ATEC 6351.001Procedural AnimationIntroduction to Procedural Methods in 3D Computer Animation

Dr. Midori Kitagawa

In class Pay attention Take notes Learn Be ready for a pop quiz

Week 8: Procedural Modeling

Procedural modeling methods Assignment 13

Procedural Modeling Methods Fractal Branching object generation and

animation system L-system

Fractal A natural phenomenon or a

mathematical set that exhibits a repeating pattern that displays at every scale.

Fractal in nature Plants

Fractal in nature Landscapes

Fractal in nature Natural phenomena

Helge von Koch (1870-1924) Koch curve (1904)

Koch snowflake Has a finite area and an infinite

perimeter.

Benoit Mandelbrot (1924 – 2010) One of the first to use the computer to

visualize fractal geometry. Discovered the Mandelbrot set in 1979. Defined fractal as “A rough or

fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced size copy of the whole. ”

Mandelbrot set Infinitely complex, i.e., small scale

details are not identical to the whole.

Branching object generation and animation system http://

www.utdallas.edu/atec/midori/BOGAS/BOGAS.htm

http://www.youtube.com/watch?v=Xb50LQ8lhAU

L-systems L-system is a string rewriting system

introduced by the biologist Aristid Lindenmayer in 1968.

Theoretical framework for studying the development of simple multi-cellular organisms.

Subsequently applied to investigate higher plants and plant organs .

L-systems

Turtle geometry In L-systems, geometry is described

using turtle geometry. The turtle knows:1. Direction that it is

pointing2. Position

Turtle geometry operations Move forward (F) Changing directions: turn (+, -), pitch

(^,&), roll (<, >) Control structures: conditions, loops, if,

etc.

L-system Consists of a premise (axiom) and

rewriting rules (production rules):w = premisep1 = rule 1p2 = rule 2:pN = rule N

The most basic type of rule is: pred=succwhere pred (predecessor) is a symbol to be replaced and succ (successor) is a symbol or a string to replace pred.

L-system commandsF Move forward creating geometry+ Turn left- Turn right^ Pitch up& Pitch down< Roll counter-clockwise> Roll clockwise[ Push the current state (i.e., start a new command sequence)] Pop the current state (i.e., execute previous command sequence)" Increment current length\ Decrement current length? Increment current thickness! Decrement current thickness

L-systems in Houdini Demo