Curve construction based on five trigonometric blending functions

Five new trigonometric blending functions with two exponential shape parameters are given in this paper. Based on these blending functions, trigonometric Bézier curves analogous to the quartic Bézier curves, with two exponential shape parameters, are presented. The ellipses and parabolas can be represented exactly by using the trigonometric Bézier curves. Based on the blending functions, trigonometric B-spline curves with three local shape parameters and a global shape parameter are also constructed. The obtained spline curves can be C2∩FC2k+3 (k∈ℤ+) continuous by fixing some values of the shape parameters. Without solving a linear system, the spline curves can be also used to interpolate sets of points with C2 continuity partly or entirely.

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