Triangulation of an implicit surface of genus 3
Triangulation of a parametric surface (Monkey Saddle)

Triangulation of a surface means

Approaches

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 simply achieved by triangulating the area of definition (see second figure, depicting the Monkey Saddle). However, the triangles may vary in shape and extension in object space, posing a potential drawback. This can be minimized through adaptive methods that consider 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.

See also

References

  1. ^ M. Schmidt: Cutting Cubes – visualizing implicit surfaces by adaptive polygonization. Visual Computer (1993) 10, pp. 101–115
  2. ^ J. Bloomenthal: Polygonization of implicit surfaces, Computer Aided Geometric Design (1988), pp. 341–355
  3. ^ E. Hartmann: Geometry and Algorithms for COMPUTER AIDED DESIGN, p. 81
  4. ^ E. Hartmann: A marching method for the triangulation of surfaces, The Visual Computer (1998), 14, pp. 95–108
  5. ^ S. Akkouche & E Galin: Adaptive Implicit Surface Polygonization Using Marching Triangles, COMPUTER GRAPHICS forum (2001), Vol. 20, pp. 67–80

Software