L-systems and Beyond

Course Notes, SIGGRAPH 2003
Organizer: Przemyslaw Prusinkiewicz¹
Instructors:

• Pavol Federl¹
• Radoslaw Karwowski¹
• Radomir Mech²
• Przemyslaw Prusinkiewicz¹

Course Description

L-systems are a biologically-motivated formalism that can be used as a tool for modeling and visualizing biological structures, and as a computing technique gleaned from nature to solve other modeling problems. Their appeal lies in a compact, intuitive description of algorithms, and the possibility of using this description directly as an input to the modeling software. The course will present recent theoretical results, implementations, applications and research directions pertinent to L-systems and their extensions. The applications include, on one hand, the modeling and visualization of plants at different levels of abstraction and for a variety of purposes, and, on the other hand, geometric modeling of curves and surfaces. These applications are united by their treatment of the modeled objects as dynamical structures subject to local operations, and can be implemented using the same modeling software. The course will be of a particular interest to researchers and students working on geometric modeling and the modeling of nature.

Prerequisites

The course will assume basic knowledge of geometric modeling algorithms, in particular subdivision curves and surfaces, and of numerical methods for solving algebraic and (ordinary and partial) differential equations. Prior exposure to L-systems, fractals, and the modeling of plants is desirable, but not necessary.

Download the entire course notes (15Mb), or download by section:

• Introduction (100kb)
• Part 1: Introduction to L-systems
  • Structured dynamical systems (100kb)
  • Introduction to modeling with L-systems (200kb)
• Part 2: Plant modeling with L-systems
  • L-systems: from the theory to visual modeling of plants (13Mb)
  • Visual models of plants interacting with their environment (13Mb)
  • The use of positional information in the modeling of plants (13Mb)
  • L-systems and partial differential equations (200kb)
  • Solving linear algebraic and differential equations with L-systems (400kb)
  • Integrating biomechanics into developmental plant models expressed using L-systems (1.2Mb)
• Part 3: Geometric modeling with L-systems
  • L-system description of subdivision curves (400kb)
  • L-system implementation of multiresolution curves based on cubic B-spline subdivision (150kb)
  • Relational specification of surface subdivision algorithms (350kb)
• Part 4: Implementations of L-systems
  • Design and implementation of the L+C modeling language (350kb)
  • Generating subdivision curves with L-systems on a GPU (400kb)