1. ATEC 6351.001 Procedural Animation Introduction to Procedural Methods in 3D Computer Animation Dr. Midori Kitagawa

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

3. Week 8: Procedural Modeling  Procedural modeling methods  Assignment 13

4. Procedural Modeling Methods  Fractal  Branching object generation and animation system  L-system

5. Fractal  A natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale.

6. Fractal in nature  Plants

7. Fractal in nature  Landscapes

8. Fractal in nature  Natural phenomena

9. Helge von Koch (1870-1924)  Koch curve (1904)

10. Koch snowflake  Has a finite area and an infinite perimeter.

11. 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. ”

12. Mandelbrot set  Infinitely complex, i.e., small scale details are not identical to the whole.

13. Branching object generation and animation system  http://www.utdallas.edu/atec/midori/BO GAS/BOGAS.htm http://www.utdallas.edu/atec/midori/BO GAS/BOGAS.htm  http://www.youtube.com/watch?v=Xb50 LQ8lhAU

14. 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.

15. L-systems

16. Turtle geometry  In L-systems, geometry is described using turtle geometry.  The turtle knows: 1. Direction that it is pointing 2. Position

17. Turtle geometry operations  Move forward (F)  Changing directions: turn (+, -), pitch (^,&), roll ( )  Control structures: conditions, loops, if, etc.

18. 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.

19. L-system commands FMove 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

20. L-systems in Houdini  Demo