Simplex Spline Bases on the Powell-Sabin 12-Split: Part I

TL;DR

This paper reviews the construction and properties of a specific spline basis called the S-basis, designed for smooth quadratic splines on the Powell-Sabin 12-split, a common subdivision in geometric modeling.

Contribution

It provides a detailed review of the S-basis construction and key properties for $C^1$ quadratic splines on the Powell-Sabin 12-split, enhancing understanding of spline basis design.

Findings

The S-basis is a valid $C^1$ quadratic spline basis.

Key properties of the S-basis are established.

The basis facilitates smooth spline construction on the Powell-Sabin 12-split.

Abstract

We review the construction and a few properties of the S-basis, a simplex spline basis for the $C^1$ quadratic splines on the Powell-Sabin 12-split.