P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Trans. on Visualization and Computer Graphics, 1(3):218-30, Sept. 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Traditional collision detection algorithms have required a large amount of geometrical intersection tests. To improve the efficiency of such algorithms, hierarchical representations of entities were developed to localise the areas where the actual collision occurred. These include sphere trees [14][21] 22] OBB trees (Oriented bounding boxes) 11] and hierarchies of k DOPs (Discrete Orientation Polytopes) 17] While speed and efficiency has been the main focus of such research, the issue of a constant frame rate is also paramount. This problem has been addressed in part by exploiting ....

....k DOPs (Discrete Orientation Polytopes) 17] While speed and efficiency has been the main focus of such research, the issue of a constant frame rate is also paramount. This problem has been addressed in part by exploiting coherence [5] and by using an interruptible collision detection algorithm [14]. The advantage of an interruptible algorithm is that the application has full control over the length of time that collision processing may take. However, inaccuracies in the handling of collisions may cause the viewer to perceive unrealistic behaviour of colliding entities. The following ....

[Article contains additional citation context not shown here]

Hubbard, P.M. Collision Detection for Interactive Graphics Applications. IEEE Transactions on Visualization and Computer Graphics. 1(3) 218-230. 1995.

....For general polygonal models, bounding volume hierarchies (BVH s) have been widely used for collision detection and separation distance queries. Di#erent hierarchies differ based on the underlying bounding volume or traversal schemes. These include the AABB trees [20] OBB trees [21] sphere trees [22], k dops [23] Swept Sphere Volumes [24] and convex hull based trees [25] 2.2 Penetration Depth Computation Several algorithms have been proposed to compute or estimate the PD. The Minkowski sums of two convex polytope can be computed in O(n ) worst case time by computing the overlaying ....

Philip M. Hubbard, "Collision detection for interactive graphics applications," IEEE Trans. Visualization and Computer Graphics, vol. 1, no. 3, pp. 218--230, Sept. 1995.

....objects, bounding volumes hierarchies are usually computed o#ine. Some typical Note that, actually, the velocities computations and the culling tests are interleaved in order to return earlier when a face is moving forwards. Hovever, all faces still have to be tested. examples of BVs are spheres[5], axis aligned bouding boxes (AABBs) oriented bounding boxes[4] OBBs) and k dops[6] In order to include the backward motion (BM) culling test in the BVHs traversal algorithm, this paper suggests to extend the BV BV overlap test in the following way: 1. If one of the two BVs has already been ....

P. M. Hubbard. Collision detection for interactive graphics applications. Ph.D. Thesis, April 1995.

.... the physical world is in general continuous over time, and many systems attempt to speed up collision checking by exploiting this temporal coherence, instead of repeating a full collision check ab initio at each time step [11] Swept volumes in space or space time have been used towards this goal [4, 9]. Though fixed time sampling is customary for motion integration, collisions tend to be rather irregularly spaced over time. If we know precisely the motion laws of the objects, then it makes sense to try to predict exactly when collisions will happen, instead of hoping to locate them with time ....

P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Trans. Visualization and Computer Graphics, 1(3):218--230, Sept. 1995.

.... of the covariance matrix of the point coordinates) and the other two directions are determined by another method (e.g. by computing the minimumarea bounding rectangle of the projection of the points into a plane orthogonal to the first chosen direction) Other generic shapes, such as a sphere [Hub95] a cone [Sam89] or a prism [FP87, BCG 96] were also used for maintaining a hierarchical data structure of point containers. Most of these heuristics require O(n) time and space for computing the bounding box (or another shape) but do not provide a guaranteed value (approximation factor of ....

.... of the point coordinates) and the other two directions are determined by another method (e.g. by computing the exact minimum area bounding rectangle of the projection of the points into a plane orthogonal to the first chosen direction see also below) Other generic shapes, such as a sphere [Hub95] a cone [Sam89] or a prism [FP87, BCG 96] were also used for maintaining a hierarchical data structure of point containers. Most of these heuristics require O(n) time and space for computing the bounding box (or another shape) but do not provide output with any guarantee (i.e. approximation ....

P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Trans. Visualization and Computer Graphics, 1(3):218--230, September 1995.

....have been widely used for collision detection and separation (or Euclidean) distance queries. They localize the problem and use the divide and conquer paradigm. BVHs often differ based on the underlying bounding volume or traversal schemes. These include the OBB trees [GLM96] sphere trees [Hub95] k dops [KHM 98] and convex hull based trees [EL01] Due to the global nature of PD problem, none of them can be directly used for PD computation between non convex models. 2.2 Penetration Depth Computation A few efficient algorithms to compute the penetration depth (PD) between convex ....

Philip M. Hubbard. Collision detection for interactive graphics applications. IEEE Trans. Visualization and Computer Graphics, 1(3):218--230, September 1995.

....involved in each stage can be found in [Zac00, Zac01] 2.1 DOP trees At the last stage of the collision detection pipeline, we are given one pair of objects and have to determine their collision status. Research has shown that hierarchical algorithms can solve this problem very efficiently [Hub95, OD99, GLM96, Zac97] Here, we will describe only one such hierarchical algorithm, namely the DOP tree. It is based on a hierarchical BV tree, where each node is enclosed by a discretely oriented polytope (DOP) see [Zac00] for further details. As with other hierarchical collision detection ....

P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Transactions on Visualization and Computer Graphics, 1(3):218--230, September 1995. ISSN 1077-2626.

....for instance HTML or XML, and is either geared for server push or client pull. VR (Virtual Reality) 8, 7, 15] is similarly multimodal, but adds input and output devices giving the user three dimensional orientation or tactile sensations. Coordination must be interfaced with collision control [17] in virtual spaces. Code comprises application specific structured documents such as Postscript, MIME email [4] or L A T E X. A device is a hardware unit serving as access point, such as a camera. A multimedia conference is a conference using multimodal resource types. Usage determines, if the ....

P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Trans. on Visualization and Computer Graphics, 1(3):218--30, Sept. 1995.

....review, but instead describe the work most relevant to our approach. Many of the skeleton construction methods are based on one of several general approaches: iterative or parallel thinning [23] analytical calculation of the medial axis (Delaunay triangulation and calculation of Voronoi regions [26, 21]) and calculation of a Distance Map and its Medial Axis Transform (MAT) 3, 13, 1, 25, 36, 30, 22, 33, 12, 27] Our implementation is of the last type, and thus this section focuses on MAT based methods. MAT based methods belong to a class of approaches that represent a shape by a spine and a ....

....is an integral part of any animated and interactive virtual environment. As dynamic objects move through the virtual world, intersection tests must be performed quickly between the moving object and all other objects near it. Many collision detection systems utilize a hierarchy of representations [21, 8, 24, 28]. In these approaches, intersection testing occurs in two main phases: a broad phase followed by a narrow phase [21] In the broad phase, intersection tests are made against simplified approximations of the object. If a possible intersection is detected from these approximate tests, the actual ....

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P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Transactions on Visualization and Computer Graphics, 1:3:218--230, September 1995.

....structure: Algorithm 3. 1 Generic rigid body simulation algorithm genericSimulate(objects : O) while simulating for all o # O step(o) C # potentialCollisions(O) for all c # C if colliding(c) processCollision(c) Detailed descriptions of variations on this approach have appeared in [39, 40, 45, 35, 60] and the algorithm is implicitly assumed for many collision detection papers [19, 64, 88, 91, 93] There are three basic optimizations described in the literature: 38 . Dynamically choose the time step by attempting to predict when the next collision might occur [40, 45, 62] Identify ....

....appeared in [39, 40, 45, 35, 60] and the algorithm is implicitly assumed for many collision detection papers [19, 64, 88, 91, 93] There are three basic optimizations described in the literature: 38 . Dynamically choose the time step by attempting to predict when the next collision might occur [40, 45, 62]. Identify potential collisions without checking every pair of objects. Several methods exist: Cohen et al. use sorted lists of bounding volumes [19] Mirtich uses spatial hashing of bounding volumes [60] and several authors have used octrees or similar structures [88, 91, 93] Improve ....

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Philip M. Hubbard. Collision detection for interactive graphics applications. IEEE Transactions on Visualization and Computer Graphics, 1(3):218--230, Sept 1995.

....wrapped around the geometric model of the duct to make it look more realistic. B. Collision Detection An important part of surgical instrument soft tissue modeling is the fast collision detection algorithms. Although collision detection has been extensively studied in computer graphics ( 14] [16]) its implementation with haptic devices is not straightforward, as discussed in Ho et al. 17] During real time simulations, we check the collisions: 1) between the forceps and the catheter as well as the duct and 2) between the catheter and the duct. For the purposes of detecting collisions ....

P. Hubbard, "Collision detection for interactive graphics applications," IEEE Trans. Visual. Comput. Graphics, vol. 1, pp. 219--230, 1995.

....at xed moments. Of course, over a timestep, the BVHs have the same motion M than the primitives they contain. 3.1 Sphere trees Various examples of bounding volumes have been studied in the literature, most of them for discrete collision detection. Well known examples are spheres [7, 3], axis aligned bounding boxes, k DOPs [4] spherical shells [11] or oriented bounding boxes [2] It was chosen to use spheres because of their adaptability to our continuous case. Two spheres intersect if and only if the distance d between their center is less than the sum of their radius. Let c ....

....a valid collision time must be in [0; 1] Figure 1: The teapot is half inside the cube s large leaf sphere, resulting in many irrelevant elementary tests. To avoid this situation, all the leaf spheres in a scene have to be approximately the same size. Various methods exist to build sphere trees[3]. We use an approach similar to that proposed by Quinlan[7] and detailed in Ruspini[9] In this bottomup approach, an object is rst covered by small spheres, which will be the leaf spheres of the nal tree. All of these small spheres have the same user de ned size, which isn t a priori related to ....

P. M. Hubbard. Collision detection for interactive graphics applications. Ph.D. Thesis, April 1995.

....for convex polyhedra [16, 3, 8] Almost all approaches for general, non convex objects utilize some sort of BV hierarchy. A few nonhierarchical approaches have been taken as well. GarciaAlonso et al. 7] partition the set of polygons of an object by a uniform grid. Sphere trees were developed by [13, 14, 19]. Gottschalk et al. 11] developed a bounding box hierarchy based on oriented boxes (OBBs) Its box overlap test is much more expensive than for DOPs. Aligned Box Trees have been presented in [21] Barequet et al. 1] presented some theoretical results on a class of BV hierarchies called BOXTREE, ....

P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Transactions on Visualization and Computer Graphics, 1(3):218--230, Sept. 1995. ISSN 1077-2626.

....SGI R10000 194 MHz. All times are (unless otherwise noted) in millseconds. 2 Related work Research so far has mainly focused on algorithms for the collision detection problem, given a pair of objects. Hierarchical algorithms for polygonal objects have been presented by [GLM96, KHM 98, Zac98, Hub95, OD99, NAT90] Non hierarchical approaches have been presented by [MPT99, Gei00] Incremental convex algorithms have been presented by [CLMP95, vdB99, Chu96] Algorithms for reducing the number of pairs to be tested have been presented by [CLMP95, BF79, PS90, YW93, Hub93] A system solving the ....

....explained above, that combining a grid with a subsequent convex algorithm (such as our separating planes algorithm) would improve the performance of the neighbor finding stage for large object numbers. Besides comparing further hierarchical algorithms using our benchmark suite (like sphere trees [Hub95] non hierarchical algorithms like [MPT99, Gei00] should be considered as well. In order to do that fairly, errors resulting from different representations must be taken into account. ....

Hubbard, P. M. Collision detection for interactive graphics applications. IEEE Transactions on Visualization and Computer Graphics, 1(3):218--230, September 1995. ISSN 1077-2626.

....To reduce it further, a bounding box collision detection technique may be employed[33] Narrow Phase Collision Detection reduces the set of candidate object pairs to the final set of collision events. This requires a sophisticated object collision detection algorithm, such as that seen in [27, 24, 33]. These techniques all require extensive knowledge of the object model (e.g. polynomials and their normals) CHAPTER 3. NAVL SYSTEM ARCHITECTURE 50 Broad Phase Collision Detection Narrow Phase Collision Detection Database Traversal Modeling Transformation Trival Object Culling ....

....simply re rasterize the previous image[19] CHAPTER 3. NAVL SYSTEM ARCHITECTURE 51 rather than perform a complete transformation and projection. For collision detection, coherence allows the collision detection mechanism to disregard object pairs that are known not to be within collision distance[27, 24] 3.6 Chapter Summary This chapter introduces the NAVL system architecture. The architecture is made up of three components: 1. Network Architecture 2. Object Distribution and Coherency Model 3. Rendering and Collision Detection The network architecture uses a distributed client server ....

Philip M. Hubbard. Collision Detection for Interactive Graphics Applications. PhD thesis, Department of Computer Science, Brown University, October 1993.

....used for path planning purposes in the platform Move3D (see [23] KCD allows efficient planning of guaranteed collision free paths. We report experimental results in Section 4, before concluding. 2 Related Work Extensive and recent surveys on collision detection are published (e.g. 17] 12] [10]) Software of several collision detectors are freely available for research purposes. In this section we concentrate on the observations we made while reading about and experimenting with collision detection algorithms in the frame of path planning applications in industrial models. Collision ....

P. M. Hubbard. Collision Detection for Interactive Graphics Applications. PhD thesis, Department of Computer Science, Brown University, October 1994.

....a term coined by [Kitamura et al. 1994] refers to any collision detection method which first performs one or more iterations of approximate tests to identify interfering objects in the entire workspace and then performs a more accurate test to identify the object parts causing interference. [Hubbard 1995] and [Cohen 1995] also propose hybrid algorithms for collision detection. The former refers to the two levels of the algorithm as the broad phase, where approximate intersections are detected, and the narrow phase, where exact collision detection is performed. Such an approach is essential for ....

....consist of oriented bounding boxes and spherical shells, which enclose curved surfaces such as Bezier patches and NURBS. They are particularly suited to collision detection between the higherorder surface representations discussed in the previous section. 2.2. 3 Broad Phase Collision Detection [Hubbard 1995] highlights three potential weaknesses of collision detection algorithms. The most serious of these is the all pairs weakness discussed above, where every object in the scene must be compared with every other one at every collision timestep of the animation. Most research has concentrated on ....

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Hubbard, P.M. (1995) Collision Detection for Interactive Graphics Applications. IEEE Trans. on Vis. and Comp. Graphs. 1(3) 218-230.

....volumes that represent the solids trajectories during a time step rather than between static instances of the solids. In the context of a large environment with lots of moving objects, using space time bounds on the object s motion may lead to the quick rejection of a number of intersection tests [9, 6, 7]. In previous works on laparoscopic surgery [3] a dynamic collision detection was performed by testing for an intersection between the segment traversed by the tool extremity during a time step and the polygonal mesh representing the organ. A bucket data structure discretizing the organ s ....

P. Hubbard. Collision detection for interactive graphics applications. IEEE Transactions on Visualization and Computer Graphics, 1(3):218--230, 1995.

....Traditional collision detection algorithms have required a large amount of geometrical intersection tests. To improve the efficiency of such algorithms, hierarchical representations of entities were developed to localise the areas where the actual collision occurred. These include sphere trees [14][20] 21] OBB trees (Oriented bounding boxes) 11] and hierarchies of k DOPs (Discrete Orientation Polytopes) 17] While speed and efficiency has been the main focus of such research, the issue of a constant frame rate is also paramount. This problem has been addressed in part by exploiting ....

....k DOPs (Discrete Orientation Polytopes) 17] While speed and efficiency has been the main focus of such research, the issue of a constant frame rate is also paramount. This problem has been addressed in part by exploiting coherence [5] and by using an interruptible collision detection algorithm [14]. The advantage of an interruptible algorithm is that the application has full control over the length of time that the collision detection algorithm may take. It can then use this to control frame rate, keeping it constant and high. The disadvantages of this approach are that inaccuracies in ....

[Article contains additional citation context not shown here]

Hubbard, P.M. (1995) Collision Detection for Interactive Graphics Applications. IEEE Transactions on Visualization and Computer Graphics. 1(3) 218-230.

....robotics, for instance, checking for collision between complex geometric models is frequently a computational bottleneck. Therefore, collision detection packages commonly use simple bounding objects, such as axis aligned bounding boxes [4, 14, 16] discrete oriented polytopes [9, 13] or spheres [10], to quickly eliminate pairs whose bounding objects are collision free. Since intersecting simple bounding objects is computationally more ecient than checking objects themselves, this heuristic performs well in practice. Suri, Hubbard and Hughes [21] and Zhou and Suri [23] give theoretical ....

P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Trans. Visualization and Computer Graphics, 1(3), pp. 218-230, 1995.

....robotics, for instance, checking for collision between complex geometric models is frequently a computational bottleneck. Therefore, collision detection packages commonly use simple bounding objects, such as axis aligned bounding boxes [4, 14, 16] discrete oriented polytopes [9, 13] or spheres [10], to quickly eliminate pairs whose bounding objects are collision free. Since intersecting simple bounding objects is computationally more ecient than checking objects themselves, this heuristic performs well in practice. Suri, Hubbard and Hughes [21] and Zhou and Suri [23] give theoretical ....

P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Trans. Visualization and Computer Graphics, 1(3), pp. 218-230, 1995.

....include [Ba 96, Be 90, Za 94] We also give [Ab 96] as an example of a highly successful industrial implementation of this collision detection paradigm at least, when the environment is static and objects do not move against each other. Octrees were used in [Mo 88, No 89] sphere trees in [Hu 95]. The above mentioned SIGGRAPH 96 published yet another paper [Go 96] with a very promising collision detection performance. The method uses suc2 cessfully hierarchies of BBs in dynamic environments. The method does not enforce an alignment of the boxes: rather then realigning boxes after each ....

P.M. Hubbard. Collision detection for interactive graphics applications. IEEE Transactions of Visualization and Computer Graphics, pp. 218-230, 1995.

.... of the point coordinates) and the other two directions are determined by another method (e.g. by computing the exact minimum area bounding rectangle of the projection of the points into a plane orthogonal to the first chosen direction see also below) Other generic shapes, such as a sphere [Hubbard 1995], a cone [Samet 1989] or a prism [Faugeras and Ponce 1987; Barequet et al. 1996] were also used for maintaining a hierarchical data structure of point containers. Most of these heuristics require O(n) time and space for computing the bounding box (or another shape) but do not provide output with ....

Hubbard, P. M. 1995. Collision detection for interactive graphics applications. IEEE Trans. on Visualization and Computer Graphics 1, 3 (September), 218--230.

....between convex polytopes [GJK88, Bar90, LC91, DHKS93, GHZ99, EL00] Hierarchical Approaches: Some of the commonly used algorithms for general polygonal models are based on hierarchical data structures. These include bounding volume hierarchies where the bounding volume may correspond to a sphere [Hub95] axis aligned boundingbox, oriented bounding box [GLM96] a k DOP [KHM 98] or a swept sphere volume [LGLM99] These algorithms can only compute all pairs of overlapping triangles and not the intersection region. Algorithms for separation distance computation based on boundingvolume ....

P. M. Hubbard. Collision detection for interactive graphics applications. IEEETransactions on Visualization andComputer Graphics, 1(3):218-- 230, September 1995.

....depicts a few representative runs of our experiments, based on two methods: the mesh based method, and the bounding volume hierarchy method. Details of our algorithms, implementation issues, and experimental results are reported in [3, 4] For other recent related work on collision detection, see [1, 2, 6, 7] 2 Mesh Based Method This method is motivated by recent results on efficient ray segment shooting queries using meshes (triangulations) of low stabbing number [5, 8] The complexity of an intersection query with an object F is proportional to the number of cells (tetrahedra) of the mesh that are ....

P. M. Hubbard. Collision detection for interactive graphics applications IEEE Transactions of Visualization and Computer Graphics, 1:218--230, 1995.

....6 respectively. 2 Collision Detection Hybrid collision detection [17] refers to any collision detection method which first performs approximate tests to identify interfering objects in the entire workspace, and then performs more accurate tests to identify the object parts causing interference. [12] and [4] also propose hybrid algorithms for collision detection. The former refers to the two levels of the algorithm as the broad phase, where approximate intersections are detected, and the narrow phase, where exact collision detection is performed. Such an approach is essential for acceptable ....

....problem that arises is the O(N 2 ) problem of detecting collisions between all N objects. The aim of the broadphase of a collision detection algorithm is to quickly eliminate objects which could not possibly be intersecting. 4 dimensional structures called space time bounds have been used in [12] and [2] to provide a conservative estimate of where an object may be in the future. The fourth dimension represents time. Overlaps of these bounds trigger the narrow phase. Using the space time bounds, attention is focused on the objects that are likely to collide, and those far away can be ....

P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Transactions on Visualization and Computer Graphics, 1(3):218--230, September 1995. ISSN 1077-2626.

.... of the covariance matrix of the point coordinates) and the other two directions are determined by another method (e.g. by computing the minimum area bounding rectangle of the projection of the points into a plane orthogonal to the first chosen direction) Other generic shapes, such as a sphere [Hub95] a cone [Sam89] or a prism [PF87, BCG 96] were also used for maintaining a hierarchical data structure of point containers. Most of these heuristics require O(n) time and space for computing the bounding box (or another shape) but did not provide a guaranteed value (approximation factor of ....

P.M. Hubbard, Collision detection for interactive graphics applications, IEEE Trans. Visualization and Computer Graphics, 1:218--230, 1995.

....the efficiency of such algorithms, hierarchical representations of entities were generated, to localise the areas where the actual collision occurred. Such representations approximate the topology of an object at different levels of detail. These include Sphere Trees [Palmer and Grimsdale 1995][Hubbard 1995,1996] Quinlan 1994] OBB trees (Oriented Bounding Boxes) Gottschalk et al. 1995] ShellTrees [Krishnan et al. 1998] and hierarchies of k DOPs (Discrete Orientation Polytopes) Klosowski et al. 1997] Most of these algorithms are actually hybrid algorithms, involving two or more phases of ....

....approximating tree as we need them, and test for intersections between them For the narrow phase of our algorithm, we have developed an interruptible algorithm based on sphere trees. We have adapted a staircase algorithm from [Palmer and Grimsdale 1995] and have made it interruptible, as in [Hubbard 1995]. The sphere trees are generated during a pre processing phase, each tress consisting of 4 levels of spheres, each level representing a closer approximation to the surface of the object (see Figure. 2) 3.3.1 Building Sphere Trees [Hubbard 1996] lists three requirements for generating ....

[Article contains additional citation context not shown here]

Hubbard, P.M. (1995) Collision Detection for Interactive Graphics Applications. IEEE Transactions on Visualization and Computer Graphics. 1(3) 218-230.

.... the physical world is in general continuous over time, and many systems attempt to speed up collision checking by exploiting this temporal coherence, instead of repeating a full collision check ab initio at each time step [12] Swept volumes in space or space time have been used towards this goal [3, 10]. Though fixed time sampling is customary for motion integration, collisions tend to be rather irregularly spaced over time. If we know precisely the motion laws of the objects, then it makes sense to try to predict exactly when collisions will happen, instead of hoping to locate them with time ....

P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Trans. Visualization and Computer Graphics, 1(3):218--230, Sept. 1995.

....bounding boxes. Edelsbrunner [7] and Mehlhorn [23] describe provably efficient algorithms for axis aligned bounding boxes in d space, algorithms that find the k intersecting pairs in O(n log d Gamma1 n k) time and O(n log d Gamma2 n) space. A variety of heuristic methods are used in practice [2, 16, 18], and empirical evidence suggest that these algorithms perform well; the sweep and prune algorithm implemented in the I COLLIDE package of Cohen et al. 2] currently appears to be the method of choice. It might seem desirable to use a broad phase that replaces axis aligned bounding boxes with ....

P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Trans. Visualization and Computer Graphics, 1(3), pp. 218--230, 1995.

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P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Trans. on Visualization and Computer Graphics, 1(3):218-30, Sept. 1995.

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P.M. Hubbard. Collision detection for interactive graphics applications. IEEE Transactions of Visualization and Computer Graphics, pp. 218-230, 1995.

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P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Transactions on Visualization and Computer Graphics, 1 (3):218--230, September 1995. ISSN 1077-2626.

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P.M. Hubbard. Collision Detection for Interactive Graphics Applications. PhD Thesis, Computer Science Dept., Brown University, Providence, RI, 1995.

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P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Transactions on Visualization and Computer Graphics, 1(3):218--230, September 1995. ISSN 1077-2626.

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Philip Hubbard. Collision Detection for Interactive Graphics Applications. Ph.D. thesis, Brown University. 1995.

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P. M. Hubbard, Collision detection for interactive graphics applications, IEEE Transactions on Visualization and Computer Graphics, 1 (1995), pp. 218--230.

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HUBBARD P. M.: Collision detection for interactive graphics applications. IEEE Trans. Visualization and Computer Graphics 1, 3 (Sept. 1995), 218--230. 2

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P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Trans. Visualization and Computer Graphics, 1(3):218-230, September 1995.

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P. Hubbard. Collision Detection for Interactive Graphics Applications. PhD thesis, Brown University, 1994.

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P.M. Hubbard, "Collision Detection for Interactive Graphics Applications," IEEE Transactions on Visualization and Computer Graphics, 1 (3), 218-230, 1995.

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Hubbard, P. M. Collision Detection for Interactive Graphics Applications. IEEE Transactions on Visualization and Computer Graphics. Vol 1. No 3. pp 218-230. September, 1995.

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P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Transactions on Visualization and Computer Graphics, 1(3):218--230, September 1995. ISSN 1077-2626. 3

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P.M. Hubbard, "Collision detection for interactive graphics applications", IEEE Trans. Visualization and Computer Graphics, 1 pp. 218--230 (1995).

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Hubbard, P.M. Collision Detection for Interactive Graphics Applications. IEEE Transactions on Visualisation and Computer Graphics. 1(3) 218-230.

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P.M. Hubbard. "Collision detection for interactive graphics applications", PhD thesis, Department of Computer Science, Brown University (1994).

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P. M. Hubbard. Collision detection for interactive graphics applications. Ph.D. Thesis, April 1995. 4

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P.M. Hubbard. Collision Detection for Interactive Graphics Applications. IEEE Transactions on Visualization and Computer Graphics, 1(3):218--230, 1995. 2

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Hubbard, P. (1995). Collision Detection for Interactive Graphics Applications. IEEE Transactions on Visualization and Computer Graphics, 1(3), 219-230.

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Hubbard P.M. - Collision Detection for Interactive Graphics Applications. IEEE Transactions on Visualization and Computer Graphics. 1(3) pp. 218230. (1995)

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