Noise Based TextureNoise Based Texture

CMPS260 PresentationGuoping Xu

gpxu@cse.ucsc.edu

Mar. 05, 2003

ContentContent

• Introduction

• Procedural texture

• Solid texture

• Noise

• Animation

Procedural TechniquesProcedural 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

Solid textureSolid 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

NoiseNoise

• 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.

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 NoiseFirst 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.

Perlin Noise(1)Perlin Noise(1)-Value Noise-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]

Requirements IRequirements I–Noise funciton–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 = 2i

amplitude = persistencei i is ith noise function being added

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.

Requirements IIRequirements II–Interpolation function(1)–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

Interpolation function(2)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

Interpolation function(3)Interpolation function(3)

• Cubic interpolation

very smooth

Smooth the noise

• Smooth the noise at by taking account of the influence of neighbors

Application 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

Sample picturesSample 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. Cloudusing 2D Perlin Noise

AnimationAnimation

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

References1. http://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.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.

Thank You!