Surface triangulation

Triangulation of a surface means

This article describes the generation of a net of triangles. In literature there are contributions which deal with the optimization of a given net.

Surface triangulations are important for

The triangulation of a parametrically defined surface is an easy task. You just triangulate the area of definition (see second picture). But the images of these triangles in object space may vary in shape and extension, which may be a drawback. This drawback can be minimized by adaptive methods, which use 3D-informations (step width) while triangulating the parameter area.

To triangulate an implicit surface (defined by one or more equations) is more difficult. There exist essentially two methods.

The cutting cube algorithm determines, at the same time, all components of the surface within the surrounding starting cube depending on prescribed limit parameters. An advantage of the marching method is the possibility to prescribe boundaries (see picture).

Polygonizing a surface means to generate a polygon mesh.

The triangulation of a surface should not be confused with the triangulation of a discrete prescribed plane set of points. See Delaunay triangulation.

Triangulation: cylinder, surface ${\displaystyle x^{4}+y^{4}+z^{4}=1}$

Triangulation: cylinder, surface ${\displaystyle x^{4}+y^{4}+z^{4}=1}$, POV-Ray image

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