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ON THE DERIVATIVES OF A SPECIAL FAMILY OF B-SPLINE CURVES

Miklós Hoffmann

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Abstract

This paper is devoted to the geometrical examination of a family of B-spline curves resulted by the modifiaction of one of their knot values. These curves form a surface, the other parameter lines of which are the paths of the points of the original curve at a fixed parameter value. The first and second derivatives of these curves are examined yielding geometrical results concerning their tangent lines and osculating planes.

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What this paper is about

This paper is devoted to the geometrical examination of a family of B-spline curves resulted by the modifiaction of one of their knot values. These curves form a surface, the other parameter lines of which are the paths of the points of the original curve at a fixed parameter value. The first and second derivatives of these curves are examined yielding geometrical results concerning their tangent lines and osculating planes.

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Available abstract

This paper is devoted to the geometrical examination of a family of B-spline curves resulted by the modifiaction of one of their knot values. These curves form a surface, the other parameter lines of which are the paths of the points of the original curve at a fixed parameter value. The first and second derivatives of these curves are examined yielding geometrical results concerning their tangent lines and osculating planes.

Key concepts: Osculating circle, Family of curves, Mathematics, Tangent, Knot (papermaking), Curve fitting, Mathematical analysis, Geometry

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