## Approximating Polyhedra with Spheres for Time-Critical Collision Detection (1996)

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Venue: | ACM Transactions on Graphics |

Citations: | 177 - 1 self |

### BibTeX

@ARTICLE{Hubbard96approximatingpolyhedra,

author = {Philip M. Hubbard},

title = {Approximating Polyhedra with Spheres for Time-Critical Collision Detection},

journal = {ACM Transactions on Graphics},

year = {1996},

volume = {15},

pages = {179--210}

}

### Years of Citing Articles

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### Abstract

This paper presents a method for approximating polyhedral objects to support a timecritical collision-detection algorithm. The approximations are hierarchies of spheres, and they allow the time-critical algorithm to progressively refine the accuracy of its detection, stopping as needed to maintain the real-time 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 medial-axis 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 time-critical collision-detection algorithm to have acceptable accuracy, improving significantly on that possible with hierarchies built by previous techniques. The performance of the time-critical algorithm in this appli...

### Citations

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Citation Context ...f this algorithm, however, is that it returns insufficient information for many forms of collision response (it reports only one collision point even if multiple parts of the objects collide). Baraff =-=[2]-=- presents an algorithm that exploits inter-frame coherence to efficiently detect collisions between pairs of convex objects. Nonconvex objects must be treated as a union of convex pieces, which will c... |

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Citation Context ...ent a more modern variation that uses octrees. Three recent algorithms with narrow phases that use subdivision techniques---the work of Smith et al. [44], Garcia-Alonso et al. [14] and Ponamgi et al. =-=[36]-=----deserve particular attention. Although their broad phases create the temporal inaccuracy discussed in Section 2, these algorithms have the advantage that they achieve real-time performance for some... |

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Citation Context ... Samet and Tamminen [41] apply recursive subdivision to the four dimensions of space and time. Canny [8] derives quintic polynomials whose roots represent the time and location of collisions. Cameron =-=[7]-=- extends the approach of Samet and Tamminen, adding a mechanism that prunes parts of objects that cannot collide. Von Herzen et al. [50] use Lipshitz conditions to accelerate a form of binary search t... |

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Citation Context ... in our time-critical algorithm and we concentrate on the narrow phase in the remainder of this paper. An early narrow-phase algorithm of theoretical importance is described by Dobkin and Kirkpatrick =-=[10]-=-. This algorithm detects the collision of two polyhedra in O(log 2 n) time, where n is the total number of vertices in the polyhedra. A practical disadvantage of this algorithm, however, is that it re... |

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Citation Context ...itamura et al. [26] present a more modern variation that uses octrees. Three recent algorithms with narrow phases that use subdivision techniques---the work of Smith et al. [44], Garcia-Alonso et al. =-=[14]-=- and Ponamgi et al. [36]---deserve particular attention. Although their broad phases create the temporal inaccuracy discussed in Section 2, these algorithms have the advantage that they achieve real-t... |

43 |
tracing complex scenes
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Citation Context ...ierarchy for the characteristics of ray-object intersection tests, an approach which does not necessarily lead to the tightly fitting sphere hierarchies needed for collision detection. Kay and Kajiya =-=[25]-=-, for example, build bounding shapes that are cheap to intersect with rays, but these shapes do not have the rotational invariance necessary for moving objects. Goldsmith and Salmon [16], as another e... |

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Citation Context ...otion sickness more frequently when latency is high. When poor performance does not cause "simulator sickness," it can render interactive applications unresponsive and thus ineffective; Paus=-=ch et al. [35]-=-, for example, cite studies indicating that latency decreases operator performance in vehicle simulators. Full accuracy is also uncommon in the alternatives to the time-critical algorithm. Most tradit... |

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Citation Context ...ose roots represent the time and location of collisions. Cameron [7] extends the approach of Samet and Tamminen, adding a mechanism that prunes parts of objects that cannot collide. Von Herzen et al. =-=[50]-=- use Lipshitz conditions to accelerate a form of binary search through space and time. Duff [11] applies interval analysis to generalize the idea of recursive subdivision. Snyder et al. [45] combine i... |

31 |
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Citation Context ...fit around an object, though, as it can create artifacts like "caps" over concavities. The most successful approach for tightly approximating an object with spheres is the work of O'Rourke a=-=nd Badler [34]-=-. Their algorithm fits spheres to a polyhedron by anchoring big spheres to points on the polyhedron and shrinking the spheres until they just fit inside the polyhedron. Badler, O'Rourke and Toltzis [1... |

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Citation Context ...rigid object, which is not true of a precomputed octree or axis-aligned grid. The preprocess that builds the BSP tree can also optimize the tree's collision-localizing properties, as Naylor describes =-=[33]-=-. We are aware of no reports that subdivision algorithms outperform the BSP algorithm, but further comparisons between the time-critical algorithm and other approaches like the subdivision algorithms ... |

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Citation Context ...walk-throughs by Funkhouser and S'equin [13] and Maciel and Shirley [29], the IRIS Performer application framework of Rolhf and Helman [40] and the human-figure animation algorithm of Granieri et al. =-=[17]-=-. This paper extends our earlier paper [20], which introduced the idea of time-critical collision detection but presented a less sophisticated approach to hierarchies. Our companion papers [23, 22]---... |

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Citation Context ...-axis surfaces, spheres, time-critical computing. 1 Introduction Performance is paramount for most interactive graphics applications, such as virtual reality systems and vehicle simulators. As Brooks =-=[6]-=- discusses for the case of virtual reality, these applications will Copyright 1996, ACM. All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or clas... |

19 |
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Citation Context ... have faces lying roughly on the medial axis. Figure 5(b) shows an analogous 2D situation. This idea could work for nonpolyhedral objects, but this paper focuses on the polyhedral case. Goldak et al. =-=[15]-=- develop this idea into an algorithm. Their algorithm identifies the Voronoi vertices (corners of Voronoi cells) that lie on the medial-axis surface. In their description of the algorithm, Goldak et a... |

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15 | The use of awareness in collision prediction
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Citation Context ... between convex polyhedra. We use bounds on maximum acceleration to derive space-time bounds [20, 22], four-dimensional structures whose intersections predict bounding-sphere collisions. Foisy et al. =-=[12]-=- also use maximum accelerations to predict collisions, employing a queuing scheme to efficiently update the predictions. In our experience, adaptive techniques must clamp the time step at a minimum te... |

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An efficient bounding sphere
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Citation Context ... the set, P , of points on the polyhedron's surface (as defined in the previous section). Thus, s 12 is the bounding sphere for the forming points associated with s 1 and s 2 ; we use Ritter's method =-=[39]-=- to compute a nearly-optimal bounding sphere. Figure 7 illustrates a 2D example of merging. After the merge, s 12 stores the union of the forming points from s 1 and s 2 , and any future merge involvi... |

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11 |
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(Show Context)
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11 |
Realtime collision detection for virtual reality applications
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- 1993
(Show Context)
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10 |
How to construct the skeleton of CSG objects
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- 1990
(Show Context)
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8 | M.: Bintrees, CSG trees, and time - Samet, Tamminen - 1985 |

7 |
Hierarchical sphere model (HSM) and its application for checking an interference between moving robots
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(Show Context)
Citation Context ...the most challenging to meet, and it limits the applicability of previous work on hierarchies. Octree-like recursive subdivision is the basis for hierarchy-building algorithms described by Liu et al. =-=[28]-=- and by us in a previous paper [20]. An octree for an object defines a sphere-tree if each occupied octant is circumscribed by a sphere. A preprocess based on this approach has the advantages that it ... |

5 |
Hasida Toltzis. A spherical representation of a human body for visualizing movement
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(Show Context)
Citation Context ...4]. Their algorithm fits spheres to a polyhedron by anchoring big spheres to points on the polyhedron and shrinking the spheres until they just fit inside the polyhedron. Badler, O'Rourke and Toltzis =-=[1]-=- extend this approach to build two-level hierarchies, but they do not consider the more general hierarchies of greater depth necessary for a time-critical detection algorithm. Section 10 examines this... |

4 |
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Citation Context ...algorithms for 3D Voronoi diagrams. Bowyer [5] presents a straightforward algorithm that incrementally adds points to the diagram. This algorithm is not numerically robust, however, so Inagaki et al. =-=[24]-=- rephrase the algorithm to use topological properties rather than necessarily-inexact geometric computations. Unfortunately, these extensions compromise accuracy. As a remedy, we extend the algorithm ... |

4 |
CSG trees, and time
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