Point set triangulation

A triangulation of a set of points ${\displaystyle {\mathcal {P}}}$ in the Euclidean space ${\displaystyle \mathbb {R} ^{d}}$ is a simplicial complex that covers the convex hull of ${\displaystyle {\mathcal {P}}}$, and whose vertices belong to ${\displaystyle {\mathcal {P}}}$. In the plane (when ${\displaystyle {\mathcal {P}}}$ is a set of points in ${\displaystyle \mathbb {R} ^{2}}$), triangulations are made up of triangles, together with their edges and vertices. Some authors require that all the points of ${\displaystyle {\mathcal {P}}}$ are vertices of its triangulations. In this case, a triangulation of a set of points ${\displaystyle {\mathcal {P}}}$ in the plane can alternatively be defined as a maximal set of non-crossing edges between points of ${\displaystyle {\mathcal {P}}}$. In the plane, triangulations are special cases of planar straight-line graphs.

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