Implicit Curves and Surfaces in CAGD
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
Implicitization using moving curves and surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Approximate implicitization using monoid curves and surfaces
Graphical Models and Image Processing
Regular algebraic curve segments (I)-definitions and characteristics
Computer Aided Geometric Design
Mathematical Methods for Curves and Surfaces
An approach to weak approximate implicitization
Mathematical Methods for Curves and Surfaces
Approximation by Interval Bezier Curves
IEEE Computer Graphics and Applications
Least-Squares Fitting of Algebraic Spline Curves via Normal Vector Estimation
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
Computers & Mathematics with Applications
Interval implicitization of parametric surfaces
ICICA'10 Proceedings of the First international conference on Information computing and applications
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In this paper, we propose a new concept called interval implicitization of rational curves, that is. finding an interval algebraic curve with lower degree which bounds a given parametric rational curve such that some objective function involving the width and the tension of the interval algebraic curve is minimized. An algorithm is presented to compute the interval implicit representation of a rational curve by solving two optimal problems, each with a quadratic (or linear) objective function and linear constraints. Some examples are also provided to demonstrate the algorithm.