On Sun, 09 Apr 2000 15:38:38 -0400, John VanSickle wrote:
>It occurs to me that when a ray-intersection test takes place, the
>instances where the test nearly succeeds, or nearly fails, can be
>determined from the numbers comapared during the test.  If I am
>correct, for instance, a b^2-4*a*c test is made for quadratics,
>the values of b^2 and 4*a*c will be very close during the cases I
>am drawing attention to, meaning that if a cone of rays covering
>the pixel had been shot, instead of the one ray, some would have
>hit the object and some would have missed, and more inportantly,
>the relative proportions of these two groups of rays can be
>calculated from the exact results of the ray-intersection test;
>for instance, if b^2 exactly equals 4*a*c, we can say that the
>ray intersects the surface at one point, and is tangential there
>as well, and therefore half of the rays bundled around the tested
>ray would miss, and the others hit. 

This is true only if the bundled rays cover an area much smaller than
the object. Assume that the object covers only part of a pixel, and
touches the center of the pixel, like this:

  +------+
  |    _ |
  |   / \|
  |   \_/|
  |      |
  +------+

A ray shot down the middle of the pixel touches the object
tangentially, and the test above yeilds zero, but the object covers
less than half of the pixel. 

I am not sure if this makes much of a difference in the final picture
(especially since the object would probably vanish completely if moved a
bit to the right), and it might help in determining whether antialiasing
should be used on this pixel.

	hp

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