1. ATCM 3310 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 9: Procedural Modeling
Procedural modeling methods
Assignment 12

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 ( )
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

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 .
2D app --

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 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

20. L-systems in Houdini
Demo