The programs I've written dealing with geodesic dome geometry make a lot of use of projection via affine transform. Basic stuff, but I think interesting and visual in itself and often poorly explained. So I might write up a post or two and put together a couple of web toys just dealing with that as some groundwork, before moving on to anything having to do with geodesic domes directly.
A web toy dealing with projections/mapping/warping needs a visual test subject. A usual approach is to take a sample bitmap and show the result of running it through the transform. This can produce less than appealing results, because of the inherent limited resolution of the source bitmap. Depending on the transform, very small (subpixel) areas of the source image can end up taking up very large areas of the result image. Intermediate pixels then need to be synthesized/interpolated, and the results get bumpy/blurry.
I find it more convenient to deal with a synthetic, functional, test subject. Given a point (x,y) in the real image plane, a function is invoked to return the color of that point in test subject. This sort of test subject can have effectively infinite (within the limits of floating point) resolution.
Since the test subject has effectively infinite resolution, it is also easy to oversample the source with respect to the output bitplane and then average the sub-pixel results to obtain a greater effective visual resolution.
I'll be using these test subjects in subsequent articles to illustrate the effects of transform math.