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We present a data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion. The algorithm is applicable to all general polygonal models. It pre-computes a hierarchical representation of models using tight-fitting oriented bounding box trees (OBBTrees). At runtime, the algorithm traverses two(More)
In this paper, we present a formal approach to reciprocal n-body collision avoidance, where multiple mobile robots need to avoid collisions with each other while moving in a common workspace. In our formulation, each robot acts fully independently, and does not communicate with other robots. Based on the definition of velocity obstacles [5], we derive(More)
we present an exact and interactive collision detection system, I-COLLIDE, for large-scale environments. Such environments are characterized by the number of objects undergoing rigid motion and the complexity of the models. The algorithm does not assume the objects' motions can be expressed as a closed form function of time. The collision detection system(More)
In this paper, we propose a new concept - the "Reciprocal Velocity Obstacle"- for real-time multi-agent navigation. We consider the case in which each agent navigates independently without explicit communication with other agents. Our formulation is an extension of the Velocity Obstacle concept [3], which was introduced for navigation among (passively)(More)
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.(More)
We present novel algorithms for fast proximity queries using swept sphere volumes. The set of proximity queries includes collision detection and both exact and approximate separation distance computation. We introduce a new family of bounding volumes that correspond to a core primitive shape grown outward by some o set. The set of core primitive shapes(More)
We present a novel painting system with an intuitive haptic interface, which serves as an expressive vehicle for interactively creating painterly works. We introduce a deformable, 3D brush model, which gives the user natural control of complex brush strokes. The force feedback enhances the sense of realism and provides tactile cues that enable the user to(More)
The need to perform fast and accurate proximity queries arises frequently in physically-based modeling, simulation, animation, real-time interaction within a virtual environment, and game dynamics. The set of proximity queries include intersection detection, tolerance verification, exact and approximate minimum distance computation, and (disjoint) contact(More)
We present new distance computation algorithms using hierarchies of rectangular swept spheres. Each bounding volume of the tree is described as the Minkowski sum of a rectangle and a sphere, and fits tightly to the underlying geometry. We present accurate and efficient algorithms to build the hierarchies and perform distance queries between the bounding(More)