Fast computation of generalized Voronoi diagrams using graphics hardware Conference Paper uri icon

abstract

  • We demonstrate a new approach for computing generalized 2D and 3D Voronoi diagrams using interpolation-based polygon rasterization hardware. We compute a discrete Voronoi diagram by rendering a three dimensional distance mesh for each Voronoi site. The polygonal mesh is a bounded-error approximation of a (possibly) non-linear function of the distance between a site and a 2D planar grid of sample points. For each sample point, we compute the closest site and the distance to that site using polygon scan-conversion and the Z-buffer depth comparison. The algorithm has been implemented on SGI workstations and PCs using OpenGL, and applied to complex datasets. We demonstrate the application of our algorithm to fast motion planning in static and dynamic environments.

author list (cited authors)

  • Hoff, K. E., Culver, T., Keyser, J., Lin, M., & Manocha, D.

publication date

  • January 2000