1. Introduction to Texture Mapping
CSE 470/598
Introduction to Computer Graphics Arizona State University

2. Texture Mapping Concepts
A method to create complexity in an image without the overhead of building large geometric models.

3. Basic Idea Application of an image onto a model
An image is mapped onto the 2D domain of a 3D model
Correspondence between domain of surface and texture gives method to apply image

4. Texture Form
Textures are almost always rectangular m x n array of pixels called texels (texture elements)
Textures are frequently square and of sizes that are powers of two to support downsize filtering (mipmapping)
It is not necessary to always use the entire texture

5. Texture Coordinates [0, 1] t [1, 0] [0,0] s
A texture is usually addressed by values between zero and one
The “addresses” of points on the texture consist of two numbers (s, t)
A vertex can be associated with a point on the texture by giving it one of these texture coordinates glTexCoord*(s,t); glVertex*(x,y,z); Texture coords part of state like colors and normals.
…although it is really just an array of pixels
[0, 1] t
[1, 0]
[0,0] s
[s,t]-space  [u,v]-space of surface  [x,y,z]-space of surface

6. Pixels & Texture Coordinates
[0, 1]
s, t = .33, .33 t
For example: a 32 x 32 pixel image
Glubyte mychecker[32][32][3]; glEnable(GL_TEXTURE_2D);
[1, 0]
[0,0] s
glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, 32, 32,
0, GL_RGB, GL_UNSIGNED_BYTE,
mychecker);

7. Texture Coordinates to Polygons
1,0
1,1
Texture Coordinates
s, t = .33, .33
0,0
1,0
Each vertex of each polygon in assigned a texture coordinate.
OGL finds the appropriate texture coordinate for points “between” vertices during rasterization. – same idea as smooth shading!

8. Example domains of the 3D model
Parametric surfaces come with a 2D domain. Meshes: flatten parts to create a 2D domain

9. Textured

10. Modes of Operation
Decal: only the texture color determines the color we see in the frame buffer: GL_DECAL
Modulation: texture color multiplies the color computed for each face (default)
Blend: Similar to modulation but add alpha-blending glTexEnvi(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_MODULATE)

11. Programming with Texture Maps
Create texture and load with glTexImage() by either a. read a jpeg, bmp, …. file b. define texture within application c. copy image from color buffer
Define parameters as to how texture is applied glTexParameter*() Next slides describe the options here…. See Table 9.6 in OGL Red Book
Enable texture maps glEnable(GL_TEXTURE_2D)
Define texture coordinates for vertices glTexCoord*(s,t); glVertex*(x,y,z);

12. Texture Memory
Texels go into texture memory; depends on implementation – special memory or frame buffer
Transfer of texels from application program to texture memory can be significant if texture large
Texture memory is limited resource –proxy commands to query availability
New graphics cards have MBs of texture memory
Texture objects help to optimize access to textures
In recent years, texturing has moved from software to high performance graphics hardware

13. Texture Objects When using more than one texture …
Stores texture data and makes it available
Fastest way to apply/bind/reuse textures
Set-up similar to display lists 1. Name the texture object 2. Bind (create) texture object to texture data/properties 3. Prioritize texture object (if maxing out texture memory) 4. Bind texture object making data currently available

14. Texture Mapping Issues
What should happen when we zoom in close or zoom out far away?
How do we generate texture coordinates ?
What happens if we use texture coordinates less than zero or greater than one?
Are texture maps only for putting color on objects?

15. Texture to Surface Mapping
Texture map to surface takes place during rendering Similar to smooth shading method: Triangle rasterized Each pixel mapped back to the texture Use known values at vertices to interpolation over the texture
Each pixel is associated with small region of surface and to a small area of texture. 3 possibilites for association: 1) one texel to one pixel (rare) 2) magnification 3) minification
 Filtering
Magnification one texel to many pixels
Minification many texels to one pixel

16. Zoom In
many pixels correspond to one texel  “blockiness” / jaggies / aliasing
solution: apply averaging (magnification filter)

17. Zoom-In: Magnification Filter
Pixel cooresponds to a small portion of one texel
Results in many pixels getting same texel
Without a filtering method, aliasing is common
Magnification filter: smooths transition between pixels
pixel
Texture space

18. Zoom-In: Magnification Filter
Options for smoothing: Simplest: GL_NEAREST Just use the closest texel’s color (default – jaggies common) Also called point sampling
Better: GL_LINEAR Weighted average of the four nearest texels Also called bilinear sampling (interpolation)
glTexParameter(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
Bilinear interpolation b1 = (s – s0)/(s2 – s0) b2 = (t – t0)/(t2 – t0)
c = (1-b2)*( (1-b1)*c0 + b1*c1)
+ b2*( (1-b1)*c2 + b1*c3) c3 c0 c1
(s0, t0)
(s2, t0)

19. Zoom Out: Minification Filter
One pixel corresponds to many texels
Common with perspective foreshortening (see example on next slide)
Options:
GL_NEAREST
GL_LINEAR GL_*_MIPMAP_*_ where * = NEAREST OR LINEAR
 mipmapping
glTexParameter(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);

20. Mipmap Improvements
Perspective foreshortening and poor texture mapping causes checkerboard to deform
Mipmaps improve the mapping, returning more form to the checkerboard

21. Better Min Filter: Mipmaps
“mip” stands for multum in parvo, or “many things in a small place”
Basic idea: Create many textures of decreasing size and use one of these subtextures when appropriate

22. Mipmap Representation I
Create several copies Filter down in size Pre-filter textures = mipmaps
Appropriate sized texture selected based on number of pixels occupied by geometry

23. Mipmap Representation II
See plate 20 in ogl for an interesting illustration in the change between mipmaps
Optimize storage (Schematic of method)

24. Mipmap Generation
Must provide all sizes of texture from input to 1x1 in powers of 2
gluBuild*DMipmaps() will help with that!

25. Filtering in Summary Zoom-in calls for mag filter
Zoom-out calls for min filter
More advanced filters require more time/computation but produce better results
Mipmapping is an advanced min filter
Caution: requesting mipmapping without pre-defining mipmaps will turn off texturing; (see Filtering in OGL)

26. Wrapping Modes: Repeat or Clamp
Can assign texture coords outside of [0,1] and have them either clamp or repeat the texture map
Repeat Issue: Making the texture borders match-up 2 1 2 1
clamped
repeat

27. Assigning Texture Coordinates
Parametric surfaces make assignment easy
However, distortion of texture will occur
Can minimize distortions by preserving aspect ratio of texture and geometry
Two solutions: 1) repeat texture 2) use just a portion of the texture (to match the aspect ratio)
geometry
texture

28. 1D Textures Similar to 2D texture but height = 1
Can create pattern of colors for line segments or curves
Contouring
Can use for Cel shading
from intel

29. 3D Textures 3D texture elements are called voxels (volume elements)
Embed an object in the voxels to determine color at vertices
Commonly used in medical or geoscience applications Medical: CT or MRI layered 3D data Geoscience: rock strata or gas measurements
Caution: Texture memory can run out fast!
Example: Uni Hamburg’s Virtual Mummy

30. Resources
From the SIGGRAPH tutorial pages:
Texture Mapping -
Advanced OpenGL Texture Mapping -
Texture Mapping as a Fundamental Drawing Primitive