CS 435 Autumn 1997 --- Introduction to Interactive Graphics

Introduction to Advanced Modeling Techniques

Normal Geometric Representations

• Polygonal Models
• Spline Patch Models

Advanced Modeling Techniques

• Fractals

• L-Systems

• Particle Systems

• Procedural Models

• Implicit Surfaces

Fractals:

• Fractals:

  • Authors: Mandelbrot, Voss, Musgrave, Hart, Peitgen, Jurgens, Saupe, ...
    
  • Characteristics
    
    • self-similarity
    • non-unit dimensions
  • often used to describe natural objects
  • Two main classes: Deterministic and Random.
  • Examples:
    The Mandelbrot set:
    Fractal Mountains:
    
  • See "Chaos and Fractals: New Frontiers of Science" by Peitgen, Jurgens, Saupe.

• Authors: Lindemyer & Prusinkiewicz, Alvy Ray Smith
  
• Rule based grammers for describing natural objects
  
• Great for plants, trees, shells
  
• Example:
  
• Simple Example of a another tree created by the following production rule:
  a -> a[+a]a[-a-a]a
  with initial axiom a
  
  
• All rules applied simultaneously.
• Also probabilistic and context-sensitive L-systems.
• Most recent work is on Open L-systems that react to their environment.
• See also the work by Prusinkiewicz & Hammel

• Authors: Reeves, Sims
  
• simple rendering
  
• Large numbers of small particles
  
• Physics controls their movement
  
• Used to simulate water, snow, fire
  (e.g., Star Trek II: The Wrath of Khan - Genesis effect (750,000 particles) )
• Two main parts:
  -Large collection of simple geometric particles
  - Algorithms for controlling the particles Three parts:
  
  • Particle creation
  • particle movement
  • particle death
• Structured Particle Systems
  an extensions that allow simulation of trees, grass, etc.
• Diffusion Limited Aggregation (DLA)
  • Natural process hypothesized to describe how many natural things form,
    including dendrite clusters to the formation of galaxies.
  • Based on random walks (fBm motion) of particles.
  • Several initial sticky particles are placed in space.
  • A large number of additional particles are moved on random walks;
  • if they touch one of the sticky particles, they stick and may become sticky also.
• See also Rick Parent's chapter on Particle Animation

• Authors: Ebert, Perlin, Hart, Musgrave
  
• Use algorithms, code segments, procedure to define the geometry of your object.
• Add as much physics or art as you want
• Advantages: flexibility, data amplification, procedural abstraction.
• Examples:
  • Volume metaball Cloud This image is a volume rendered and procedural altered metaball. The image has low-albedo gas illumination and atmospheric attenuation.

  • My version of the blizzard of '96 This image shows how metaballs, volume swirling snow, and polygonal models can be combined to produce great images. You could say that during the blizzard I created a virtual snowman and my own blizzard.

• Authors: Wyvills, Hart, Blinn
• Describe objects with implicit equations: F(x,y,z)=0
• Blend objects together using smooth function:
  R = distance where function has a value of 0.

• Graph of Blending Function:
• Create iso-surface of blended density fields.
• Example: 10 Years of Implicit Surfaces by Brian Wyvill
• Images courtesy of Brian Wyvill (blob@cpsc.ucalgary.ca).