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1998•Chinese Journal of ComputersRequires access

APPROXIMATE IMPLICITIZATION OF RATIONAL CURVES

Fa Chen

Open publisher page 4 citations

Abstract

Given a parametric rational curve or surface,the procedure of finding its implicit equationis called implicitization of the rational curve or surface. The problem of implicitizing rational curvesand surfaces has much important theoretic meanings in Computer Aided Geometric Design and Computer Graphics, and much work has been done in this area. But the practical usefulness of implicitization is hampered by the complex representation of the implicit equations of high degree rationalcurves and surfaces. This paper put forward a new concept called approximate implicitization of rational curves and give an efficient algorithm to find the approximate implicit representation of a rational curve. Examples are provided to illustrate the efficiency of the algorithm and the importanceof the new concept.

About this research paper

What this paper is about

Given a parametric rational curve or surface,the procedure of finding its implicit equationis called implicitization of the rational curve or surface. The problem of implicitizing rational curvesand surfaces has much important theoretic meanings in Computer Aided Geometric Design and Computer Graphics, and much work has been done in this area. But the practical usefulness of implicitization is hampered by the complex representation of the implicit equations of high degree rationalcurves and surfaces. This paper put forward a new concept called approximate implicitization of rational curves and give an efficient algorithm to find the approximate implicit representation of a rational curve. Examples are provided to illustrate the efficiency of the algorithm and the importanceof the new concept.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Given a parametric rational curve or surface,the procedure of finding its implicit equationis called implicitization of the rational curve or surface. The problem of implicitizing rational curvesand surfaces has much important theoretic meanings in Computer Aided Geometric Design and Computer Graphics, and much work has been done in this area. But the practical usefulness of implicitization is hampered by the complex representation of the implicit equations of high degree rationalcurves and surfaces. This paper put forward a new concept called approximate implicitization of rational curves and give an efficient algorithm to find the approximate implicit representation of a rational curve. Examples are provided to illustrate the efficiency of the algorithm and the importanceof the new concept.

Key concepts: Mathematics, Parametric equation, Geometric design, Representation (politics), Parametric surface, Surface (topology), Rational surface, Rational function

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