pdetriq

(Not recommended) Triangle quality measure

pdetriq is not recommended. Use meshQuality instead.

Syntax

q = pdetriq(p,t)

Description

q = pdetriq(p,t) returns a row vector of numbers from 0 through 1 representing the triangle quality of all the elements of the [p,e,t] mesh.

pdetriq evaluates the quality of a triangle as

$$q=\frac{4a\sqrt{3}}{h_1^2+h_2^2+h_3^2}$$

where a is the area and h₁, h₂, and h₃ are the lengths of the edges of the triangle.

The value 0 corresponds to a degenerate triangle with zero area. The value 1 corresponds to a triangle with h₁ = h₂ = h₃.

Examples

Mesh Element Quality for [p,e,t] Data

Evaluate the quality for each triangle of a [p,e,t] mesh.

Generate and plot a mesh for the geometry consisting of a circle with a diamond hole.

[p,e,t] = initmesh(@scatterg);
pdemesh(p,e,t)
axis equal

Evaluate the triangle quality for each mesh triangle. Plot the resulting quality values.

q = pdetriq(p,t);
figure
pdeplot(p,e,t,'XYData',q);
axis equal

Input Arguments

p — Mesh nodes

matrix

Mesh nodes, specified as a 2-by-Np matrix of nodes (points), where Np is the number of nodes in the mesh. For details on the mesh data representation, see initmesh.

Data Types: double

t — Mesh elements

matrix

Mesh elements, specified as a 4-by-Nt matrix of triangles, where Nt is the number of triangles in the mesh. For details on the mesh data representation, see initmesh.

Data Types: double

Output Arguments

q — Triangle quality

row vector

Triangle quality, returned as a row vector of numbers from 0 through 1.

References

[1] Bank, Randolph E. PLTMG: A Software Package for Solving Elliptic Partial Differential Equations, User's Guide 6.0. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1990.

Version History

Introduced before R2006a

R2018a: Not recommended

pdetriq is not recommended. Use meshQuality instead. There are no plans to remove pdetriq.