Topics. Recursive tree models. Procedural approach L-systems. Image-based approach. Billboarding

Transcription

1 Plant Modeling

2 Topics Recursive tree models Billboarding Procedural approach L-systems Image-based approach

3 Tree Model

4 The structure of a tree Trunk (linkage) Branches (linkage, child of trunk node) Leaves/Buds/flowers/fruit (child of branches)

5 Trunk Trunk circular extrusion along a path For one segment, the radius of the cross section will remain constant or decrease from base to tip Specifying a radius at each end and interpolate Path set of points Straight line Add random rotation for each segment Specify desired length, number of branches

6 Branching The trunk can spawn branches Each branch can spawn new branches For a branch, specify Starting position how close to base of the segment? Branching angle which direction does the branch extend in? Length how long should the branch be? Randomness, but impose limits on all of those values Unity demo θ t θ b

7 We can create leaves as the ending nodes of the tree. But Too many leaves Too much computational and storage cost In practice (especially in games) We use textures as the ending nodes Each texture models multiple leaves The alpha channel of the texture indicates transparency. Known as billboarding. Leaves

8 Another Example

9 Another Example

10 Another Example

11 Leaves More textures => more realism Fewer textures => less realism We use more textures when we are closer to the trees We use fewer textures when we are far away Level-of-Details (LOD)

12 L-Systems

13 L-Systems A model of morphogenesis, based on formal grammars (set of rules and symbols) Introduced in 1968 by the Swedish biologist A. Lindenmayer Originally designed as a formal description of the development of simple multicellular organisms Later on, extended to describe higher plants and complex branching structures

14 Self-similarity in Nature Approximate Only occurs over a few discrete scales (3 in this Fern) Self-similarity in plants is a result of developmental processes, since in their growth process some structures repeat regularly. (Mandelbrot, 1982)

15 Types of L-systems Context-free: production rules refer only to an individual symbol Context-sensitive: the production rules apply to a particular symbol only if the symbol has certain neighbours Deterministic: If there is exactly one production for each symbol, Stochastic: If there are several, and each is chosen with a certain probability during each iteration

16 D0L-systems Simplest class of L-systems, deterministic and context free. Example: Alphabet = {a,b} Rules = {a ab, b a} Axiom: b Syntax of a production rule: Initiator Generator b a a b a b a a b a a b _/ / \ a b a a b a b a Example of a derivation in a DOL-System

17 An Example root: B p: B F B F[-B]F[+B][B] F: move forward +: turn left -: turn right [: Store the current position ]: restore the previous position n = 1-5

18 Stochastic L-systems Avoid regularity in the system by specifying different productions for the same symbol and choose between them based on probabilities and random numbers. For example, the productions : p1 : a -> (0.7) b a p2 : a -> (0.3) c a are 2 rewriting rules for the letter a. In one derivation step, either p1 or p2 will be applied to each occurrence of a, according to the given distribution (0.7 and 0.3).

19 3D L-Systems

20 3D Bracketed L-Systems

21 SpeedTree Specialized commercial tool to model trees Mix of procedural and hand drawing modeling SpeedTree Model Library (150+ species, 500+ models, textures and meshes)

22 References Aristid Lindenmayer. Mathematical models for cellular interaction in development. parts I and II. Journal of Theoretical Biology, 18: and , P. Prusinkiewicz and A. Lindenmayer. The Algorithmic Beauty of Plants. Springer-Verlag, Algorithmic Beauty of Plants An Introduction to L-Systems Speedtree

23 Image-Based Trees

24 Image-Based Tree Modeling Using color photos to recover the branches and leaves of a tree Occlusion is a big problem One way is to use synthesize invisible regions hnu0

25 Dense Foliage Reconstruction By Disney Research, SIGGRAPH e-foliage/

26 More Problems How to model growth? What about buds, flowers? Animation?