to.

edgesmarkers

A vector of lenght #edges with entries either '1' or '0'. An entry '1' indicates that the corresponding element in edge is a boundary edge; an entry '0' indicates that the corresponding edge is not a boundary edge.

neighbors

A #triangles-by-3 matrix. Each row contains the indices of the three neighbouring triangles. An entry '-1' indicates that one edge of the triangle is a boundary edge.

holes

A #holes-by-3 matrix containing the x, y, z coordinates of a point internal to each hole of the mesh. These points are used to carve holes in the triangulation, when the domain has holes. These are passed unchanged from the input.

order

Either '1' or '2'. It specifies wether each mesh triangle should be represented by 3 nodes (the triangle' vertices) or by 6 nodes (the triangle's vertices and midpoints). These are respectively used for linear (order = 1) and quadratic (order = 2) Finite Elements.

Examples

library(fdaPDE)

## Upload the hub2.5D the data
data(hub2.5D)
hub2.5D.nodes = hub2.5D$hub2.5D.nodes
hub2.5D.triangles = hub2.5D$hub2.5D.triangles

## Create mesh from nodes and connectivity matrix:
mesh = create.mesh.2.5D(nodes = hub2.5D.nodes, triangles = hub2.5D.triangles)
plot(mesh)