A new approach for surface intersection
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Implicitization using moving curves and surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Computing the isolated roots by matrix methods
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
On the validity of implicitization by moving quadrics for rational surfaces with no base points
Journal of Symbolic Computation
Geometric applications of the Bezout matrix in the Lagrange basis
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Implicitization of bihomogeneous parametrizations of algebraic surfaces via linear syzygies
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Matrix representations for toric parametrizations
Computer Aided Geometric Design
Bezoutian and quotient ring structure
Journal of Symbolic Computation
Implicitizing rational hypersurfaces using approximation complexes
Journal of Symbolic Computation
Resultant-based methods for plane curves intersection problems
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Matrix-based implicit representations of rational algebraic curves and applications
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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In this paper, we introduce matrix representations of algebraic curves and surfaces for Computer Aided Geometric Design (CAGD). The idea of using matrix representations in CAGD is quite old. The novelty of our contribution is to enable non square matrices, extension which is motivated by recent research in this topic. We show how to manipulate these representations by proposing a dedicated algorithm to address the curve/surface intersection problem by means of numerical linear algebra techniques.