On 28 Oct 1999 11:50:18 -0400, ingo wrote:
>Ron Parker wrote:
>
>>Even better would be a texture based on the second derivative
>>of the surface, but such a thing is hard to calculate.
>>
>
>ehm, could you explain this please, in laymens terms?

The first derivative is the slope (roughly.)

The second derivative is the rate of change of the slope. Smooth,
gently curving regions would have a low second derivative, while 
sharply curving regions would have a high second derivative. The
curvature of the surface corresponds strongly to its accessibility.

Unfortunately, it's very difficult - if not impossible - to 
calculate for CSG objects and some primitives, and it's pretty 
meaningless for meshes: the second derivative of a mesh is either
zero or infinite (undefined, really) anywhere on its surface.  A
CSG of two spheres would have the same problem, except that the
curvature would be the radius of one of the spheres or undefined.
The paper I have here goes into excruciating detail on that problem.

One method the paper I have doesn't cover into in great detail is based
on monte-carlo methods: Just fire a bunch of random rays along near-
perpendiculars to the surface normal from locations just "above" the 
intersection point with the surface and estimate the local curvature
from the resulting (nearby) intersections.  If there are none, you 
can assume that the surface curves away from the normal and the 
local accessibility is therefore infinite.

-- 
These are my opinions.  I do NOT speak for the POV-Team.
The superpatch: http://www2.fwi.com/~parkerr/superpatch/
My other stuff: http://www2.fwi.com/~parkerr/traces.html

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