Five-and Six-Order Trigonometric Spline Curves

Five-and Six-Order Trigonometric Spline Curves

Abstract: Using trigonometric functions, two groups of functions with parameters are#br# constructed, which consist of six and seven functions respectively. The properties of the two#br# groups of functions are analyzed. Based on them, two kinds of new spline curves are defined,#br# which have the same structure with quintic and sextic B-spline curves respectively. The new#br# curves not only inherit the basic properties of B-spline curve, but also have some new advantages.#br# For example, when the knot points are equidistant, the new curves can reach C5 continuous at the#br# knot points, and the shape of the new curves can be adjusted by changing the value of the shape#br# parameter with the control points unchanged. In addition, the methods of making the new curves#br# interpolating the first and end points of the control polygon, and the methods of constructing#br# closed curves, etc, are given. The examples in the paper show the new method is correct and#br# feasible.#br# Key words: curve design; trigonometric function; spline curve; shape parameter; continuity

Online:2015-04-30 Published:2015-03-30

Abstract

Abstract: Using trigonometric functions, two groups of functions with parameters are
constructed, which consist of six and seven functions respectively. The properties of the two
groups of functions are analyzed. Based on them, two kinds of new spline curves are defined,
which have the same structure with quintic and sextic B-spline curves respectively. The new
curves not only inherit the basic properties of B-spline curve, but also have some new advantages.
For example, when the knot points are equidistant, the new curves can reach C5 continuous at the
knot points, and the shape of the new curves can be adjusted by changing the value of the shape
parameter with the control points unchanged. In addition, the methods of making the new curves
interpolating the first and end points of the control polygon, and the methods of constructing
closed curves, etc, are given. The examples in the paper show the new method is correct and
feasible.

Key words: curve design, trigonometric function, spline curve, shape parameter, continuity

Yan Lanlan, Han Xuli, Huang Tao. Five-and Six-Order Trigonometric Spline Curves[J]. Journal of Graphics.

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Five-and Six-Order Trigonometric Spline Curves

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