Fast computation of generalized Voronoi diagrams using graphics hardware

: We present a new approach for computing generalized Voronoi diagrams in two and three dimensions using interpolation-based polygon rasterization hardware. The input primitives may be points, lines, polygons, curves, or surfaces. The algorithm computes a discrete Voronoi diagram by rendering a three dimensional distance mesh corresponding to each primitive. The polygonal mesh is a bounded-error approximation of a nonlinear distance function. The algorithm divides the space into regular cells. For each cell it computes the closest primitive and the distance to that primitive using polygon scan-conversion and Z-buffer depth comparison. We present efficient techniques to detect Voronoi boundaries and compute Voronoi neighbors. The algorithm has been implemented on SGI workstations and PCs using OpenGL and applied to complex 2D and 3D datasets. We also demonstrate the applications of our algorithm to fast motion planning in static and dynamic environments, and improving the performance of...

• Type: Conference
• Year: 2000
• Where: COMPGEOM
• Authors: Kenneth E. Hoff III, Tim Culver, John Keyser, Ming C. Lin, Dinesh Manocha
• Keywords: COMPGEOM 2000, Discrete Geometry, Discrete Voronoi Diagram, Polygon Rasterization, Voronoi Diagrams