/l-systems-opengl

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Introduction

L-systems are used for modelling the growth of plants through recursion. This project is an implmentation of an L-system in C++11 to render a tree in OpenGL.

What is an L-System?

L-systems, introduced and name after a biologist Lindenmayer, are parallel rewriting systems which use formal languages (generated by context-free or context-sensitive grammars). An L-system consists of the following:

  1. Alphabet: The set of symbols allowed in the language
  2. Production rules: A set of rules which define how each symbol can be expanded to a larger string of symbols
  3. Axiom: The initial string used for recursive generation

This may seem similar to fractals, which are a specific kind of l-system.

A simple bracketed l-system (which allows saving and restoring state) can generate very complex strings which can be interpreted as instructions in turtle-like graphics.

Our L-System

The l-system we used is a bracketed stochastic 0L-system. What this means is that we have a context-free grammar as production rules. Stochastic means that there are multiple production rules for a single symbol in our alphabet and there is a finite probability of expanding using each of these.

  • Alphabet: { F, X, [, ], -, + }

  • Production rules::

    {
    X -(0.25)-> F-[[X]+X]+F[[X]+X]-X
    X -(0.25)-> F-[[X]+X]+F[-FX]+X
    X -(0.25)-> F[+X][-X]FX";
    X -(0.25)-> F[+X]F[-X]+X";

    F -> FF
}

  • Axiom: "X"

Turtle interpretation of symbols

  1. F = Move forward, drawing a line
  2. + = Rotate head left by
  3. - = Rotate head right by
  4. [ = Save state of turtle (State: x, y, rotation, thickness)
  5. ] = Restore state of turtle

Other implementation details

For drawing leaves, the terminal symbol X has been used along with the next symbol of the string. If the symbol X is encountered, with the following symbol as [, then a leaf is drawn.

Branch width contraction occurs at every branching point in the tree.

Trunk tapering is performed until the first branch is encountered, after which branch contraction is performed.

Color of leaves is taken from a uniform random distribution, based on a variable used to denote season.

  • Summer/spring

summer/spring

  • Autumn

autumn

  • Winter

winter

Every execution of the program leads to a slightly different tree structure due to the stochastic l-system, random angle of branching, and random leaf colors.

Requirements

  • GPU with OpenGL 3.3+ support
  • Ubuntu

Dependencies

  • GLFW - required for creating an OpenGL context. Instructions for installing can be found here.
  • CMake - install using sudo apt install cmake

Project Structure

This project consists of the following files:

  • graphics.h - class containing primitive (line and circle) drawing methods
  • turtle.h - class implementing turtle like graphics for interpreting L-system generated code
  • primitives.cpp - demonstrates the primitive drawing method by rendering a bicycle wheel
  • tree.cpp - procedurally generates a tree changing colours with the seasons using an L-system

Buidling

Clone or unzip the project to your favorite folder. Then run:

mkdir build
cd build
cmake ..
make
./tree

To run the primitive drawing demonstration program, make sure your active directory is set to build/ and run ./primitives.

Contributors

  • Arnav Dhamija
  • Pranav Asthana