Applications of power series in computational geometry
Computer-Aided Design
Intersection of parametric surfaces in the Bernstein—Be´zier representation
Computer-Aided Design
Improperly parametrized rational curves
Computer Aided Geometric Design
The characterization of parametric surface sections
Computer Vision, Graphics, and Image Processing
Mathematical aspects of scientific software
Computer Aided Geometric Design
Piecewise parametric approximations for algebraic curves
Computer Aided Geometric Design
Hermite interpolation of rational space curves using real algebraic surfaces
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Generalized Characteristic Polynomials
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Implicit and parametric curves and surfaces for computer aided geometric design
Implicit and parametric curves and surfaces for computer aided geometric design
Computations with parametric equations
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Approximate implicitization via curve fitting
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Approximate distance fields with non-vanishing gradients
Graphical Models
Rational quadratic approximation to real algebraic curves
Computer Aided Geometric Design - Special issue: Geometric modeling and processing 2004
Rational quadratic approximation to real algebraic curves
Computer Aided Geometric Design
Certified approximation of parametric space curves with cubic B-spline curves
Computer Aided Geometric Design
Journal of Symbolic Computation
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A method is proposed for computing an implicit approximant at a point to a parametric curve or surface. The method works for both polynomially and rationally parameterized curves and surfaces and achieves an order of contact that can be prescribed. In the case of nonsingular curve points, the approximant must be irreducible, but in the surface case additional safeguards are incorporated into the algorithm to ensure irreducibility. The method also yields meaningful results at most singularities. In principle, the method is capable of exact implicitization and has a theoretical relationship with certain resultant-based elimination methods.