1 / 29

L-Systems

L-Systems. Lindenmayer Systems. Prusinkiewicz and Lindenmayer. Recursive branching structure. Complex but constrained. Recursive Branching Structure. Botany - structure. Stems, roots, buds, leaves, flowers. Herbaceous or woody. Dichotomous or monopodial. Terminal bud or lateral bud.

zea
Download Presentation

L-Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. L-Systems Lindenmayer Systems Prusinkiewicz and Lindenmayer Recursive branching structure Complex but constrained.

  2. Recursive Branching Structure

  3. Botany - structure Stems, roots, buds, leaves, flowers Herbaceous or woody Dichotomous or monopodial Terminal bud or lateral bud Vegetative bud or flower bud Alernate, opposite, or whorled.

  4. Botany - growth influences Lineage - age Cellular descent - nutrients and hormones Tropisms - e.g., phototropism, geotropism Obstacles - collision response: temporary or permanent.

  5. DOL-Systems Production rules: ai -> bi D - deterministic 0 - zero contextual systems (context-free) Axiom - initial string Parallel rewriting rules.

  6. Geometric replacement - replace each symbol of string with a graphic element - connectivity assumptions Turtle graphics - each symbol is a command to a drawing pen. Geometric Interpretation of String

  7. A -> BCB B -> XX C -> TT Axiom: A Geometric Replacement - Example A BCB XXTTXX

  8. X: T: X X T T X X Geometric Replacement XXTTXX

  9. Parameters - d: linear step size - d: angular step size. Turtle Graphics “drawing turtle” is controlled by symbols of string Symbols read from string in left to right order State of turtle: position and direction: (x, y, a)

  10. F Move forward a distance d while drawing a line. Its state will change from (x,y,a) to (x+d*cos a, y+d*sin a, a) f Move forward a distance d without drawing a line. Its state will change as above. + Turn left by an angle d. Its state will change from (x,y, a) to (x,y, a + d) - Turn right by an angle d. Its state will change from (x,y, a) to (x,y, a - d). Turtle Graphics

  11. A -> BCB B -> FF C -> TT T -> -F++F- Axiom: A Turtle Graphics - Example A BCB FFTTFF FF -F++F- -F++F- FF

  12. d: d: 45 degrees Initial state: (10,10,0) F F -F++F- -F++F- F F Turtle Graphics - Example FF -F++F- -F++F- FF

  13. Bracketed L-Systems Brackets - push and pop states - multiple types of brackets - brackets have attachment semantics X X [ XX ] { XX } X X

  14. Properties Can be recursive - reduce size based on branching level - self-similarity under scale Attribute symbols: line length, width, color, etc. Database amplification Track string development => growth process.

  15. S -> F A F A -> [ + F B F ] F [ + F F F ] F F F F A -> F B -> [ - F B F ] B -> F Axiom: S F [ + F [ - F F F ] F ] F Non-Deterministic

  16. Stochastic L-Systems S 1.0 -> F A F A 0.8 -> [ + F B F ] A 0.2 -> F B 0.4 -> [ - F B F ] B 0.6 -> F

  17. Context-Sensitive L-Systems S -> F A T A>T -> [ + F B F ] A>F -> F F<B -> [ - F A F ] F<B >F -> [ - F A F ] T -> F

  18. F -> F1 F1 -> F2 F2 -> F3 F 3-> F4 Animating Plant Growth Flexible movement of structure Changes in topology due to growth process Elongation of existing structures F -> FF

  19. Parametric L-Systems S -> A(0) A(t) -> A(t+1) A(t): t>=1.0 -> F

  20. Timed L-Systems Global time variable Local age value (u0, b0) -> ( (u1,a1), (u2, a2), … , (un, an) ) Jump from terminal age to terminal age.

  21. Interacting with the Environment Physical obstacles Wind Gravity Nutrients, moisture from soil Sunlight: length of day, shadows.

  22. Open L-Systems Mech and Prusinkiewicz Communication terms - Request and transmit information w/ environment - Distribution of nutrients, sunlight, etc.

  23. L-Systems - Summary Branching structure, self-similarity Controlled complexity , data base amplification Geometric replacement, Turtle graphics Non-deterministic, stochastic, context sensitive, timed, open Animation - dynamics of static structure - time-varying drawing parameters - topology changes - growth of individual elements.

More Related