Quality meshing: angle and area constraints


Triangle generates a conforming Delaunay triangulation whenever the -q or -a switch is used. These switches also set angle and area constraints for the mesh.

The -q switch sets a minimum angle constraint. A number may follow the `q'; otherwise, the default minimum angle is twenty degrees. For the point set spiral.node below, consider the differences among

triangle spiral
triangle -q spiral
triangle -q32.5 spiral

Note that the angle constraint does not apply to small angles between input segments; such angles cannot be removed.

The -a switch sets a maximum area constraint. There are three ways to use this switch. The first way is to specify a maximum area on the command line. The next example is a mesh in which no triangle has area greater than 0.2.

triangle -a.2 spiral

The second manner of using the -a switch is applicable only when creating a new mesh from a PSLG. The file describing the PSLG itself contains area constraints, each of which is applied to a segment-bounded region; see the .poly file description for details. For an example, look at the last seven lines of la.poly, which describes a vertical cross section of soil in the Los Angeles Basin. Below is an illustration of the results when the -a switch is or is not invoked.

triangle -pq la
triangle -pqa la

The third manner is applicable only when refining a preexisting mesh. See the refinement page for details.


Return to Triangle home page.
jrs@cs.cmu.edu