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 such trees and tests for overlaps between oriented bounding boxes based on a separating axis theorem, which takes less than 200 operations in practice. It has been implemented and we compare its performance with other hierarchical data structures. In particular, it can robustly and accurately detect all the contacts between large complex geometries composed of hundreds of thousands of polygons at interactive rates.

In this paper, we survey the state of the art in collision detection between general geometric models. The set of models include polygonal objects, spline or algebraic surfaces, CSG models, and deformable bodies. We present a number of techniques and systems available for contact determination. We also describe several N-body algorithms to reduce the number of pairwise intersection tests. 1 Introduction The goal of collision detection (also known as interference detection or contact determination) is to automatically report a geometric contact when it is about to occur or has actually occurred. The geometric models may be polygonal objects, splines, or algebraic surfaces. The problem is encountered in computer-aided design and machining (CAD/CAM), robotics and automation, manufacturing, computer graphics, animation and computer simulated environments. Collision detection enables simulationbased design, tolerance verification, engineering analysis, assembly and dis-assembly, motion pla...

We present an efficient O(n + 1/ε^4.5)-time algorithm for computing a (1 + 1/ε)-approximation of the minimum-volume bounding box of n points in R³. We also present a simpler algorithm (for the same purpose) whose running time is O(n log n+n/ε³). We give some experimental results with implementations of various variants of the second algorithm. The implementation of the algorithm described in this paper is available online [Har00].

In a geometric context, a collision or proximity query reports information about the relative configuration or placement of two objects. Some of the common examples of such queries include checking whether two objects overlap in space, or whether their boundaries intersect, or computing the minimum Euclidean separation distance between their boundaries. Hundreds of papers have been published on di#erent aspects of these queries in computational geometry and related areas such as robotics, computer graphics, virtual environments, and computer-aided design. These queries arise in di#erent applications including robot motion planning, dynamic simulation, haptic rendering, virtual prototyping, interactive walkthroughs, computer gaming, and molecular modeling. For example, a large-scale virtual environment, e.g., a walkthrough, creates a model of the environment with virtual objects. Such an environment is used to give the user a sense of presence in a synthetic world and it s

Hierarchical data structures have been widely used to design e cient algorithms for interference detection for robot motion planning and physically-based modeling applications. Most of the hierarchies involve use of bounding volumes which enclose the underlying geometry. These bounding volumes are used to test for interference orcompute distance bounds between the underlying geometry. The e ciency of a hierarchy is directly proportional to the choice ofabounding volume. In this paper, we introduce spherical shells, a higher order bounding volume for fast proximity queries. Each shell corresponds to a portion of the volume between two concentric spheres. We present algorithms to compute tight tting shells and fast overlap between two shells. Moreover, we show that spherical shells provide local cubic convergence to the underlying geometry. As aresult, in many cases they provide faster algorithms for interference detection and distance computation as compared toearlier methods. We also describe an implementation and compare it with other hierarchies. 1

We introduce the boxtree, a versatile data structure for representing triangulated or meshed surfaces in 3D. A boxtree is a hierarchical structure of nested boxes that supports efficient ray tracing and collision detection. It is simple and robust, and requires minimal space. In situations where storage is at a premium, boxtrees are effective alternatives to octrees and BSP trees. They are also more flexible and efficient than R-trees, and nearly as simple to implement. Keywords: collision detection, hierarchical data structures, ray shooting. 1. Introduction In 1981 Ballard 1 presented a simple data structure for representing digitized curves by means of nested strips. This work is an attempt to generalize his strip tree structure to the case of surfaces in 3D. As is well known, curves can seem quite tame when compared to surfaces. For example, collision detection in 3D is orders of magnitude more difficult than in 2D. Expectedly, generalizing a strip tree into a boxtree raises a ...

We present an accelerated proximity query algorithm between moving convex polyhedra. The algorithm combines Voronoi-based feature tracking with a multi-level-of-detail representation, in order to adapt to the variation in levels of coherence and speed up the computation. It provides a progressive refinement framework for collision detection and distance queries. We have implemented our algorithm and have observed significant performance improvements in our experiments, especially on scenarios where the coherence is low. 1 Introduction Proximity queries, i.e. distance 1 computations and the closely related collision detection problems, are ubiquitous in robotics, design automation, manufacturing, assembly and virtual prototyping. The set of tasks include motion planning, sensor-based manipulation, assembly and disassembly, dynamic simulation, maintainability study, simulation-based design, tolerance verification, and ergonomics analysis. Proximity queries have been extensively stud...

We present a fast and accurate collision detection algorithm for haptic interaction with polygonal models. Given a model, we pre-compute a hybrid hierarchical representation, consisting of uniform grids (represented using a hash table) and trees of tight-fitting oriented bounding box trees (OBBTrees). At run time, we use hybrid hierarchical representations and exploit frame-to-frame coherence for fast proximity queries. We describe a new overlap test, which is specialized for intersection of a line segment with an oriented bounding box for haptic simulation and takes 42-72 operations including transformation costs. The algorithms have been implemented as part of H-COLLIDE and interfaced with a PHANToM arm and its haptic toolkit, GHOST, and applied to a number of models. As compared to the commercial implementation, we are able to achieve up to 20 times speedup in our experiments and sustain update rates over 1000Hz on a 400MHz Pentium II. In practice, our prototype implementation can a...

We present a new multi-dimensional data structure, which we call the skip quadtree (for point data in R 2) or the skip octree (for point data in R d, with constant d> 2). Our data structure combines the best features of two well-known data structures, in that it has the well-defined “box”-shaped regions of region quadtrees and the logarithmic-height search and update hierarchical structure of skip lists. Indeed, the bottom level of our structure is exactly a region quadtree (or octree for higher dimensional data). We describe efficient algorithms for inserting and deleting points in a skip quadtree, as well as fast methods for performing point location and approximate range queries. 1

. We propose a hardware-assisted visibility ordering algorithm. From a given viewpoint, a (back-to-front) visibility ordering of a set of objects is a partial order on the objects such that if object obstructs object , then precedes in the ordering. Such orderings are useful because they are the building blocks of other rendering algorithms such as direct volume rendering of unstructured grids. The traditional way to compute the visibility order is to build a set of visibility relations (e.g., ), and then run a topological sort on the set of relations to actually get the partial ordering. Our technique instead works by assigning a layer number to each primitive, which directly determines the visibility ordering. Objects that have the same layer number are independent, and can be placed anywhere with respect to each other. We use a simple technique which exploits a combination of the z- and stencil buffers to compute the layer number of each primitive...