Hybrid trigonometric Bézier interpolation with uniform, chordal and centripetal parameterization in 3-Euclidean space and its application

Interpolation in trigonometric Bézier curves refers to constructing a curve that smoothly passes through a given set of control points. In this paper, data points are interpolated by the General Hybrid Trigonometric B\'ezier (GHTB) curve. The curve contains four free parameters that allow flexibility in curve construction. The determination of control points on the GHTB curve, based on a certain degree, results in the interpolation of the curve that passes through the data points. Uniform, centripetal, and chordal parameterization methods are applied to GHTB curves. The three parametrization techniques — uniform, centripetal, and chordal — of the GHTB curve are discussed. Subsequently, the demonstration of these parametrization methods is carried out using sets of data points in both 2-dimensional and 3-dimensional Euclidean space. The curvatures and torsion of the parametrized curves for various values of free parameters in the GHTB curve are observed.