Fully Dynamic Constrained Delaunay Triangulations

Abstract

We present algorithms for the efficient insertion and removal of constraints in Delaunay Triangulations. Constraints are considered to be points or any kind of polygonal lines. Degenerations such as edge overlapping, self-intersections or duplicated points are allowed and are automatically detected and fixed on line. As a result, a fully Dynamic Constrained Delaunay Triangulation is achieved, able to efficiently maintain a consistent triangulated representation of dynamic polygonal domains. Several applications in the fields of data visualization, reconstruction, geographic information systems and collision-free path planning are discussed.