jigglemesh

(Not recommended) Jiggle internal points of triangular mesh

This page describes the legacy workflow. New features might not be compatible with the legacy workflow. For the corresponding step in the recommended workflow, see generateMesh.

Syntax

p1 = jigglemesh(p,e,t)

p1 = jigglemesh(p,e,t,Name,Value)

Description

p1 = jigglemesh(p,e,t) jiggles the triangular mesh by adjusting the node point positions. Typically, the quality of the mesh increases after jiggling.

p1 = jigglemesh(p,e,t,Name,Value) jiggles the mesh using one or more Name,Value arguments.

Examples

Jiggle Mesh

Create a triangular mesh of the square geometry by using initmesh. To avoid jiggling, call initimesh with the Jiggle value set to off.

[p,e,t] = initmesh("lshapeg","Jiggle","off"); 

Evaluate quality of the mesh elements using the pdetriq function.

q = pdetriq(p,t); 

Plot the mesh.

pdeplot(p,e,t,"XYData",q,"ColorBar","on","XYStyle","flat")
axis equal

Jiggle the mesh using the default parameter values. Plot the result.

p1 = jigglemesh(p,e,t); 
q = pdetriq(p1,t); 
pdeplot(p1,e,t,"XYData",q,"ColorBar","on","XYStyle","flat")
axis equal

Now jiggle the original mesh again, this time using 50000 iterations.

p2 = jigglemesh(p,e,t,"Opt","off","Iter",5e4); 
q = pdetriq(p2,t); 
pdeplot(p2,e,t,"XYData",q,"ColorBar","on","XYStyle","flat")
axis equal

Input Arguments

p — Mesh points

2-by-Np matrix

Mesh points, specified as a 2-by-Np matrix. Np is the number of points (nodes) in the mesh. Column k of p consists of the x-coordinate of point k in p(1,k) and the y-coordinate of point k in p(2,k). For details, see Mesh Data as [p,e,t] Triples.

e — Mesh edges

7-by-Ne matrix

Mesh edges, specified as a 7-by-Ne matrix, where Ne is the number of edges in the mesh. An edge is a pair of points in p containing a boundary between subdomains, or containing an outer boundary. For details, see Mesh Data as [p,e,t] Triples.

t — Mesh elements

4-by-Nt matrix

Mesh elements, specified as a 4-by-Nt matrix. Nt is the number of triangles in the mesh.

The t(i,k), with i ranging from 1 through end - 1, contain indices to the corner points of element k. For details, see Mesh Data as [p,e,t] Triples. The last row, t(end,k), contains the subdomain number of the element.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: p1 = jigglemesh(p,e,t,"Iter",Inf)

Opt — Optimization method

"mean" (default) | "minimum" | "off"

Optimization method, specified as the comma-separated pair consisting of "Opt" and "mean", "minimum", or "off".

Jiggling a mesh moves each mesh point not located on an edge segment towards the center of mass of the polygon formed by the adjacent triangles. The optimization method controls how many times jigglemesh repeats this process:

• If Opt is "off", jigglemesh repeats this process Iter times. The default value of Iter in this case is 1.

• If Opt is "mean", jigglemesh repeats this process until the mean triangle quality stops increasing significantly or until the maximum number of iterations is reached. The default value of Iter in this case is 20.

• If Opt is "minimum", jigglemesh repeats this process until the minimum triangle quality stops increasing significantly or until the maximum number of iterations is reached. The default value of Iter in this case is 20.

Example: p1 = jigglemesh(p,e,t,"Opt","off","Iter",1000);

Data Types: char | string

Iter — Maximum number of iterations

1 or 20 (default) | positive integer

Maximum number of iterations, specified as the comma-separated pair consisting of "Iter" and a positive number. The default value depends on the Opt argument value. If Opt is set to "mean" (default) or "minimum", the default maximum number of iterations is 20. If Opt is set to "off", the default maximum number of iterations is 1.

Example: p1 = jigglemesh(p,e,t,"Opt","off","Iter",1000);

Data Types: double

Output Arguments

p1 — Modified mesh points

2-by-Np matrix

Modified mesh points, returned as a 2-by-Np matrix. Np is the number of points (nodes) in the mesh. Column k of p consists of the x-coordinate of point k in p(1,k) and the y-coordinate of point k in p(2,k). For details, see Mesh Data as [p,e,t] Triples.

Version History

Introduced before R2006a