# create.mesh.2.5D: Create a 'mesh.2.5D' object from the nodes locations and the... In fdaPDE: Functional Data Analysis and Partial Differential Equations (PDE); Statistical Analysis of Functional and Spatial Data, Based on Regression with PDE Regularization

 create.mesh.2.5D R Documentation

## 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)
```

fdaPDE documentation built on Nov. 10, 2022, 5:06 p.m.