Parallelized ear clipping for the triangulation and constrained Delaunay triangulation of polygons

Triangulation by Ear Clipping

A classic problem in computer graphics is to decompose a simple polygon into a collection of triangles whose vertices are only those of the simple polygon. By definition, a simple polygon is an ordered sequence of n points, ~ V0 through ~ Vn−1. Consecutive vertices are connected by an edge 〈~ Vi, ~ Vi+1〉, 0 ≤ i ≤ n − 2, and an edge 〈~ Vn−1, ~ V0〉 connects the first and last points. Each vertex ...

Improved algorithms for ear-clipping triangulation

Delaunay-restricted Optimal Triangulation of 3D Polygons

Triangulation of 3D polygons is a well studied topic of research. Existing methods for finding triangulations that minimize given metrics (e.g., sum of triangle areas or dihedral angles) run in a costly $O(n^4)$ time \cite{Barequet95,Barequet96}, while the triangulations are not guaranteed to be free of intersections. To address these limitations, we restrict our search to the space of triangle...

Constrained Delaunay Triangulation Using Delaunay Visibility

An algorithm for constructing constrained Delaunay triangulation (CDT) of a planar straight-line graph (PSLG) is presented. Although the uniform grid method can reduce the time cost of visibility determinations, the time needed to construct the CDT is still long. The algorithm proposed in this paper decreases the number of edges involved in the computation of visibility by replacing traditional...

The Strange Complexity of Constrained Delaunay Triangulation

The problem of determining whether a polyhedron has a constrained Delaunay tetrahedralization is NP-complete. However, if no five vertices of the polyhedron lie on a common sphere, the problem has a polynomial-time solution. Constrained Delaunay tetrahedralization has the unusual status (for a small-dimensional problem) of being NP-hard only for degenerate inputs.