A quadratic trigonometric weighted spline with local support basis functions

Abstract

A proficient freeform curve design technique is developed by constructing B-spline like local support basis functions using a quadratic trigonometric function introduced. The built basis functions fulfill the properties of the local support, partition of unity and the positivity. The freeform designed curve method, by these constructed local support basis functions, owns the geometric properties such as convex hull and variation diminishing. In the suggested scheme, the Non-uniform freeform curve depiction is presented for deliberation by a transformed Bézier form. The demonstration of the scheme is supportive for various shape effects such as interval tension. As a privilege, the proposed method is C2 for its default case and is C1 in general. The proposed method provides a quadratic alternative to the cubic B-splines.