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Last Time
Shading Interpolation
Texture Mapping introduction
11/7/2002
(c) University of Wisconsin, CS 559

2. (c) University of Wisconsin, CS 559
Today
Texture Mapping details
Modeling Intro (maybe)
Homework 5
11/7/2002
(c) University of Wisconsin, CS 559

3. Basic OpenGL Texturing
Specify texture coordinates for the polygon:
Use glTexCoord2f(s,t) before each vertex:
Eg: glTexCoord2f(0,0); glVertex3f(x,y,z);
Create a texture object and fill it with texture data:
glGenTextures(num, &indices) to get identifiers for the objects
glBindTexture(GL_TEXTURE_2D, identifier) to bind the texture
Following texture commands refer to the bound texture
glTexParameteri(GL_TEXTURE_2D, …, …) to specify parameters for use when applying the texture
glTexImage2D(GL_TEXTURE_2D, ….) to specify the texture data (the image itself)
MORE…
11/7/2002
(c) University of Wisconsin, CS 559

4. Basic OpenGL Texturing (cont)
Enable texturing: glEnable(GL_TEXTURE_2D)
State how the texture will be used:
glTexEnvf(…)
Texturing is done after lighting
You’re ready to go…
11/7/2002
(c) University of Wisconsin, CS 559

5. (c) University of Wisconsin, CS 559
Nasty Details
There are a large range of functions for controlling the layout of texture data:
You must state how the data in your image is arranged
Eg: glPixelStorei(GL_UNPACK_ALIGNMENT, 1) tells OpenGL not to skip bytes at the end of a row
You must state how you want the texture to be put in memory: how many bits per “pixel”, which channels,…
Textures must be square with width/height a power of 2
Common sizes are 32x32, 64x64, 256x256
Smaller uses less memory, and there is a finite amount of texture memory on graphics cards
11/7/2002
(c) University of Wisconsin, CS 559

6. Controlling Different Parameters
The “pixels” in the texture map may be interpreted as many different things. For example:
As colors in RGB or RGBA format
As grayscale intensity
As alpha values only
The data can be applied to the polygon in many different ways:
Replace: Replace the polygon color with the texture color
Modulate: Multiply the polygon color with the texture color or intensity
Similar to compositing: Composite texture with base color using operator
11/7/2002
(c) University of Wisconsin, CS 559

7. Example: Diffuse shading and texture
Say you want to have an object textured and have the texture appear to be diffusely lit
Problem: Texture is applied after lighting, so how do you adjust the texture’s brightness?
Solution:
Make the polygon white and light it normally
Use glTexEnvi(GL_TEXTURE_2D, GL_TEXTURE_ENV_MODE, GL_MODULATE)
Use GL_RGB for internal format
Then, texture color is multiplied by surface (fragment) color, and alpha is taken from fragment
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8. (c) University of Wisconsin, CS 559
Some Other Uses
There is a “decal” mode for textures, which replaces the surface color with the texture color, as if you stick on a decal
Texture happens after lighting, so the light info is lost
BUT, you can use the texture to store lighting info, and generate better looking lighting (override OpenGL’s lighting)
You can put the color information in the polygon, and use the texture for the brightness information
Called “light maps”
Normally, use multiple texture layers, one for color, one for light
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9. (c) University of Wisconsin, CS 559
Textures and Aliasing
Textures are subject to aliasing:
A polygon pixel maps into a texture image, essentially sampling the texture at a point
The situation is very similar to resizing an image, but the resize ratios may change across the image
Standard approaches:
Pre-filtering: Filter the texture down before applying it
Post-filtering: Take multiple pixels from the texture and filter them before applying to the polygon fragment
11/7/2002
(c) University of Wisconsin, CS 559

10. Point Sampled Texture Aliasing
Texture map
Polygon far from the viewer in perspective projection
Rasterized and textured
Note that the back row is a very poor representation of the true image
11/7/2002
(c) University of Wisconsin, CS 559

11. Mipmapping (Pre-filtering)
If a textured object is far away, one screen pixel (on an object) may map to many texture pixels
The problem is: how to combine them
A mipmap is a low resolution version of a texture
Texture is filtered down as a pre-processing step:
gluBuild2DMipmaps(…)
When the textured object is far away, use the mipmap chosen so that one image pixel maps to at most four mipmap pixels
Full set of mipmaps requires double the storage of the original texture
11/7/2002
(c) University of Wisconsin, CS 559

12. Many Texels for Each Pixel
Texture map with pixels drawn on it.
Some pixels cover many texture elements (texels)
Polygon far from the viewer in perspective projection
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Mipmaps
For far objects
For middle objects
For near objects
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14. (c) University of Wisconsin, CS 559
Mipmap Math
Define a scale factor, =texels/pixel
A texel is a pixel from a texture
 is actually the maximum from x and y
The scale factor may vary over a polygon
It can be derived from the transformation matrices
Define =log2 
 tells you which mipmap level to use
Level 0 is the original texture, level 1 is the next smallest texture, and so on
If <0, then multiple pixels map to one texel: magnification
11/7/2002
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15. (c) University of Wisconsin, CS 559
Post-Filtering
You tell OpenGL what sort of post-filtering to do
Magnification: When <0 the image pixel is smaller than the texel:
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, type)
Type is GL_LINEAR or GL_NEAREST
Minification: When >0 the image pixel is bigger than the texel:
GL_TEX_MIN_FILTER
Can choose to:
Take nearest point in base texture, GL_NEAREST
Linearly interpolate nearest 4 pixels in base texture, GL_LINEAR
Take the nearest mipmap and then take nearest or interpolate in that mipmap, GL_NEAREST_MIPMAP_LINEAR
Interpolate between the two nearest mipmaps using nearest or interpolated points from each, GL_LINEAR_MIPMAP_LINEAR
11/7/2002
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16. (c) University of Wisconsin, CS 559
Filtering Example
Level 2
NEAREST_MIPMAP_NEAREST:
level 0, pixel (0,0)
LINEAR_MIPMAP_NEAREST:
level 0, pixel (0,0) * 0.51
+ level 1, pixel (0,0) * 0.49
Level 1
NEAREST_MIPMAP_LINEAR:
level 0, combination of
pixels (0,0), (1,0), (1,1), (0,1)
Level 0
s=0.12,t=0.1
=1.4
=0.49
11/7/2002
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17. (c) University of Wisconsin, CS 559
Boundaries
You can control what happens if a point maps to a texture coordinate outside of the texture image
All texture images are assumed to go from (0,0) to (1,1) in texture space
The problem is how to extend the image to make an infinite space
Repeat: Assume the texture is tiled
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT)
Clamp to Edge: the texture coordinates are truncated to valid values, and then used
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP)
Can specify a special border color:
glTexParameterfv(GL_TEXTURE_2D, GL_TEXTURE_BORDER_COLOR, R,G,B,A)
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18. (c) University of Wisconsin, CS 559
Repeat Border
(1,1)
(0,0)
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Clamp Border
(1,1)
(0,0)
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Border Color
(1,1)
(0,0)
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21. (c) University of Wisconsin, CS 559
Other Texture Stuff
Texture must be in fast memory - it is accessed for every pixel drawn
If you exceed it, performance will degrade horribly
Skilled artists can pack textures for different objects into one image
Texture memory is typically limited, so a range of functions are available to manage it
Specifying texture coordinates can be annoying, so there are functions to automate it
Sometimes you want to apply multiple textures to the same point: Multitexturing is now in most new hardware
11/7/2002
(c) University of Wisconsin, CS 559

22. (c) University of Wisconsin, CS 559
Yet More Texture Stuff
There is a texture matrix: apply a matrix transformation to texture coordinates before indexing texture
There are “image processing” operations that can be applied to the pixels coming out of the texture
There are 1D and 3D textures
Mapping works essentially the same
3D textures are very memory intensive, and how they are used is very application dependent
1D saves memory if the texture is inherently 1D, like stripes
11/7/2002
(c) University of Wisconsin, CS 559

23. Procedural Texture Mapping
Instead of looking up an image, pass the texture coordinates to a function that computes the texture value on the fly
Renderman, the Pixar rendering language, does this
Available in a limited form with vertex shaders on current generation hardware
Advantages:
Near-infinite resolution with small storage cost
Idea works for many other things
Has the disadvantage of being slow in many cases
11/7/2002
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24. (c) University of Wisconsin, CS 559
Other Types of Mapping
Environment mapping looks up incoming illumination in a map
Simulates reflections from shiny surfaces
Bump-mapping computes an offset to the normal vector at each rendered pixel
No need to put bumps in geometry, but silhouette looks wrong
Displacement mapping adds an offset to the surface at each point
Like putting bumps on geometry, but simpler to model
All are available in software renderers like RenderMan compliant renderers
All these are becoming available in hardware
11/7/2002
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25. (c) University of Wisconsin, CS 559
The Story So Far
We’ve looked at images and image manipulation
We’ve looked at rendering from polygons
Next major section:
Modeling
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26. (c) University of Wisconsin, CS 559
Modeling Overview
Modeling is the process of describing an object
Sometimes the description is an end in itself
eg: Computer aided design (CAD), Computer Aided Manufacturing (CAM)
The model is an exact description
More typically in graphics, the model is then used for rendering (we will work on this assumption)
The model only exists to produce a picture
It can be an approximation, as long as the visual result is good
The computer graphics motto: “If it looks right it is right”
Doesn’t work for CAD
11/7/2002
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27. (c) University of Wisconsin, CS 559
Issues in Modeling
There are many ways to represent the shape of an object
What are some things to think about when choosing a representation?
11/7/2002
(c) University of Wisconsin, CS 559

28. Categorizing Modeling Techniques
Surface vs. Volume
Sometimes we only care about the surface
Rendering and geometric computations
Sometimes we want to know about the volume
Medical data with information attached to the space
Some representations are best thought of defining the space filled, rather than the surface around the space
Parametric vs. Implicit
Parametric generates all the points on a surface (volume) by “plugging in a parameter” eg (sin cos, sin sin, cos)
Implicit models tell you if a point in on (in) the surface (volume) eg x2 + y2 + z2- 1 = 0
11/7/2002
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29. Techniques We Will Examine
Polygon meshes
Surface representation, Parametric representation
Prototype instancing and hierarchical modeling
Surface or Volume, Parametric
Volume enumeration schemes
Volume, Parametric or Implicit
Parametric curves and surfaces
Surface, Parametric
Subdivision curves and surfaces
Procedural models
11/7/2002
(c) University of Wisconsin, CS 559