Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Parallel computational geometry
Parallel computational geometry
Robot Motion Planning
A solution to the Path Planning problem using angle preprocessing
Robotics and Autonomous Systems
Transforming Triangulations on Nonplanar Surfaces
SIAM Journal on Discrete Mathematics
| Hi-index | 0.00 |
The new approach we propose in this paper is a plane partition with similar features to those of the Voronoi Diagram, but the Euclidean minimum distance criterion is replaced for the minimal angle criterion. The result is a new tessellation of the plane in regions called Polar Diagram, in which every site is owner of a polar region as the locus of points with smallest polar angle respect to this site. We prove that polar diagrams, used as preprocessing, can be applied to many problems in Computational Geometry in order to speed up their processing times. Some of these applications are the convex hull, visibility problems, and path planning problems.