Efficient degree reduction of B\'ezier curves with box constraints using dual bases

TL;DR

This paper presents an efficient algorithm for degree reduction of Bézier curves with box constraints, combining iterative methods, dual basis construction, and modifications to improve computational efficiency.

Contribution

It introduces a novel combination of existing dual basis methods with an iterative approach for constrained Bézier curve degree reduction.

Findings

Algorithm improves computational efficiency

Effectively handles box constraints in degree reduction

Builds on and combines previous dual basis methods

Abstract

In this paper, we give an efficient algorithm of degree reduction of B\'ezier curves with box constraints. The idea is to combine the previous iterative approach, that has been presented recently in (P. Gospodarczyk, Comput. Aided Des. 62 (2015), 143--151), with a fast method of construction of dual bases from (P. Wo\'zny, J. Comput. Appl. Math. 260 (2014), 301--311) and a new efficient method of modification of dual bases.