- 1. Texturering & Modeling a Procedual Approach
2. Chapter 4CELLULAR TEXTURING 3. Agenda The New Bases
Implementation Strategy Dicing Space Neighbor Testing The Subtle
Population Table Extensions and Alternatives Sample Code 3 4.
Cellular TexturingThe function that launched a thousand textures.4
5. Cellular TexturingPerlins Noise Function Steve WorleyCEO,
founderWorley Laboratories1995 Present (17 years) Menlo Park,
CaliforniaResearch and development of graphics toolsDeveloped and
released 6 different software products:Gaffer: lighting snad
shading methodsPolk, Taft: collections of artist
utilitiesSasquatch: procedural hair and fur modeler and rendererG2:
interactive lighting and shading systemFPrime: the industrys first
real-time render-accurate preview renderer, using interactive
raytracing. 5 6. Cellular TexturingPerlins Noise Function Cell
random , , , , , , table storage 6 7. Cellular Texturing R3 ,
scalar value return Point (x, y, z) Input value scalar value .
scalar value regular pattern .< Perlins Noise Function(3D Basis)
:(a) Wrinkles, (b) Color >7 8. Cellular Texturing Many Texture
Algorithms Fourier methods Reaction diffusion textures, An
algorithm by Miyata-> Extensive Precomputation , scalar value
return .(a) (b)< Many Texture Algorithms :(a) Reaction diffusion
- horse ,(b) An algorithm by Miyata Edo Castle > Many texture
algorithms form , Perlins noise function . -> new texture
function , Basis Function . 8 9. The New Bases 2 feature points R3
. local points scalar function . local points ( Bombing, Lewis
Methods) The Perlins noise basis function precomputation table
storage noise noise function 9 10. The New Bases Definition
Randomly Distributed Feature Points in R3 F1 (x) : Distance to
Closest Feature Point from any Point x in R3 ( F1 (x) R3 Voronoi
region ) F2(x): Distance to Second Closest Feature Point Fn(x):
Distance to n th Closest Feature Point (a)(b) (c)< F1(x)
Function : (a) 2D Plane On surface, (b) 2D Plane Off surface, (c)
3D plane >10 11. The New Bases Fn(x) Properties Fn(x) continuous
. Fn(x) n .( ) ->0 F ( x) F ( x) F ( x)Ingeneral : 12, (3F ( x))
Fnn 1 ( x) The gradient of Fn(x): x n feature point unit direction
vector 11 12. The New BasesVoronoi diagram p q dist(p, q),, n P
P={p1, p2, p3, ..., pn} P Voronoi Diagram P n cell , dist(pi, q)
< dist(pj, q) q p1 cell P cell 12 13. The New
Baseshttp://www.snibbe.com/projects/interactive/boundaryfunctions
13 14. The New Bases14 15. The New Bases15 16. Implementation
Strategy Cellular 0 17. Implementation Strategy Feature Points
basis function function 17 18. Dicing Space Feature Point 18 19.
Dicing Space Sample LocationFeature Point 19 20. Dicing
SpaceFeature Points Seed SolutionFast Random Number Generator Seed
32 (hash)20 21. Dicing Spaceshort lookup table of 256
possibilitiesSeed Possible point populations Magic PropertyPoints
Isotropic Precomputed 21 22. Neighbor Testing 22 23. Neighbor
Testing 23 24. The Subtle Population Table , , point () point ,
cube point , feature point , texture function grid bias Poisson
distribution 24 25. The Subtle Population Tableunit volume feature
point ,unit cube m feature point . (P(,m) : unit cube m feature
point , Poisson )P(,m) = ^(m)/{ e^()* m!)}25 26. The Subtle
Population Table X 9 , 2.5 5 ?26 27. The Subtle Population Table
Cube Feature Point Point Neighbor Cube Input Constant Scaling Scale
Normalize 27 28. Extensions and Alternatives Ken Musgrave Noise
Function distance . ( Euclidean distance d2=dx*dx+dy*dy+dz*dz;
)Biasedstretched A*dx*dx+B*dy*dy+C*dz*dz Manhattan distance
fabs(dx)+fabs(dy)+fabs(dz) Radial
Manhattan:A*fabs(dR)+B*fabs(dTheta)+C*dz Superquadratic:
pow(fabs(dx), A) + pow(fabs(dy), B) + pow(fabs(dz),C) 28 29.
Extensions and Alternatives (a) F1(x) - simple - color spline and
bump map - feature points -> voronoi - example : Polka Dots (
)(b) F2(x)() & F2(x)()- - color spline and bump map linear
combination . 29 30. Extensions and Alternatives (c) F2(x) F1(x) ;
2D - x F2(x) > F1(x) - color spline and bump map - F2(x) = F1(x)
0 voronoi boundaries - to make latticework of connected ridges,
forming a vein-like tracery (d) Constant Base Color plus Fractal
Noise over F1 Regions, F2(x) F1(x) Bump Mapping ; 3D Flagstone
texture - F1 function feature point identity ID number return ,
number voronoi cell values . -> cell shade . - F2(x) - F1(x)
Bump Mapping - cell fractal noise 30 31. Extensions and
Alternatives(e) Linear Combination of Fn : C1F1 + C2F2 + C3F3 +
C4F4 (Flagstone-like area) - low n basis function combinations - Cn
. 31 32. Extensions and Alternatives(f) Fractal Version - noise
fractal noise . - different weight & Scaling factors -
computing a function: range of i (i=0~5) - Gn color and bumps index
* upper- spotted pattern, F1 fractal version- tongue : fractal
noise - body : linear gradient color variation * lower - More
Fractal versions ; Cut Tori32 33. Extensions and Alternatives(g) F1
Fractal Crumple : Seawater (upper) - version - Bump Map , tinfoil(
) surface crumple . - surface break up . - fractal noise bumps
subtle roughening . - crumple appearance reflective, bumpedmap
plane .(f) More Distance Metrics - Manhattan Metric (lower) - A
radial coordinate version : Death Star33 34. Extensions and
Alternatives(g) Spatially Varying Density - Object Geometry -
algorithm 3D compute , 2D variants . - 4D variants animated .34 35.
Sample Codestatic int
Poisson_count[256]={4,3,1,1,1,2,4,2,2,2,5,1,0,2,1,2,2,0,4,3,2,1,2,1,3,2,2,4,2,2,5,1,2,3,2,2,2,2,2,3,
2,4,2,5,3,2,2,2,5,3,3,5,2,1,3,3,4,4,2,3,0,4,2,2,2,1,3,2,2,2,3,3,3,1,2,0,2,1,1,2,
2,2,2,5,3,2,3,2,3,2,2,1,0,2,1,1,2,1,2,2,1,3,4,2,2,2,5,4,2,4,2,2,5,4,3,2,2,5,4,3,
3,3,5,2,2,2,2,2,3,1,1,4,2,1,3,3,4,3,2,4,3,3,3,4,5,1,4,2,4,3,1,2,3,5,3,2,1,3,1,3,
3,3,2,3,1,5,5,4,2,2,4,1,3,4,1,5,3,3,5,3,4,3,2,2,1,1,1,1,1,2,4,5,4,5,4,2,1,5,1,1,
2,3,3,3,2,5,2,3,3,2,0,2,1,1,4,2,1,3,2,1,2,2,3,2,5,5,3,4,5,5,2,4,4,5,3,2,2,2,1,4,
2,3,3,4,2,5,4,2,4,2,2,2,4,5,3,2};#define DENSITY_ADJUSTMENT
0.398150static void AddSamples(long xi, long yi, long zi, long
max_order,double at[3], double *F,double (*delta)[3], unsigned long
*ID);35 36. Sample Code/* The main function! */void Worley(double
at[3], long max_order,double *F, double (*delta)[3], unsigned long
*ID){double x2,y2,z2, mx2, my2, mz2;double new_at[3];long
int_at[3], i; /* Initialize the F values to "huge" so they will be
replaced by thefirst real sample tests. Note well be storing and
comparing theSQUARED distance from the feature points to avoid lots
of slowsqrt() calls. Well use sqrt() only on the final answer. */
for (i=0; i>24]; /* 256 element lookup table. Use MSB */
seed=1402024253*seed+586950981; /* churn the seed with good Knuth
LCG */ for (j=0; j0 && d2 *//* Bump down more distant
information to make room for this new point. */for (i=max_order-1;
i-->index;){F[i+1]=F[i];ID[i+1]=ID[i];delta[i+1][0]=delta[i][0];delta[i+1][1]=delta[i][1];delta[i+1][2]=delta[i][2];}/*
Insert the new points information into the list.
*/F[index]=d2;ID[index]=this_id;delta[index][0]=dx;delta[index][1]=dy;delta[index][2]=dz;}
}return;}42 43. Conclusion texture design . Perlins fractal noise ,
noise algorithm ACellular Texture Basis Function . , image . 43 44.
Reference Worley, Steven (1996). A cellular texture basis function.
Proceedings of the 23rd annual conference on Computer graphics and
interactive techniques
http://www.gutgames.com/post/Cellular-Textures.aspx
http://www.blackpawn.com/texts/cellular/default.html
http://codevania.springnote.com/pages/3175790.xhtml
http://demonstrations.wolfram.com/FractalCellularTextures/
http://fgiesen.wordpress.com/2010/03/28/how-to-generate-cellular-textures/
http://hq.scene.ro/blog/read/cellular-texture/
http://my.opera.com/community/forums/topic.dml?id=1300002
http://www.gamedev.net/page/resources/_/technical/graphics-programming-and-theory/cellular-textures-the-light-speed-approach-r2668
http://www.drx.dk/cel.phphttp://cell-auto.com/optimisation/
http://petewarden.com/notes/archives/2005/05/testing.htm
http://www.cs.unc.edu/~blloyd/comp238/shader.html
http://mathworld.wolfram.com/VoronoiDiagram.html
http://www.snibbe.com/projects/interactive/boundaryfunctions
http://www.snibbe.com/index.php/projects/interactive/bubbleharp/
http://gogocj2012.blog.me/5013759505244 45. Q&A 46.
