3D graphics eBook - Course Materials Repository

Texture mapping 216
constant distance along a vertical line and the floors/ceilings
would be a constant distance along a horizontal line. A fast affine
mapping could be used along those lines because it would be
correct. A different approach was taken for Quake, which would
calculate perspective correct coordinates only once every 16 pixels
of a scanline and linearly interpolate between them, effectively
running at the speed of linear interpolation because the perspective
correct calculation runs in parallel on the co-processor. [3] The
polygons are rendered independently, hence it may be possible to
switch between spans and columns or diagonal directions
depending on the orientation of the polygon normal to achieve a
more constant z, but the effort seems not to be worth it.
Another technique was subdividing the polygons into smaller
polygons, like triangles in 3d-space or squares in screen space, and
using an affine mapping on them. The distortion of affine mapping
Screen space sub division techniques. Top left:
Quake-like, top right: bilinear, bottom left: const-z
becomes much less noticeable on smaller polygons. Yet another technique was approximating the perspective with a
faster calculation, such as a polynomial. Still another technique uses 1/z value of the last two drawn pixels to linearly
extrapolate the next value. The division is then done starting from those values so that only a small remainder has to
be divided, [4] but the amount of bookkeeping makes this method too slow on most systems. Finally, some
programmers extended the constant distance trick used for Doom by finding the line of constant distance for
arbitrary polygons and rendering along it.
Resolution
The resolution of a texture map is usually given as a width in pixels, assuming the map is square. For example, a 1K
texture has a resolution of 1024 x 1024, or 1,048,576 pixels.
Graphics cards cannot render texture maps beyond a threshold that depends on their hardware, possibly the amount
of available RAM.
References
[1] Jon Radoff, Anatomy of an MMORPG, http:/ / radoff. com/ blog/ 2008/ 08/ 22/ anatomy-of-an-mmorpg/
[2] Blythe, David. Advanced Graphics Programming Techniques Using OpenGL (http:/ / www. opengl. org/ resources/ code/ samples/ sig99/
advanced99/ notes/ notes. html). Siggraph 1999. (see: Multitexture (http:/ / www. opengl. org/ resources/ code/ samples/ sig99/ advanced99/
notes/ node60. html))
[3] Abrash, Michael. Michael Abrash's Graphics Programming Black Book Special Edition. The Coriolis Group, Scottsdale Arizona, 1997. ISBN
1-57610-174-6 ( PDF (http:/ / www. gamedev. net/ reference/ articles/ article1698. asp)) (Chapter 70, pg. 1282)
[4] US 5739818 (http:/ / v3. espacenet. com/ textdoc?DB=EPODOC& IDX=US5739818), Spackman, John Neil, "Apparatus and method for
performing perspectively correct interpolation in computer graphics", issued 1998-04-14