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For every edge on the boundary, adds a second degenerate triangle

Source: R/utils_initdata.R
add_exterior_triangles.Rd

Edges at the boundary will only border a single triangle. In order to deal with boundary conditions properly, this step ensures that every edge has two associated triangles (which use the edge) as well as two associated points (endpoints). The triangles that are added are degenerate triangles centered at the midpoint of each boundary edge.

Usage

add_exterior_triangles(data)

Arguments

data

A list containing the mesh data structures:

  • pts is a V-by-M data table with columns X and Y containing the coordinates of cells and additional metadata.

  • tris is a F-by-4 data table containing the X,Y coordinates of each triangle's centroid in the first two columns, and area and largest height of each triangle in the last two columns.

  • edges is a E-by-14 data table with columns from_pt, to_pt, from_tri, to_tri, x0_pt, x1_pt, y0_pt, y1_pt, x0_tri, x1_tri, y0_tri, y1_tri, length_pt, length_tri. If only one triangle uses an edge, then the from_tri, x0_tri, and y0_tri fields will contain NaN values.

  • tri_to_pt is a F-by-V sparse matrix with value 1 at (i,j) if triangle i uses point j as a vertex.

Value

A list containing the mesh data structures with (possibly) additional triangles. The tris table is updated to include the added external triangles. The edge table is updated so that boundary edges point to the newly added triangles. Also pts is unchanged, tri_to_pt is updated. Because new external triangles only have 2 associated points, tri_to_pt has rows that sum to either 2 or 3.