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This brings back memories - Dr. Bresenham was my graphics instructor. We drew lines & circles - lots of them. :) But the most important thing I learned in his

by chiph 11y ago

This brings back memories - Dr. Bresenham was my graphics instructor. We drew lines & circles - lots of them. :) But the most important thing I learned in his class was that having a well-sorted-out compiler is more important than the choice of language. Most of the class used Borland Turbo Pascal for their projects (it was up to version 5 by that point, I think). I wanted to learn C, and with his approval I used their new version 1.0 Turbo C compiler. What I found was that the Pascal code, with no heroic coding efforts, ran 3-4 times faster than the supposedly "closer to the metal" C.

kazinator 11y ago
I was a maverick at university; I used Bresenham's to draw hyperbolas. I had this idea that since hyperbolas are related to 1/z, maybe the approach could be used for scan-converting textures through a perspective transform, but never developed it farther.
- ggchappell 11y ago
  Ah, that's an interesting idea. We might say that Bresenham's Algorithm is not really about drawing lines; it's about doing a best-possible discrete approximation to linear interpolation, using integer arithmetic. And since we can easily[1] change that line to any conic section we want, we should be able to use a variation on B's Alg. to do a perspective-correct interpolation, right? Sounds good to me. However, as perhaps you were, I'm too lazy[2] right now to work out the details. :-) -------- [1] For certain values of "easy". [2] Or perhaps "too busy". That sounds a bit better, doesn't it?
  - kazinator 11y ago
    I was pulled in so many different directions, and basically stopped hacking on computer graphics. I guessed that the downfall of the approach would be the iterations spent on the same pixel value in a texture, when, so to speak, Bresenham is "going vertical": marching through Y values while treading on the same X. If X is the texture space, it's wasteful. While rasterizing, it really behooves us to just map backwards from screen pixels, get the color value and move on. On the other hand, the approach could do anti-aliasing: average those values being tread over. That is usually solved with mipmapping, though: pre-filtered textures at multiple resolutions. Again: no iterative work per display pixel.

by chiph 11y ago

kazinator 11y ago

I was a maverick at university; I used Bresenham's to draw hyperbolas. I had this idea that since hyperbolas are related to 1/z, maybe the approach could be used for scan-converting textures through a perspective transform, but never developed it farther.

ggchappell 11y ago
Ah, that's an interesting idea. We might say that Bresenham's Algorithm is not really about drawing lines; it's about doing a best-possible discrete approximation to linear interpolation, using integer arithmetic. And since we can easily[1] change that line to any conic section we want, we should be able to use a variation on B's Alg. to do a perspective-correct interpolation, right? Sounds good to me. However, as perhaps you were, I'm too lazy[2] right now to work out the details. :-) -------- [1] For certain values of "easy". [2] Or perhaps "too busy". That sounds a bit better, doesn't it?
- kazinator 11y ago
  I was pulled in so many different directions, and basically stopped hacking on computer graphics. I guessed that the downfall of the approach would be the iterations spent on the same pixel value in a texture, when, so to speak, Bresenham is "going vertical": marching through Y values while treading on the same X. If X is the texture space, it's wasteful. While rasterizing, it really behooves us to just map backwards from screen pixels, get the color value and move on. On the other hand, the approach could do anti-aliasing: average those values being tread over. That is usually solved with mipmapping, though: pre-filtered textures at multiple resolutions. Again: no iterative work per display pixel.