A rational trigonometric spline to visualize positive data

Abstract

Abstract. In this paper, we construct a cubic trigonometric Bézier curve with two shape parameters on the basis of cubic trigonometric Bernstein-like blending functions. The proposed curve has all geometric properties of the ordinary cubic Bézier curve. Later, based on these trigonometric blending functions a 1 C rational trigonometric spline with four shape parameters to preserve positivity of positive data is generated. Simple data dependent constraints are developed for these shape parameters to get a graphically smooth and visually pleasant curve.

Enhancing curve and surface applications with trigonometric polynomial basis functions

“…PLOS ONE where B n j ðWÞ ¼ 0 for j = −1 and j � n. The formulation is based on degree three trigonometric polynomial functions with two shape parameters [9], which are defined as:…”

“…For n ≥ 4, the formulation for trigonometric polynomial functions with two shape parameters is as follow: where for j = −1 and j ≥ n . The formulation is based on degree three trigonometric polynomial functions with two shape parameters [ 9 ], which are defined as: where l 1 , l 2 ∈ [−1, 2] and ϑ ∈ [0, π /2].…”

“…Afterwards a new set of basis functions based on exponential functions is introduced [6]. Further different set of basis functions involving shape parameters and trigonometric functions for curve and surface design is introduced [7][8][9][10].…”