Kenneth E. Hoff

Fast computation of generalized Voronoi diagrams using graphics hardware

We present 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. We construct distance meshes for points, line segments, polygons, polyhedra, curves, and curved surfaces in 2D and 3D. We generalize to weighted and farthest-site Voronoi diagrams, and present efficient techniques for computing the Voronoi boundaries, Voronoi neighbors, and the Delaunay triangulation of points. We also show how to adaptively refine the solution through a simple windowing operation. 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, selection in complex user-interfaces, and creation of dynamic mosaic effects. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling; I.3.3 [Computer Graphics]: Picture/Image Generation. Additional

Visibility culling using hierarchical occlusion maps

We present hierarchical occlusion maps (HOM) for visibility culling on complex models with high depth complexity. The culling algorithm uses an object space bounding volume hierarchy and a hierarchy of image space occlusion maps. Occlusion maps represent the aggregate of projections of the occluders onto the image plane. For each frame, the algorithm selects a small set of objects from the modelas occludersand renders them to form an initial occlusion map, from which a hierarchy of occlusion maps is built. The occlusion maps are used to cull away a portion of the model not visible from the current viewpoint. The algorithm is applicable to all models and makes no assumptions about the size, shape, or type of occluders. It supports approximate culling in which small holes in or among occluders can be ignored. The algorithm has been implemented on current graphics systems and has been applied to large models composed of hundreds of thousands of polygons. In practice, it achieves significant speedup in interactive walkthroughs of models with high depth complexity. CR

Fast and simple 2D geometric proximity queries using graphics hardware

We present a new approach for computing generalized proximity information of arbitrary 2D objects using graphics hardware. Using multi-pass rendering techniques and accelerated distance computation, our algorithm performs proximity queries not only for detecting collisions, but also for computing intersections, separation distance, penetration depth, and contact points and normals. Our hybrid geometry and image-based approach balances computation between the CPU and graphics subsystems. Geometric object-space techniques coarsely localize potential intersection regions or closest features between two objects, and image-space techniques compute the low-level proximity information in these regions. Most of the proximity information is derived from a distance field computed using graphics hardware. We demonstrate the performance in collision response computation for rigid and deformable body dynamics simulations. Our approach provides proximity information at interactive rates for a variety of simulation strategies for both backtracking and penalty-based collision responses.

Interactive motion planning using hardware-accelerated computation of generalized Voronoi diagrams

We present techniques for fast motion planning by using discrete approximations of generalized Voronoi diagrams, computed with graphics hardware. Approaches based on this diagram computation are applicable to both static and dynamic environments of fairly high complexity. We compute a discrete Voronoi diagram by rendering a 3D distance mesh for each Voronoi site. The sites can be points, line segments, polygons, polyhedra, curves and surfaces. The computation of the generalized Voronoi diagram provides fast proximity query toolkits for motion planning. The tools provide the distance to the nearest obstacle stored in the Z-buffer, as well as the Voronoi boundaries, Voronoi vertices and weighted Voronoi graphs extracted from the frame buffer using continuation methods. We have implemented these algorithms and demonstrated their performance for path planning in a complex dynamic environment composed of more than 140,000 polygons.

Fast backface culling using normal masks

This paper presents a novel method for fast and efficient backface culling: we reduce the backface test to one logical operation per polygon while requiring only two bytes extra storage per polygon. The normal mask is introduced, where each bit is associated with a cluster of normals in a normal-space partitioning. A polygons normal is approximated by the cluster of normals in which it falls; the clusters normal mask is stored with the polygon in a preprocessing step. Although conceptually the normal masks require as many bits as the number of clusters, we observe that only two bytes are actually necessary. For each frame (and for each viewing volume), we calculate the backface mask by ORing the normals masks of all normal clusters that are backfacing. The backface test finally reduces to a single logical AND operation between the polygons normal mask and the backface mask. CR

Increased photorealism for interactive architectural walkthroughs

This paper presents a new method for interactive rendering of globally illuminated static scenes. Global illumination is decomposed into view-independent (diffuse) and view-dependent (non-diffuse) components. The two are recombined during rendering using a hybrid geometryand image-based approach along with multi-pass blending techniques. This approach allows the preprocessing of both components and the fast rendering of globally illuminated scenes. The view-independent component uses a traditional precomputed geometry-based radiosity solution that is rendered using standard graphics hardware. The view-dependent component is decomposed into “what is reflected” (radiance with depth) and “how it is reflected” (BRDF), and precomputed and rendered using image-based approaches. Radiance is stored as images with depth, and rendered using perspective reprojection; the BRDF is decomposed into an integration of incoming radiance and a directional modulation. The radiance integration term is approximated by convolving the reflected image with precomputed kernel textures based on material properties. The directional modulation is stored as a reflectance modulation texture based on material properties and is rendered using spheremapping during a blending pass.

Accelerated walkthrough of large spline models

CAD and rmimation applications. In this pa-per, we present algorithms for interactive walkthrough ofcomplex NURBS models composed of tens of thousands ofpatches on current graphics systems. Given a spline model,the algorithm precomputes simplification of a collection ofpatches and represents them hierarchically. Given a chang-ing viewpoint, the algorithm combines these simplificationswith dynamic tessellations to generate appropriate levels ofdetail. We also propose a system pipeline for parallel im-plementation on multi-processor configurations. Diiferentcomponents,

Closest point query among the union of convex polytopes using rasterization hardware

Abstract We present a novel approach using rasterization hardware to perform the following query: Given a collection of convex polytopes in 3D, find the closest point from some given point inside the polytopes to the surface of the union of the polytopes. The algorithm takes advantage of multipass rendering, clipping, and depth tests. We also demonstrate its application to penetration depth computation.