C^2連続化したAkima曲線とその性質 C^2 Continualized Akima Curves and Their Properties
This paper presents three kinds of new <I>C<SUP>2</SUP></I> Akima curves: (1) which preserves the global shape of the <I>C<SUP>1</SUP></I> Akima curve, (2) which preserves directions of Akima's tangents and (3) which is closest to the <I>C<SUP>1</SUP></I> Akima curve from the point of the method of least squares. These curves are useful in the field of smooth curve fitting, computer graphics and computer aided geometric design, because these generate less oscillating global shape and can have straight line sections incorporated in themselves. These are also locally controllable and generated span - by - span. The new curves are based on the quartic <I>S</I>- splines with all the knots of multiplicity 2, which are obtained by degree - elevation in each span of the cubic interpolating <I>B</I>- splines. The relevant additional control points are determined on the basis of the local estimation scheme of tangents by Akima. For practical use, properties of these curves are analyzed in detail theoretically and experimentally.
図学研究 (67), 17-23, 1995-03-01