3D Textures

1
3D Textures

• Soon Tee Teoh
• CS 116B

2
2D Texture Maps in Ray-Tracing

• We have seen 2D texture-mapping in OpenGL.
• How do we do 2D texture mapping in ray-tracing?
• Simply generate the (s,t) texture coordinates
  from the surface coordinates of the object, and
  read from the texture map to get the color.

z
t
Wrapping a texture around a cylinder
t z s q/360
q
s
3
3D Texture Maps in Ray-Tracing

• A 2D texture map is a pattern that is pasted onto
  a surface.
• A 3D texture map defines a color at each 3D
  coordinate (x,y,z).
• 3D texture also called solid texture.
• For example, a 3D wood texture or marble texture
  can be defined.
• When mapped onto 3D geometry, it is as though the
  3D geometry has been carved out of the wood or
  marble material.

4
Functional 3D Texture Definition

• Whether in 2D or 3D, the texture pattern can be
  either defined by a function or by some 2D or 3D
  data.
• Lets try to generate some nice 3D textures
  functionally.
• The texture function can be generalized as f,
  where f(x,y,z) (r,g,b)
• In other words, given 3D coordinates, the texture
  function returns a color.

5
Noise and Turbulence

• Ken Perlins SIGGRAPH 85 paper An Image
  Synthesizer introduces 3D texture-mapping, and
  also suggests an approach to generate interesting
  3D textures.
• The method uses noise and turbulence.
• The noise function is a continuous function that
  varies in 3D space at uniform frequency.
• Simple noise function
• Create a 3D grid.
• Generate a random number at each grid point.
• Use tri-linear interpolation to get value at any
  position.
• Turbulence Obtained by mixing several noise
  functions together
• turb(s,x,y,z) noise(sx,sy,sz)/2
  noise(2sx,2sy,2sz)/4 noise(4sx,4sy,4sz)/8
• where s is the scaling factor
• A more general formula for turb is
• You get the above example by setting N3, ab2

N-1
noise (sbix, sbiy, sbiz) ai1
turb(s,x,y,z) S
i0
6
Noise and Turbulence
Turbulence
Noise
Scale 4
3
2 1
7
Marble Texture Function

• Marble function
• marble(x,y,z) undulate(sin(z A
  turb(s,x,y,z)))
• where A and s are parameters the user can set to
  control the appearance of the marble
• The undulate function is a spline-shaped function
  that the user can define

undulate(u)
u
8
Wood Texture Function

• A simple wood texture with concentric rings
  around the center
• rings(r) ((int)r) 2
• where r sqrt(x2y2) to make rings about the
  z-axis
• The value of the function jumps between 0 and 1
• Next Rings of thickness M. Function jumps
  between D and DA
• wood(x,y,z) D A x rings(r/M)
• Next Add some wobble to the rings
• wood(x,y,z) D A x rings(r/M K sin (q/N))
• where q is the angle about the z axis, and D, A,
  M, K and N are user-defined parameters to control
  the appearance of the texture
• Next Add a twist to the wood grain
• wood(x,y,z) D A x rings(r/M K sin (q/N
  Bz))
• where B is also a user-defined parameter

9
3D Textures in OpenGL

• Using 3D Textures in OpenGL is a straight-forward
  extension of 2D textures.
• The following functions should look familiar.

glTexImage3D(GL_TEXTURE_3D, 0, GL_RGBA, texWidth,
texHeight, texDepth, 0, dataFormat, dataType,
volTexArray) glEnable(GL_TEXTURE_3D) glTexPara
meteri(GL_TEXTURE_3D, GL_TEXTURE_MAG_FILTER,
GL_NEAREST) glTexParameteri(GL_TEXTURE_3D,
GL_TEXTURE_MIN_FILTER, GL_NEAREST) glTexCoord3f(
sCoord, tCoord, rCoord)