L-systems in Geometric Modeling

TL;DR

This paper demonstrates that parametric context-sensitive L-systems with affine geometry can succinctly describe fundamental geometric modeling algorithms like B-splines and Bezier curves, extending previous applications beyond subdivision curves.

Contribution

It introduces a generalized framework using L-systems for describing key geometric algorithms, expanding their applicability in geometric modeling.

Findings

L-systems can describe B-spline and Bezier algorithms.

The approach generalizes previous L-system applications.

Extensions to rational curves are demonstrated.

Abstract

We show that parametric context-sensitive L-systems with affine geometry interpretation provide a succinct description of some of the most fundamental algorithms of geometric modeling of curves. Examples include the Lane-Riesenfeld algorithm for generating B-splines, the de Casteljau algorithm for generating Bezier curves, and their extensions to rational curves. Our results generalize the previously reported geometric-modeling applications of L-systems, which were limited to subdivision curves.