ATCM 3310 Procedural Animation Introduction to Procedural Methods in 3D Computer Animation Dr. Midori Kitagawa

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

Week 9: Procedural Modeling Procedural modeling methods Assignment 12

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. ” http://webecoist.momtastic.com/2008/09/07/17-amazing-examples-of-fractals-in-nature/

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 . 2D app -- http://www.kevs3d.co.uk/dev/lsystems/

L-systems

Turtle geometry In L-systems, geometry is described using turtle geometry. The turtle knows:
1. Direction that it is pointing
2. 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 = premise
p1 = rule 1
p2 = rule 2
:
pN = rule N The most basic type of rule is: pred=succ
where pred (predecessor) is a symbol to be replaced and succ (successor) is a symbol or a string to replace pred.

L-system commands F 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 ! Increment current thickness http://www.kevs3d.co.uk/dev/lsystems/

L-systems in Houdini Demo