Triangulation (geometry)

In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices. Triangulations of a three-dimensional volume would involve subdividing it into tetrahedra ("pyramids" of various shapes and sizes) packed together.

In most instances, the triangles of a triangulation are required to meet edge-to-edge and vertex-to-vertex.

Different types of triangulations may be defined, depending both on what geometric object is to be subdivided and on how the subdivision is determined.

The concept of a triangulation may also be generalized somewhat to subdivisions into shapes related to triangles. In particular, a pseudotriangulation of a point set is a partition of the convex hull of the points into pseudotriangles, polygons that like triangles have exactly three convex vertices. As in point set triangulations, pseudotriangulations are required to have their vertices at the given input points.

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