Topology analysis and geometric feature determination for curves and surfaces are basic
problems in geometric modeling and computer aided design. When the curves and surfaces …

A local generic position method is proposed to isolate the real roots of a bivariate polynomial
system∑={f (x, y), g (x, y)}. In this method, the roots of the system are represented as linear …

In this paper, an algorithm is given for determining the topology of an algebraic space curve
and to compute a certified G 1 rational parametric approximation of the algebraic space …

Approximating complex curves with simple parametric curves is widely used in CAGD, CG,
and CNC. This paper presents an algorithm to compute a certified approximation to a given …

DOI: I0.1360/JOS172181 Page 1 ISSN 1000-9825, CODEN RUXlfEW Journal of Software,
Vol.17, No. 10, October 2006, pp.2181-2L91 DOI: I0.1360/JOS172181 ? 2006 by Journal of …

Abstract The Pythagorean-Hodograph curve (PH curve) is a valuable curve type extensively
utilized in computer-aided geometric design and manufacturing. This paper presents an …

A simple algorithm for computing an approximate parameterization of real space algebraic
curves using their graphs of critical points is designed and studied in this paper. The first …

An algorithm is proposed to determine the topology of an implicit real algebraic surface in ℝ
3. The algorithm consists of three steps: surface projection, projection curve topology …

Abelian integrals play a key role in the infinitesimal version of Hilbert's 16th problem. Being
able to evaluate such integrals—with guaranteed error bounds—is a fundamental step in …

We consider the convolution of two compatible conic segments. First, we find an exact
parametric expression for the convolution curve, which is not rational in general, and then …