Τίτλος:
Implicitizing rational curves by the method of moving quadrics
Γλώσσες Τεκμηρίου:
Αγγλικά
Περίληψη:
A new technique for finding implicit matrix-based representations of rational curves in arbitrary dimension is introduced. It relies on the use of moving quadrics following curve parameterizations, providing a high-order extension of the implicit matrix representations built from their linear counterparts, the moving planes. The matrices we obtain offer new, more compact, implicit representations of rational curves. Their entries are filled by linear and quadratic forms in the space variables and their ranks drop exactly on the curve. Typically, for a general rational curve of degree d we obtain a matrix whose size is half of the size of the corresponding matrix obtained with the moving planes method. We illustrate the advantages of these new matrices with some examples, including the computation of the singularities of a rational curve. © 2019 Elsevier Ltd
Συγγραφείς:
Busé, L.
Laroche, C.
Yıldırım, F.
Περιοδικό:
CAD Computer Aided Design
Εκδότης:
Elsevier Ireland Ltd
Λέξεις-κλειδιά:
Computational geometry; Number theory, Arbitrary dimension; Implicit representation; Implicitization; Matrix based representation; Matrix representation; Moving quadric; Parameterized; Rational curves, Matrix algebra
DOI:
10.1016/j.cad.2019.05.019
