b-Spline Curves and Surfaces as a Minimization of Quadratic Operators

TL;DR

This paper demonstrates that b-spline curves and surfaces with uniform knots can be characterized as the minima of positive quadratic operators, providing a new mathematical perspective on their structure.

Contribution

It introduces a novel characterization of b-spline curves and surfaces as minima of quadratic operators, expanding theoretical understanding.

Findings

b-spline curves and surfaces can be represented as minima of quadratic operators

The characterization applies to uniform knot b-splines without multiplicity

Provides a new theoretical framework for understanding b-splines

Abstract

The goal of this short note is to prove that every b-spline curve or surface (generated by uniform knots, without multiplicity) may be defined as minimum of positive quadratic operator.