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105
OBBTree: A hierarchical structure for rapid interference detection
 PROC. ACM SIGGRAPH, 171–180
, 1996
"... 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 and curved models. It precomputes a hierarchical representation of models using tightfitting oriented bo ..."
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Cited by 795 (48 self)
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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 and curved models. It precomputes a hierarchical representation of models using tightfitting oriented bounding box trees. At runtime, the algorithm traverses the tree and tests for overlaps between oriented bounding boxes based on a new 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 accurately detect all the contacts between large complex geometries composed of hundreds of thousands of polygons at interactive rates, almost one order of magnitude faster than earlier methods.
Approximating Polyhedra with Spheres for TimeCritical Collision Detection
 ACM Transactions on Graphics
, 1996
"... This paper presents a method for approximating polyhedral objects to support a timecritical collisiondetection algorithm. The approximations are hierarchies of spheres, and they allow the timecritical algorithm to progressively refine the accuracy of its detection, stopping as needed to maintain ..."
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Cited by 207 (1 self)
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This paper presents a method for approximating polyhedral objects to support a timecritical collisiondetection algorithm. The approximations are hierarchies of spheres, and they allow the timecritical algorithm to progressively refine the accuracy of its detection, stopping as needed to maintain the realtime performance essential for interactive applications. The key to this approach is a preprocess that automatically builds tightly fitting hierarchies for rigid and articulated objects. The preprocess uses medialaxis surfaces, which are skeletal representations of objects. These skeletons guide an optimization technique that gives the hierarchies accuracy properties appropriate for collision detection. In a sample application, hierarchies built this way allow the timecritical collisiondetection algorithm to have acceptable accuracy, improving significantly on that possible with hierarchies built by previous techniques. The performance of the timecritical algorithm in this appli...
Collision detection for interactive graphics applications
 IEEE Transactions on Visualization and Computer Graphics
, 1995
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Function Representation in Geometric Modeling: Concepts, Implementation and Applications
, 1995
"... This paper presents a state of the art report of our project, the main objectives of which are:  Categorization and summary of the geometric concepts required in a functionally based modeling environment;  Elaboration of a rich system of geometric operations closed on functionally represented ob ..."
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Cited by 152 (37 self)
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This paper presents a state of the art report of our project, the main objectives of which are:  Categorization and summary of the geometric concepts required in a functionally based modeling environment;  Elaboration of a rich system of geometric operations closed on functionally represented objects;  Treatment of multidimensional and particularly spacetime objects in a uniform manner; 6
Efficient Collision Detection for Animation and Robotics
, 1993
"... We present efficient algorithms for collision detection and contact determination between geometric models, described by linear or curved boundaries, undergoing rigid motion. The heart of our collision detection algorithm is a simple and fast incremental method to compute the distance between two ..."
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Cited by 121 (19 self)
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We present efficient algorithms for collision detection and contact determination between geometric models, described by linear or curved boundaries, undergoing rigid motion. The heart of our collision detection algorithm is a simple and fast incremental method to compute the distance between two convex polyhedra. It utilizes convexity to establish some local applicability criteria for verifying the closest features. A preprocessing procedure is used to subdivide each feature's neighboring features to a constant size and thus guarantee expected constant running time for each test. The expected constant time performance is an attribute from exploiting the geometric coherence and locality. Let n be the total number of features, the expected run time is between O( p n) and O(n) ...
Interactive Collision Detection
 In Proceedings of IEEE Symposium on Research Frontiers in Virtual Reality
, 1993
"... Collision detection and response can make a virtualreality application seem more believable. Unfortunately, existing collisiondetection algorithms are too slow for interactive use. We present a new algorithm that is not only fast but also interruptible, allowing an application to trade quality for ..."
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Cited by 96 (3 self)
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Collision detection and response can make a virtualreality application seem more believable. Unfortunately, existing collisiondetection algorithms are too slow for interactive use. We present a new algorithm that is not only fast but also interruptible, allowing an application to trade quality for more speed. Our algorithm uses simple fourdimensional geometry to approximate motion, and sets of spheres to approximate threedimensional surfaces. The algorithm allows a sample application to run 5 to 7 times faster than it runs with existing algorithms. 1 Introduction The physical world we live in is filled with solid objects. When solid objects collide, they do not penetrate one another (unless they flex or break). A computer simulation of a virtual world will seem more believable if it exhibits this property. We use the term collisionhandling algorithm for the part of the simulation system that enforces the solidness of objects. Researchers have developed a variety of collisionhand...
Incremental algorithms for collision detection between solid models
 IEEE Transactions on Visualization and Computer Graphics
, 1995
"... solid models ..."
Affine Arithmetic and its Applications to Computer Graphics
, 1993
"... We describe a new method for numeric computations, which we call affine arithmetic (AA). This model is similar to standard interval arithmetic, to the extent that it automatically keeps track of rounding and truncation errors for each computed value. However, by taking into account correlations betw ..."
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Cited by 77 (6 self)
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We describe a new method for numeric computations, which we call affine arithmetic (AA). This model is similar to standard interval arithmetic, to the extent that it automatically keeps track of rounding and truncation errors for each computed value. However, by taking into account correlations between operands and subformulas, AA is able to provide much tighter bounds for the computed quantities, with errors that are approximately quadratic in the uncertainty of the input variables. We also describe two applications of AA to computer graphics problems, where this feature is particularly valuable: namely, ray tracing and the construction of octrees for implicit surfaces.
Interval Methods for MultiPoint Collisions between TimeDependent Curved Surfaces
 Computer Graphics
, 1993
"... We present an efficient and robust algorithm for finding points of collision between timedependent parametric and implicit surfaces. The algorithm detects simultaneous collisions at multiple points of contact. When the regions of contact form curves or surfaces, it returns a finite set of points un ..."
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Cited by 67 (0 self)
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We present an efficient and robust algorithm for finding points of collision between timedependent parametric and implicit surfaces. The algorithm detects simultaneous collisions at multiple points of contact. When the regions of contact form curves or surfaces, it returns a finite set of points uniformly distributed over each contact region. Collisions can be computed for a very general class of surfaces: those for which inclusion functions can be constructed. Included in this set are the familiar kinds of surfaces and time behaviors encountered in computer graphics. We use a new interval approach for constrained minimization to detect collisions, and a tangency condition to reduce the dimensionality of the search space. These approaches make interval methods practical for multipoint collisions between complex surfaces. An interval Newton method based on the solution of the interval linear equation is used to speed convergence to the collision time and location. This method is mor...