Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1008.1664

L-systems in Geometric Modeling

Przemyslaw Prusinkiewicz·Mitra Shirmohammadi·Faramarz Samavati
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

cs.GRcs.FL

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Przemyslaw Prusinkiewicz, Mitra Shirmohammadi, Faramarz Samavati. 2010-08-10. L-systems in Geometric Modeling. https://doi.org/10.4204/eptcs.31.3

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Constrained Program Generation for 3D Reaction Animation with a 0.8B Model

Visualizing a chemical reaction requires making its molecular changes visible while keeping the animation faithful to the stated chemistry. Equations, structural diagrams and molecular viewers provide complementary descriptions, but assembling an interactive three-dimensional explanation still requires specifying the changes and checking their consistency. We present ChemXRG, a domain-specific language (DSL) framework that addresses this gap by representing a reaction animation as an executable program. Persistent atom identifiers and explicit bond, charge and grouping operations connect the symbolic reaction to the displayed transformation. This shared representation lets generation, verification and rendering operate on the same account of what changes. Given known, atom-mapped reactant and product structures, reaction-grounded constraints fix input-determined facts and restrict action choices; execution checks validate the resulting transformation before geometry and frames are constructed. We implement this paradigm with a reaction-program corpus and ChemQwen, a trained 0.8B DSL generator. Paired and component evaluations show improved compiler acceptance and normalized full-program agreement under input-conditioned constraints, while identifying remaining failures that require execution checks. A public browser application demonstrates the connection from symbolic reaction descriptions to inspectable programs and interactive 3D animations.

cs.GR↗
arXiv2026

NaRPA: Navigation and Rendering Pipeline for Astronautics

This paper presents the applications of scientific ray-tracing in modeling and simulating light transport for space-borne image data generation. A ray-tracing engine, the Navigation and Rendering Pipeline for Astronautics (NaRPA), is introduced as a rendering framework to generate virtual datasets and support simulations for robust navigation pipelines. Sensor and environment models that enable the synthesis of space-to-space and ground-to-space virtual observations are presented. The work demonstrates the capabilities of simulating passive and active vision-based sensors using NaRPA to facilitate the design, testing, and verification of aerospace visual navigation algorithms. Additionally, the paper describes a velocimeter LiDAR model and its statistical validation with experimental data.

cs.GR↗
arXiv2026

VoroUDF: Meshing Unsigned Distance Fields with Voronoi Optimization

We present VoroUDF, an algorithm for reconstructing high-quality triangle meshes from Unsigned Distance Fields (UDFs). Our algorithm supports non-manifold geometry, sharp features, and open boundaries, without relying on error-prone inside/outside estimation, restrictive look-up tables nor topologically noisy optimization. Unlike fixed-grid approaches, our Voronoi-based formulation optimizes a set of movable seeds that travel freely along the iso-surface, jointly minimizing a tangent-plane fitting energy, driven by a fixed set of surface samples queried once from the UDF and its gradient, and a repulsion energy that keeps the seeds evenly distributed. It achieves significantly improved topological consistency and geometric fidelity compared to existing methods, while producing lightweight meshes suitable for downstream real-time and interactive applications.

cs.GR↗