Approximation by Conic Splines

Ghosh, Sunayana; Petitjean, Sylvain; Vegter, Gert

doi:10.1007/s11786-007-0004-8

Cited by 2 publications

(1 citation statement)

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“…Several 2D interpolation schemes to produce curves close to circles were proposed in [9]. The certified approximation were considered by some authors and they focused on the case of planar curves [15,16,17,18].…”

Section: Introductionmentioning

confidence: 99%

Certified approximation of parametric space curves with cubic B-spline curves

Shen

Yuan

Gao

2012

Computer Aided Geometric Design

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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 parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given precision and preserve the geometric features of the given curve such as the topology, singular points, etc. The approximated curve is divided into segments called quasi-cubic Bézier curve segments which have properties similar to a cubic rational Bézier curve. And the approximate curve is naturally constructed as the associated cubic rational Bézier curve of the control tetrahedron of a quasi-cubic curve. A novel optimization method is proposed to select proper weights in the cubic rational Bézier curve to approximate the given curve. The error of the approximation is controlled by the size of its tetrahedron, which converges to zero by subdividing the curve segments. As an application, approximate implicit equations of the approximated curves can be computed. Experiments show that the method can approximate space curves of high degrees with high precision and very few cubic Bézier curve segments.

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