2. Noise Based Texture Noise Based Texture CMPS260 Presentation Guoping Xu gpxu@cse.ucsc.edu Mar. 05, 2003

3. Content Introduction Procedural texture Solid texture Noise Animation

4. Procedural Techniques Used to produce realistic textures —marble, wood, stone, bricks, etc Used to produce realistic objects —water, smoke, steam, fire, etc Offer flexibility to create objects —the designer is not constrained by the complex laws of physics

5. Solid texture We can use space function to represent a solid material. Solid texture We will obtain the surface texture if we evaluate this space function at the visible surface points of an object Shape and texture are independent

6. Noise Why noise? Noise is a texturing primitive, we can use it to create a large variety of natural looking textures. Many things in nature are fractal, they have various levels of detail. So, combining noise into various space functions will produce natural looking procedural textures.

7. Generating Noise Value Noise Given a pseudorandom number between -1 and 1 at each lattice point, a noise function is computed from these random values Gradient Noise First generate a pseudorandom gradient vector at each lattice point and then use the gradients to generate the stochastic function Value-Gradient Noise A combination of value noise and gradient noise. e.g. weighted sum of two, or cubic Hermite interpolation.

8. Perlin Noise(1) -Value Noise Perlin Noise function recreates the fractal property by simply adding up noisy functions at a range of different scales Perlin noise is a popular noise To create a Perlin noise function, you will need two things, a Noise Function, and an Interpolation Function [1]

9. Requirements I–Noise funciton A seeded random number generator Generate the same number( 0 ~ 1 ) for the same seed Sum of noise functions= Perlin Noise Those noises are of different frequency and amplitude frequency = 2 i amplitude = persistence i i is ith noise function being added

10. Gradient Noise Precompute array of n pseudorandom vectors at lattice points Calculate the noise from the nearest corner gradient vectors according to its location For example, in 3D, find the cube associated to the point, then according to the difference vector to each corner and the gradient there, calculate the noise interested.

11. Requirements II –Interpolation function(1) We can use different order of interpolation Linear interpolation linearly interpolate between two end point x(t)=a*(1-t)+b*t 0<=t<=1 –not smooth

12. Interpolation function(2) Cosine interpolation f(t)=(1-cos(  t))/2 x(t)=a*(1-f(t))+b*f(t) 0<=t<=1 much smoother, but need to speedup the cos(  t ) calculation

13. Interpolation function(3) Cubic interpolation very smooth

14. Smooth the noise Smooth the noise at by taking account of the influence of neighbors

15. Application You can use 2D Perlin Noise to landscapes and clouds You can use 3D Perlin Noise to produce volumetric clouds, or animate 2D clouds You can use 4D Perlin Noise to create animated 3D clouds, except that it would be really slow

16. Sample pictures 1.Marble texture texture=cosine( x + perlin(x,y,z) ) 2.Wood texture G=perlin(x,y,x)*20, grain=g-int(g) 3.Standard 3 dimensional perlin noise. 4 octaves, persistence 0.25 and 0.5 4.Cloud using 2D Perlin Noise

17. Animation Consider 2 ways of animating solid spaces Changing the solid space over time Has time as a parameter that changes the definition of the space over time Moving the point being rendered through the solid space

18. References 1.http://freespace.virgin.net/hugo.elias/models/m_perlin.htmhttp://freespace.virgin.net/hugo.elias/models/m_perlin.htm 2.Perlin, K., An Image Synthesizer. Proceedings of SIGGRAPH '85 (San Francisco,July 22-26 1985). In Computer Graphics 19, 3 (July 1985), 287-296. 3.http://mrl.nyu.edu/~perlin/paper445.pdfhttp://mrl.nyu.edu/~perlin/paper445.pdf 4.Perlin, K and Hoffert, E., Hypertexture, Computer Graphics, Vol. 23, No. 3, July 1989, 253-262. 5.Ebert, D., Musgrave, F., etc.,Texturing and Modeling, a Procedural Approach, AP Professional, 1994.

19. Thank You!