A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Automatic parameterization of rational curves and surfaces 1: conics and conicoids
Computer-Aided Design
Automatic parametrization of rational curves and surfaces II: cubics and cubicoids
Computer-Aided Design
Automatic parameterization of rational curves and surfaces III: algebraic plane curves
Computer Aided Geometric Design
On computing the intersection of a pair of algebraic surfaces
Computer Aided Geometric Design
Parametrization of cubic algebraic surfaces
Proceedings on Mathematics of surfaces II
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
The Calculation of Multivariate Polynomial Resultants
Journal of the ACM (JACM)
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
The Subresultant PRS Algorithm
ACM Transactions on Mathematical Software (TOMS)
Geometric Modeling with Algebraic Surfaces
Proceedings of the 3rd IMA Conference on the Mathematics of Surfaces
I3D '90 Proceedings of the 1990 symposium on Interactive 3D graphics
On the lower degree intersections of two natural quadrics
ACM Transactions on Graphics (TOG)
Enhancing Levin's method for computing quadric-surface intersections
Computer Aided Geometric Design
Computing all parametric solutions for blending parametric surfaces
Journal of Symbolic Computation
Journal of Computer Science and Technology - Special issue on computer graphics and computer-aided design
Parametrization of approximate algebraic surfaces by lines
Computer Aided Geometric Design
ACM Communications in Computer Algebra
Topology of real algebraic space curves
Journal of Symbolic Computation
Generators of the ideal of an algebraic space curve
Journal of Symbolic Computation
Parametrization of approximate algebraic surfaces by lines
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
Journal of Symbolic Computation
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For an irreducible algebraic space curve C that is implicitly defined as the intersection of two algebraic surfaces, f (x, y, z) = 0 and g (x, y, z) = 0, there always exists a birational correspondence between the points of C and the points of an irreducible plane curve P, whose genus is the same as that of C. Thus C is rational if the genus of P is zero. Given an irreducible space curve C = (f ∩ g), with f and g not tangent along C, we present a method of obtaining a projected irreducible plane curve P together with birational maps between the points of P and C. Together with [4], this method yields an algorithm to compute the genus of C, and if the genus is zero, the rational parametric equations for C. As a biproduct, this method also yields the implicit and parametric equations of a rational surface S containing the space curve C.The birational mappings of implicitly defined space curves find numerous applications in geometric modeling and computer graphics since they provide an efficient way of manipulating curves in space by processing curves in the plane. Additionally, having rational surfaces containing C yields a simple way of generating related families of rational space curves.