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ATEC 6351.001Procedural AnimationIntroduction to Procedural Methods in 3D Computer Animation
Dr. Midori Kitagawa
Fractal A natural phenomenon or a
mathematical set that exhibits a repeating pattern that displays at every scale.
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. ”
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 .
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