A Rational Quadratic Trigonometric Spline (RQTS) as a Superior Surrogate to Rational Cubic Spline (RCS) with the Purpose of Designing

Abstract

A key technique for modeling 2D objects is built using a Bézier-like rational quadratic trigonometric function with two form parameters. Since they are generated employing weights, the suggested rational quadratic trigonometric spline curve schemes are helpful for shape modeling. The established method yields a curve with the best geometric properties, such as convex hull, partition of unity, affine invariance, and diminishing variation. The parameters in the suggested method’s construction are helpful for several critical shape features such as local, global, and biased tension qualities, which give good control over the curve and allow for shape modification as desired. In addition, the recommended approach is C2. Furthermore, the comparative study of both splines is discussed which revealed the proposed method as a superior alternative to rational cubic spline.

Keywords

• Bézier curves
• shape parameters
• affine invariance
• variation diminishing property
• tensions