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

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Presentation on theme: "ATEC 6351.001 Procedural Animation Introduction to Procedural Methods in 3D Computer Animation Dr. Midori Kitagawa."— Presentation transcript:

1 ATEC 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 ( )  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  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  GAS/BOGAS.htm GAS/BOGAS.htm  LQ8lhAU

14 L-systems  L-system is a string rewriting system introduced by the biologist Aristid Lindenmayer in  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 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


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