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31
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 177 (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
"... Solid objects in the real world do not pass through each other when they collide. Enforcing this property of "solidness" is important in many interactive graphics applications; for example, solidness makes virtual reality more believable, and solidness is essential for the correctness of vehicle sim ..."
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Cited by 174 (5 self)
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Solid objects in the real world do not pass through each other when they collide. Enforcing this property of "solidness" is important in many interactive graphics applications; for example, solidness makes virtual reality more believable, and solidness is essential for the correctness of vehicle simulators. These applications use a collisiondetection algorithm to enforce the solidness of objects. Unfortunately, previous collisiondetection algorithms do not adequately address the needs of interactive applications. To work in these applications, a collisiondetection algorithm must run at realtime rates, even when many objects can collide, and it must tolerate objects whose motion is specified "on the fly" by a user. This dissertation describes a new collisiondetection algorithm that meets these criteria through approximation and graceful degradation, elements of timecritical computing. The algorithm is not only fast but also interruptible, allowing an application to trade accuracy ...
Interval Analysis For Computer Graphics
 Computer Graphics
, 1992
"... This paper discusses how interval analysis can be used to solve a wide variety of problems in computer graphics. These problems include ray tracing, interference detection, polygonal decomposition of parametric surfaces, and CSG on solids bounded by parametric surfaces. Only two basic algorithms are ..."
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Cited by 132 (2 self)
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This paper discusses how interval analysis can be used to solve a wide variety of problems in computer graphics. These problems include ray tracing, interference detection, polygonal decomposition of parametric surfaces, and CSG on solids bounded by parametric surfaces. Only two basic algorithms are required: SOLVE, which computes solutions to a system of constraints, and MINIMIZE, which computes the global minimum of a function, subject to a system of constraints. We present algorithms for SOLVE and MINIMIZE using interval analysis as the conceptual framework. Crucial to the technique is the creation of "inclusion functions" for each constraint and function to be minimized. Inclusion functions compute a bound on the range of a function, given a similar bound on its domain, allowing a branch and bound approach to constraint solution and constrained minimization. Inclusion functions also allow the MINIMIZE algorithm to compute global rather than local minima, unlike many other numerica...
3D Collision Detection: A Survey
 Computers and Graphics
, 2000
"... Many applications in Computer Graphics require fast and robust 3D collision detection algorithms. These algorithms can be grouped into four approaches: spacetime volume intersection, swept volume interference, multiple interference detection and trajectory parameterization. While some approaches ar ..."
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Cited by 84 (3 self)
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Many applications in Computer Graphics require fast and robust 3D collision detection algorithms. These algorithms can be grouped into four approaches: spacetime volume intersection, swept volume interference, multiple interference detection and trajectory parameterization. While some approaches are linked to a particular object representation scheme (e.g., spacetime volume intersection is particularly suited to a CSG representation), others do not. The multiple interference detection approach has been the most widely used under a variety of sampling strategies, reducing the collision detection problem to multiple calls to static interference tests. In most cases, these tests boil down to detecting intersections between simple geometric entities, such as spheres, boxes aligned with the coordinate axes, or polygons and segments. The computational cost of a collision detection algorithm depends not only on the complexity of the basic interference test used, but also on the ...
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 83 (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...
A Framework For Efficient Minimum Distance Computations
, 1998
"... In this paper we present a framework for minimum distance computations that allows efficient solution of minimum distance queries on a variety of surface representations, including sculptured surfaces. The framework depends on geometric reasoning rather than numerical methods and can be implemented ..."
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Cited by 64 (11 self)
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In this paper we present a framework for minimum distance computations that allows efficient solution of minimum distance queries on a variety of surface representations, including sculptured surfaces. The framework depends on geometric reasoning rather than numerical methods and can be implemented straightforwardly. We demonstrate performance that compares favorably to other polygonal methods and is faster than reported results for other methods on sculptured surfaces. 1 Introduction We introduce a framework for minimum distance calculations that applies well to both polygonal and parametric model representations (Figure 1). The resulting methods scale well with problem size, have timecritical properties, and are interactive for large polygonal models and sculptured surfaces. In robotics, minimum distance queries have been used in path planning [2], path modification [25], and collision avoidance [15]. In computer graphics, minimum distance computations have played roles in physical...
Sphere Tracing: A Geometric Method for the Antialiased Ray Tracing of Implicit Surfaces
 The Visual Computer
, 1994
"... Sphere tracing is a new technique for rendering implicit surfaces using geometric distance. Distancebased models are common in computeraided geometric design and in the modeling of articulated figures. Given a function returning the distance to an object, sphere tracing marches along the ray towar ..."
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Cited by 61 (2 self)
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Sphere tracing is a new technique for rendering implicit surfaces using geometric distance. Distancebased models are common in computeraided geometric design and in the modeling of articulated figures. Given a function returning the distance to an object, sphere tracing marches along the ray toward its first intersection in steps guaranteed not to penetrate the implicit surface. Sphere tracing is particularly adept at rendering pathological surfaces. Creased and rough implicit surfaces are defined by functions with discontinuous or undefined derivatives. Current root finding techniques such as LG surfaces and interval analysis require periodic evaluation of the derivative, and their behavior is dependent on the behavior of the derivative. Sphere tracing requires only a bound on the magnitude of the derivative, robustly avoiding problems Manuscript, July 1994. Recommended for publication: The Visual Computer. 570 where the derivative jumps or vanishes. This robustness and scope ...
Timewarp rigid body simulation
 IN PROC. OF ACM SIGGRAPH
, 2000
"... The traditional highlevel algorithms for rigid body simulation work well for moderate numbers of bodies but scale poorly to systems of hundreds or more moving, interacting bodies. The problem is unnecessary synchronization implicit in these methods. Jefferson´s timewarp algorithm (Jefferson 85) is ..."
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Cited by 50 (0 self)
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The traditional highlevel algorithms for rigid body simulation work well for moderate numbers of bodies but scale poorly to systems of hundreds or more moving, interacting bodies. The problem is unnecessary synchronization implicit in these methods. Jefferson´s timewarp algorithm (Jefferson 85) is a technique for alleviating this problem in parallel discrete event simulation. Rigid body dynamics, though a continuous process, exhibits many aspects of a discrete one. With modification, the timewarp algorithm can be used in a uniprocessor rigid body simulator to give substantial performance improvements for simulations with large numbers of bodies. This paper describes the limitations of the traditional highlevel simulation algorithms, introduces Jefferson´s algorithm, and extends and optimizes it for the rigid body case. It addresses issues particular to rigid body simulation, such as collision detection and contact group management, and describes how to incorporate these into the timewarp framework. Quantitative experimental results indicate that the timewarp algorithm offers significant performance improvements over traditional highlevel rigid body simulation algorithms, when applied to systems with hundreds of bodies. It also helps pave the way to parallel implementations, as the paper discusses.
Fast continuous collision detection between rigid bodies
 Proc. of Eurographics (Computer Graphics Forum
, 2002
"... This paper introduces a fast continuous collision detection technique for polyhedral rigid bodies. As opposed to most collision detection techniques, the computation of the first contact time between two objects is inherently part of the algorithm. The method can thus robustly prevent objects interp ..."
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Cited by 49 (10 self)
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This paper introduces a fast continuous collision detection technique for polyhedral rigid bodies. As opposed to most collision detection techniques, the computation of the first contact time between two objects is inherently part of the algorithm. The method can thus robustly prevent objects interpenetrations or collisions misses, even when objects are thin or have large velocities. The method is valid for general objects (polygon soups), handles multiple moving objects and acyclic articulated bodies, and is efficient in low and high coherency situations. Moreover, the method can be used to speed up existent continuous collision detection methods for parametric or implicit rigid surfaces. The collision detection algorithms have been successfully coupled to a realtime dynamics simulator. Various experiments are conducted that show the method’s ability to produce highquality interaction (precise objects positioning for example) between models up to tens of thousands of triangles, which couldn’t have been performed with previous continuous methods. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: Animation Virtual Reality 1.
Making Them Behave: Cognitive Models for Computer Animation
, 1998
"... For applications in computer game development and character animation, recent work in behavioral animation has taken impressive steps toward autonomous, selfanimating characters. It remains difficult, however, to direct autonomous characters to perform specific tasks. We propose a new approach to h ..."
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Cited by 41 (7 self)
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For applications in computer game development and character animation, recent work in behavioral animation has taken impressive steps toward autonomous, selfanimating characters. It remains difficult, however, to direct autonomous characters to perform specific tasks. We propose a new approach to highlevel control in which the user gives the character a behavior outline, or “sketch plan”. The behavior outline specification language has syntax deliberately chosen to resemble that of a conventional imperative programming language. In terms of functionality, however, it is a strict superset. In particular, a behavior outline need not be deterministic. This added freedom allows many behaviors to be specified more naturally, more simply, more succinctly and at a much higherlevel than would otherwise be possible. The character has complete autonomy to decide on how to fill in the necessary missing details. The success of our approach rests heavily on our use of a rigorous logical language, known as the situation calculus. The situation calculus is wellknown, simple and intuitive to understand. The basic idea is that a character views its world as a sequence of “snapshots ” known as situations. An understanding of how the world can change from one situation to another can then be given to the character by describing what the effect of performing each given action would be. The character can use this knowledge to keep track of its world and to work out which actions to do next in order to attain its goals. The version of the situation calculus we use incorporates a new approach to representing epistemic fluents. The approach is based on interval arithmetic and addresses a number of difficulties in implementing