An enhanced basis for producing Bezier-like curves

TL;DR

This paper introduces a new family of Bernstein-like bases using an auxiliary function and a shape parameter, enabling flexible curve shaping while preserving key properties of the original blending functions.

Contribution

It proposes a novel structure for Bernstein-like bases that generalizes existing bases and allows shape adjustment and property preservation.

Findings

Curves can interpolate between original and linear segments.

The new bases preserve algebraic and geometric properties.

Shape parameters enable flexible curve manipulation.

Abstract

This study aims on proposing a new structure for constructing Bernstein-like bases. The structure uses an auxiliary function and a shape parameter to construct a new family of bases from any family of blending functions. The new family of bases inherit almost all algebraic and geometric properties of the initial blending functions. The corresponding curves have the freedom to travel from the curve constructed from the initial blending functions to the line segment joining the first and last control points. The new bases have the monotonicity preservation property and the shape of the curve could be adjusted by changing the parameter.