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2009•Mathematical Models and Computer SimulationsRequires access

Precision rotationally invariant curve parameterization

Elena Alshina, Elena Ivanchenko, N. N. Kalitkin, В. Ф. Тишкин

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Abstract

The problem of rotationally invariant approximation of the curve given by points is considered. The arc length is chosen for the curve parameter. The algorithm of calculating it up to the fourth order of accuracy is developed. In addition, other characteristics of the curve are constructed, viz., the slope, the curvature, and its derivative. General requirements to parametric approximation of the curve are considered that provide for rotationally invariant approximation.

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What this paper is about

The problem of rotationally invariant approximation of the curve given by points is considered. The arc length is chosen for the curve parameter. The algorithm of calculating it up to the fourth order of accuracy is developed. In addition, other characteristics of the curve are constructed, viz., the slope, the curvature, and its derivative. General requirements to parametric approximation of the curve are considered that provide for rotationally invariant approximation.

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Available abstract

The problem of rotationally invariant approximation of the curve given by points is considered. The arc length is chosen for the curve parameter. The algorithm of calculating it up to the fourth order of accuracy is developed. In addition, other characteristics of the curve are constructed, viz., the slope, the curvature, and its derivative. General requirements to parametric approximation of the curve are considered that provide for rotationally invariant approximation.

Key concepts: Parametric equation, Invariant (physics), Osculating circle, Arc length, Curvature, Mathematics, Parametric statistics, Torsion of a curve

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