Abstract
In this paper, the constructions of both open and closed trigonometric Hermite interpolation curves while using the derivatives are presented. The combination of tension, continuity, and bias control is used as a very powerful type of interpolation; they are applied to open and closed Hermite interpolation curves. Surface construction utilizing the studied trigonometric Hermite interpolation is explored and several examples obtained by the C1 trigonometric Hermite interpolation surface are given to show the usefulness of this method.
Highlights
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This paper reports a new mixture of polynomial and trigonometric functions, combined with tension, continuity, and bias control, to build the new Hermite interpolant
A trigonometric Hermite interpolation curve between two consecutive points Pi and Pi+1 is based on these points’ position and the derivative associated at each point
Summary
BiBi et al constructed various shapes and font designing of curves and described the curvature by using parametric and geometric continuity constraints of generalized hybrid trigonometric Bézier (GHT-Bézier) curves [15] In another very recent work, Usman et al [16] presented a new TC Bernstein-like basis functions analogous to standard Bernstein basis functions with single shape parameter to overcome the drawing of complex curves. This paper reports a new mixture of polynomial and trigonometric functions, combined with tension, continuity, and bias control, to build the new Hermite interpolant. This Hermite interpolation allows the animator to change the tension, continuity, and bias of these splines.
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