Please use this identifier to cite or link to this item: https://doi.org/10.1145/116913.116917
Title: Using multivariate resultants to find the intersection of three quadric surfaces
Authors: Chionh, Eng-Wee 
Goldman, Ronald N.
Miller, James R.
Issue Date: Oct-1991
Source: Chionh, Eng-Wee, Goldman, Ronald N., Miller, James R. (1991-10). Using multivariate resultants to find the intersection of three quadric surfaces. ACM Transactions on Graphics 10 (4) : 378-400. ScholarBank@NUS Repository. https://doi.org/10.1145/116913.116917
Abstract: Macaulay's concise but explicit expression for multivariate resultants has many potential applications in computer-aided geometric design. Here we describe its use in solid modeling for finding the intersections of three implicit quadric surfaces. By Bezout's theorem, three quadric surfaces have either at most eight or infinitely many intersections. Our method finds the intersections, when there are finitely many, by generating a polynomial of degree at most eight whose roots are the intersection coordinates along an appropriate axis. Only addition, subtraction, and multiplication are required to find the polynomial. But when there are possibilities of extraneous roots, division and greatest common divisor computations are necessary to identify and remove them.
Source Title: ACM Transactions on Graphics
URI: http://scholarbank.nus.edu.sg/handle/10635/99459
ISSN: 07300301
DOI: 10.1145/116913.116917
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