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Geometric collisions for time-dependent parametric surfaces

Von Herzen, Brian and Barr, Alan H. and Zatz, Harold R. (1990) Geometric collisions for time-dependent parametric surfaces. ACM SIGGRAPH Computer Graphics, 24 (4). pp. 39-48. ISSN 0097-8930. https://resolver.caltech.edu/CaltechAUTHORS:20161102-170650293

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Abstract

We develop an algorithm to detect geometric collisions between pairs of time-dependent parametric surfaces. The algorithm works on surfaces that are continuous and have bounded derivatives, and includes objects that move or deform as a function of time. The algorithm numerically solves for the parametric values corresponding to coincident points and near-misses between the surfaces of two parametric functions.Upper bounds on the parametric derivatives make it possible to guarantee the successful detection of collisions and near-misses; we describe a method to find the derivative bounds for many surface types. To compute collisions between new types of surfaces, the mathematical collision analysis is needed only once per surface type, rather than analyzing for each pair of surface types.The algorithm is hierarchical, first finding potential collisions over large volumes, and then refining the solution to smaller volumes. The user may specify the desired accuracy of the solution. A C-code implementation is described, with results for several non-bicubic and bicubic time-dependent parametric functions. An animation of the collision computation demonstrates collisions between complex parametric functions.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/0.1145/97880.97883DOIArticle
http://dl.acm.org/citation.cfm?doid=97880.97883PublisherArticle
Additional Information:© 1990 ACM. We would like to thank Carolyn Collins and Pete Wenzel for their assistance. The work presented in this paper was sponsored in part by International Business Machines, Inc., Hewlett-Packard Co., Apple Computer, Inc., and the Fannie and John Hertz Foundation.
Funders:
Funding AgencyGrant Number
IBMUNSPECIFIED
Hewlett-Packard CompanyUNSPECIFIED
Apple ComputerUNSPECIFIED
Fannie and John Hertz FoundationUNSPECIFIED
Subject Keywords:Collision Detection, Parametric Surfaces, Adaptive Sampling, Simulation, Dynamics, Constraints, Deformations, Computer Modeling
Issue or Number:4
Classification Code:1.3.5--Computational Geometry and Ob- ject Modeling; 1.3.7--Three-Dimensional Graphics and Re- alism
Record Number:CaltechAUTHORS:20161102-170650293
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161102-170650293
Official Citation:Brian Von Herzen, Alan H. Barr, and Harold R. Zatz. 1990. Geometric collisions for time-dependent parametric surfaces. SIGGRAPH Comput. Graph. 24, 4 (September 1990), 39-48. DOI=http://dx.doi.org/10.1145/97880.97883
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71703
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:03 Nov 2016 16:57
Last Modified:03 Oct 2019 16:10

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