## Collision detection and response for computer animation (1988)

Venue: | Computer Graphics |

Citations: | 231 - 2 self |

### BibTeX

@INPROCEEDINGS{Moore88collisiondetection,

author = {Matthew Moore and Jane Wilhelms},

title = {Collision detection and response for computer animation},

booktitle = {Computer Graphics},

year = {1988},

pages = {289--298}

}

### Years of Citing Articles

### OpenURL

### Abstract

When several objects are moved about by computer ani-marion, there is the chance that they will interpenetrate. This is often an undesired state, particularly if the animation is seeking to model a realistic world. Two issues are involved: detecting that a collision has occurred, and responding to it. The former is fundamentally a kinematic problem, involving the positional relationship of objects in the world. The latter is a dynamic problem, in that it involves predicting behavior according to physical laws. This paper discusses collision detection and response in general, presents two collision detection algorithms, describes modeling collisions of arbi-trary bodies using springs, and presents an analytical collision response algorithm for articulated rigid bodies that conserves linear and angular momentum.

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Citation Context ...omewhat expensive both to code and to run, it is a considerable convenience for animators, particularly when more automated methods of motion control, such as dynamics or behavioral control, are used.=-=[24, 31]-=- This paper describes two collision detection algorithms. One algorithm deals with triangulated surface representations of objects, and is appropriate for flexible or rigid surfaces. The other algorit... |

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Citation Context ...selves, with each point P having up to 8 subtrees containing points in each of the octants of space defined by the P's position. This is an obvious generalization of the well known binary search tree.=-=[13, 14]-=- A pseudorandom number generator is used to scramble the order of insertion; in this way, Knuth assures us, J13] the tree will be almost balanced, i.e. the height of the octree will be O (logm) almost... |

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Citation Context ...inary step is used. Every point is compared to every triangle. The perpendicular distance of the point from the plane defined by the triangle is first derived, by substituting into the plane equation,=-=[25]-=- for the beginning and the end of the time step. If the sign of the perpendicular distance has not changed intersection is assumed not to have occurred. If the sign has changed, then the more expensiv... |

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Citation Context ... sphere test can be applied to every pair of polyhedraa, yielding an immediate "no collision" result in most cases. Many of these bounding box tests can even be eliminated by octree or voxel methods. =-=[4,9]-=- When a point is to be tested against a polyhedron, it chn first be compared to the polyhedron's bounding box, which will probably eliminate the need to compare it against all of the faces. The boundi... |

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Citation Context ...ensive proposition, particularly when large numbers of objects are involved and the objects have complex shapes. Collision detection has been extensively pursued in the fields of CAD/CAM and roboties,=-=[2, 3, 6,7, 11, 30]-=- and it is with some diffidence that we offer any more algorithms. Some published algorithms[2, 3] solve the problem in more generality (and at higher cost) than we have found to be necessary for comp... |

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Citation Context ...ensive proposition, particularly when large numbers of objects are involved and the objects have complex shapes. Collision detection has been extensively pursued in the fields of CAD/CAM and roboties,=-=[2, 3, 6,7, 11, 30]-=- and it is with some diffidence that we offer any more algorithms. Some published algorithms[2, 3] solve the problem in more generality (and at higher cost) than we have found to be necessary for comp... |

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Citation Context ...] The object's positions and orientations as functions of time may be interpolated from keyframes or parameter specification,[27] or may be the output of special computer programs written by the user,=-=[23]-=- or may be produced by physical simulation of the effect of internal, model-derived, and user-specified forces and torques.J1, 12, 16,29, 32] In any such scheme, the main questions when animating a si... |

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Citation Context ...er animation provides a number of methods for controlling object motion.[28] The object's positions and orientations as functions of time may be interpolated from keyframes or parameter specification,=-=[27]-=- or may be the output of special computer programs written by the user,[23] or may be produced by physical simulation of the effect of internal, model-derived, and user-specified forces and torques.J1... |

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Citation Context ...ensive proposition, particularly when large numbers of objects are involved and the objects have complex shapes. Collision detection has been extensively pursued in the fields of CAD/CAM and roboties,=-=[2, 3, 6,7, 11, 30]-=- and it is with some diffidence that we offer any more algorithms. Some published algorithms[2, 3] solve the problem in more generality (and at higher cost) than we have found to be necessary for comp... |

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Citation Context ...phics, Volume 22, Number 4, August 1988 This section develops the solution in stages. First, an analytical solution for the collision of two rigid bodies is presented; this result is due to MacMillan.=-=[17]-=- MacMillan's solution is extended to tree-like articulated rigid objects with revolute joints. Then, the restriction to wee-like objects is removed, and finally the method is extended to encompass joi... |

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Citation Context ... and easy to program. It applies equally well to rigid bodies (articulated or not) and to flexible bodies, whether modeled as point masses connected by springs, or by energy of deformation techniques.=-=[29]-=- The main problem with this method is that it is computationally expensive; stiffer springs mean stiffer equations, which require smaller time steps for accurate numerical integration. [8] The numeric... |

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Citation Context ...omewhat expensive both to code and to run, it is a considerable convenience for animators, particularly when more automated methods of motion control, such as dynamics or behavioral control, are used.=-=[24, 31]-=- This paper describes two collision detection algorithms. One algorithm deals with triangulated surface representations of objects, and is appropriate for flexible or rigid surfaces. The other algorit... |

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Citation Context ....i=O R "j=0 (V2 + 02 x p2-Vl-~l x pl)"k =0 These equations can be solved by standard Gauss-Jordan elimination with maximal pivoting,[5] LU-decomposition,[22] or by more advanced sparse matrix methods.=-=[20, 21]-=- It is possible at this point in the algorithm to find the solution for an elastic collision. The actual elasticity of the collision can be taken as the lower of the elasticities of the two colliding ... |

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Citation Context ... sphere test can be applied to every pair of polyhedraa, yielding an immediate "no collision" result in most cases. Many of these bounding box tests can even be eliminated by octree or voxel methods. =-=[4,9]-=- When a point is to be tested against a polyhedron, it chn first be compared to the polyhedron's bounding box, which will probably eliminate the need to compare it against all of the faces. The boundi... |

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Citation Context ...ases: computer animation, collision detection, collision response, analytical solution, dynamical simulation. 1. OVERVIEW Computer animation provides a number of methods for controlling object motion.=-=[28]-=- The object's positions and orientations as functions of time may be interpolated from keyframes or parameter specification,[27] or may be the output of special computer programs written by the user,[... |

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Citation Context ...e objects; the latter is designed to test for interpenetration of convex polyhedra. 2.1. Collision Detection for Flexible Surfaces Surfaces are modeled as a grid of points connected to form triangles.=-=[19]-=- Collisions between surfaces axe detected by testing for penetration of each vertex point through the planes of any triangle not including that vertex (thus, selfintersection of surfaces is detected).... |

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Citation Context ...in t. If further substitutions were made, the equations could be written in the form C 5t5 .l- c 4t4 -1-c 3 t3 -I-c2t2-I-Cl tl -I- Co= O Polynomials of order 5 and above cannot be solved analytically,=-=[10]-=- so a binary search technique is used to find approximate values for t.[5] Binary search is used because it is guaranteed to converge, and because, using economizing techniques described below, this a... |

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Citation Context ...llisions lies the great middle ground of partially rough friction. Modeling partial (i.e. realistic) friction can become quite complex; the simple treatment given here is from MacMillan[17] and McLean=-=[18]-=- and is sufficient to produce visually reasonable results. The coefficient of friction, 7, is the maximum allowed ratio of force parallel to the collision plane versus force perpendicular to that plan... |

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Citation Context ... the form C 5t5 .l- c 4t4 -1-c 3 t3 -I-c2t2-I-Cl tl -I- Co= O Polynomials of order 5 and above cannot be solved analytically,[10] so a binary search technique is used to find approximate values for t.=-=[5]-=- Binary search is used because it is guaranteed to converge, and because, using economizing techniques described below, this algorithm is not used often enough to warrant large efforts at optimization... |

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Citation Context ...t being tested. (This is necessary to avoid the point passing unnoticed completely through the box during the time step. A similar growth technique is used in the LozanoPerez path planning algorithm.)=-=[15]-=- The basic algorithm is O (nm), for n triangles and m points. Use of an octree[19] and bounding boxes can reduce the time to O (mlogm) to construct the octree, and O (n logm) to search it (assuming th... |

1 | Using Dynamic Analysis for Animation of Articulated Bodies - Wilhelms - 1987 |