Please use this identifier to cite or link to this item:
|Title:||On the minors of the implicitization Bezout matrix for a rational plane curve|
|Authors:||Chionh, E.-W. |
|Source:||Chionh, E.-W., Sederberg, T.W. (2001). On the minors of the implicitization Bezout matrix for a rational plane curve. Computer Aided Geometric Design 18 (1) : 21-36. ScholarBank@NUS Repository. https://doi.org/10.1016/S0167-8396(00)00034-0|
|Abstract:||This paper investigates the first minors Mi,j of the Bezout matrix used to implicitize a degree-n plane rational curve P(t). It is shown that the degree n-1 curve Mi,j = 0 passes through all of the singular points of P(t). Furthermore, the only additional points at which Mi,j = 0 and P(t) intersect are an (i+j)-fold intersection at P(0) and a (2n-2-i-j)-fold intersection at P(∞). Thus, a polynomial whose roots are exactly the parameter values of the singular points of P(t) can be obtained by intersecting P(t) with M0,0. Previous algorithms of finding such a polynomial are less direct. We further show that Mi,j = Mk,l if i+j = k+l. The method also clarifies the applicability of inversion formulas and yields simple checks for the existence of singularities in a cubic Be&acute;zier curve.|
|Source Title:||Computer Aided Geometric Design|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Feb 22, 2018
WEB OF SCIENCETM
checked on Jan 23, 2018
checked on Feb 19, 2018
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.