Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Implicitization using moving curves and surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
The moving line ideal basis of planar rational curves
Computer Aided Geometric Design
On the validity of implicitization by moving quadrics for rational surfaces with no base points
Journal of Symbolic Computation
Resultants and moving surfaces
Journal of Symbolic Computation
Implicitization of bihomogeneous parametrizations of algebraic surfaces via linear syzygies
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Change of order for regular chains in positive dimension
Theoretical Computer Science
Implicitization of rational ruled surfaces with µ-bases
Journal of Symbolic Computation
Curve/surface intersection problem by means of matrix representations
Proceedings of the 2009 conference on Symbolic numeric computation
Matrix representations for toric parametrizations
Computer Aided Geometric Design
Minimal generators of the defining ideal of the Rees Algebra associated to monoid parameterizations
Computer Aided Geometric Design
The surface/surface intersection problem by means of matrix based representations
Computer Aided Geometric Design
Implicit matrix representations of rational Bézier curves and surfaces
Computer-Aided Design
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We describe an algorithm for implicitizing rational hypersurfaces with at most a finite number of base points, based on a technique described in Buse, Laurent, Jouanolou, Jean-Pierre [2003. On the closed image of a rational map and the implicitization problem. J. Algebra 265, 312-357], where implicit equations are obtained as determinants of certain graded parts of an approximation complex. We detail and improve this method by providing an in-depth study of the cohomology of such a complex. In both particular cases of interest of curve and surface implicitization we also present algorithms which involve only linear algebra routines.