TY - GEN
T1 - Computing self-intersection loci of parametrized surfaces using regular systems and Gröbner bases
AU - Huang, Yanli
AU - Wang, Dongming
PY - 2009
Y1 - 2009
N2 - The computation of self-intersection loci of parametrized surfaces is needed for constructing trimmed parametrizations and describing the topology of the considered surfaces in real settings. This paper presents two general and efficient methods for determining self-intersection loci of rationally parametrized surfaces. One of the methods, based on regular systems, is capable of computing the exact parametric locus of self-intersection of a given surface and the other, based on Gröbner bases, can compute the minimal variety passing through the exact parametric locus. The relation between the results computed by the two methods is established and two algorithms for computing parametric loci of self-intersection are described. Experimental results and comparisons with some existing methods show that our algorithms have a good performance for parametrized surfaces.
AB - The computation of self-intersection loci of parametrized surfaces is needed for constructing trimmed parametrizations and describing the topology of the considered surfaces in real settings. This paper presents two general and efficient methods for determining self-intersection loci of rationally parametrized surfaces. One of the methods, based on regular systems, is capable of computing the exact parametric locus of self-intersection of a given surface and the other, based on Gröbner bases, can compute the minimal variety passing through the exact parametric locus. The relation between the results computed by the two methods is established and two algorithms for computing parametric loci of self-intersection are described. Experimental results and comparisons with some existing methods show that our algorithms have a good performance for parametrized surfaces.
KW - Minimal variety
KW - Parametric locus
KW - Parametrized surface
KW - Self-intersection locus
UR - https://www.scopus.com/pages/publications/77953046738
U2 - 10.1109/SYNASC.2009.43
DO - 10.1109/SYNASC.2009.43
M3 - 会议稿件
AN - SCOPUS:77953046738
SN - 9780769539645
T3 - SYNASC 2009 - 11th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
SP - 28
EP - 36
BT - SYNASC 2009 - 11th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
T2 - 11th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2009
Y2 - 26 September 2009 through 29 September 2009
ER -