Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Implicitization using moving curves and surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Spline approximations of real algebraic surfaces
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Rational parametrization of surfaces
Journal of Symbolic Computation
Approximate implicitization using monoid curves and surfaces
Graphical Models and Image Processing
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Mathematical Methods for Curves and Surfaces
Approximate implicitization via curve fitting
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Design of rational curves and developable surfaces
Design of rational curves and developable surfaces
Approximate algebraic methods for curves and surfaces and their applications
Proceedings of the 21st spring conference on Computer graphics
Journal of Computational and Applied Mathematics
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We describe a method for approximate parameterization of a planar algebraic curve by a rational Bézier (spline) curve. After briefly discussing exact methods for parameterization and methods for rational interpolation, we describe a new technique for rational parameterization. Our approach is based on the minimization of a suitable--nonlinear objective function, which takes both the distance from the curve and the positivity of the weight function (i.e., the numerator of the rational parametric representation) into account. The solution is computed by using an SQP-type optimization technique. In addition, we use a region--growing--type approach in order to obtain a good initial solution, which is crucial for the convergence of the nonlinear optimization procedure.