1. Week 7 - Wednesday
CS361

2. Last time What did we talk about last time? Transparency
Gamma correction
Started texturing

3. Questions?

4. Project 2

5. Exam 1 Post Mortem

6. Texturing

7. Texturing We've got polygons, but they are all one color
At most, we could have different colors at each vertex
We want to "paint" a picture on the polygon
Because the surface is supposed to be colorful
To appear as if there is greater complexity than there is (a texture of bricks rather than a complex geometry of bricks)
To apply other effects to the surface such as changes in material or normal

8. Corresponder function Value transform function
Texture pipeline
We never get tired of pipelines
Go from object space to parameter space
Go from parameter space to texture space
Get the texture value
Transform the texture value
Object space
Projector function
Parameter space
Corresponder function
Texture space
Obtain value
Texture value
Value transform function
Transformed value

9. Projector function
The projector function goes from the model space (a 3D location on a surface) to a 2D (u,v) coordinate on a texture
Usually, this is based on a map from the model to the texture, made by an artist
Tools exist to help artists "unwrap" the model
Different kinds of mapping make this easier
In other scenarios, a mapping could be determined at run time

10. Corresponder function
From (u,v) coordinates we have to find a corresponding texture pixel (or texel)
Often this just maps directly from u,v  [0,1] to a pixel in the full width, height range
But matrix transformations can be applied
Also, values outside of [0,1] can be given, with different choices of interpretation

11. Texture values
Usually the texture value is just an RGB triple (or an RGBα value)
But, it could be procedurally generated
It could be a bump mapping or other surface data
It might need some transformation after retrieval

12. Student Lecture: Mipmapping and Anisotropic filtering of Textures

13. Image Texturing

14. Image texturing Usually, texturing is image texturing:
Gluing a 2D image onto a polygon
Recall that textures have certain limitations
Usually 2m x 2n texels
Some old cards require square textures
Most new cards don't have to do powers of 2
Maximum sizes vary:
2048 x 2048 might be all your laptop can do
8192 x 8192 is required by DirectX 10

15. Resizing
Sometimes a small texture will cover a much larger area on screen
This effect is called magnification
Sometimes a large texture will cover very little area on the screen
This effect is called minification
Different techniques exist to overcome these problems

16. Magnification
Magnification is often done by filtering the source texture in one of several ways:
Nearest neighbor (the worst) takes the closest texel to the one needed
Bilinear interpolation linearly interpolates between the four neighbors
Bicubic interpolation probably gives the best visual quality at greater computational expense (and is generally not directly supported)

17. Bilinear interpolation (with apologies)
Perhaps unsurprisingly, the book gives a pretty good explanation of bilinear interpolation on p. 159
I guess I should direct people there in the future

18. Blurring issues
Bilinear interpolation tends to blur sharp edges, but you can interpolate non-linearly, remapping bright colors to a bright value and dark to a dark value
Another alternative is detail textures
Overlay higher resolution textures (representing details like scratches) onto a magnified texture

19. Minification Minification is just as big of a problem (if not bigger)
Bilinear interpolation can work
But an onscreen pixel might be influenced by many more than just its four neighbors
We want to, if possible, have only a single texel per pixel
Main techniques:
Mipmapping
Summed-area tables
Anisotropic filtering

20. Mipmapping
Mipmapping is the most popular texture antialiasing solution
Mip = "multum in parvo," meaning "many things in a small place"
The trouble with minification is that a single pixel needs to be colored by lots of texels
The solution: when loading the texture, create many smaller filtered versions of the texture, then use the appropriate one for rendering

21. Mipmapping in action
Typically a chain of mipmaps is created, each half the size of the previous
That's why cards like square power of 2 textures
Often the filtered version is made with a box filter, but better filters exist
The trick is figuring out which mipmap level to use
The level d can be computed based on the change in u relative to a change in x

22. Trilinear filtering
One way to improve quality is to interpolate between u and v texels from the nearest two d levels
Picking d can be affected by a level of detail bias term which may vary for the kind of texture being used

23. Summed-area table
Sometimes we are magnifying in one axis of the texture and minifying in the other
Summed area tables are another method to reduce the resulting overblurring
It sums up the relevant pixels values in the texture
It works by precomputing all possible rectangles

24. Anisotropic filtering
Summed area tables work poorly for non-rectangular projections into texture space
Modern hardware uses unconstrained anisotropic filtering
The shorter side of the projected area determines d, the mipmap index
The longer side of the projected area is a line of anisotropy
Multiple samples are taken along this line
Memory requirements are no greater than regular mipmapping

25. MonoGame Examples

26. Quiz

27. Upcoming

28. Next time… MonoGame examples Project 2 and Assignment 3 work day?
Textures in shader code
Project 2 and Assignment 3 work day?

29. Reminders Keep working on Project 2 Finish Assignment 3
Keep reading Chapter 6
Internship opportunity:
Masonic Villages
Several previous E-town students have had good experiences there
Contact me if interested