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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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Ron Parker wrote:
>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 - ........
Ah, I see. Thanks
The monte-carlo method sounds promising.
Walking home from shopping I had an idea (well, the start of an
idea). Make several copies of the original. Modify each copy
slightly, scale, translate or surface subdivide etc. Then
difference the original and ead each copy, give each new object
a different pigment. Union all objects, slice them up and
make it into a df3-file. Use this as the base for texturing the
original object. Will it work? don't know.
Ingo
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ingo wrote:
> Walking home from shopping I had an idea (well, the start of an
> idea). Make several copies of the original. Modify each copy
> slightly, scale, translate or surface subdivide etc. Then
> difference the original and ead each copy, give each new object
> a different pigment. Union all objects, slice them up and
> make it into a df3-file. Use this as the base for texturing the
> original object. Will it work? don't know.
I don't know if it will work or not but you sure made my head hurt.
--
Ken Tyler - 1100+ Povray, Graphics, 3D Rendering, and Raytracing Links:
http://home.pacbell.net/tylereng/index.html http://www.povray.org/links/
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Ken wrote:
> I don't know if it will work or not but you sure made my head hurt.
Realy want to make your head hurt? Try calculating the stress tenser
across the event horizon of a black hole!
Ken Matassa
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Hello Ken Matassa,
a Schwarzschild or Kerr black hole :).
Fabian.
Ken Matassa wrote:
>
> Ken wrote:
>
> > I don't know if it will work or not but you sure made my head hurt.
>
> Realy want to make your head hurt? Try calculating the stress tenser
> across the event horizon of a black hole!
>
> Ken Matassa
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> 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.
Since every intersection has a normal calculation, what if you were to do a
prepass step and store all the normals for the intersections within the
image, then when you render estimate the curvature? I can see that there
might be problems around the edges of the surface, but could this work
somewhat?
-Mike
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But with mirrors etc. the number of normals to be stored would become HUGE,
requiring massive amounts of memory. Monte Carlo sampling around the curent
intersection would give nearly the same result.
Margus
Mike wrote:
>
> Since every intersection has a normal calculation, what if you were to do a
> prepass step and store all the normals for the intersections within the
> image, then when you render estimate the curvature? I can see that there
> might be problems around the edges of the surface, but could this work
> somewhat?
>
> -Mike
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> But with mirrors etc. the number of normals to be stored would become HUGE,
> requiring massive amounts of memory. Monte Carlo sampling around the curent
> intersection would give nearly the same result.
Shouldn't be if you just store the normal at the intersection point of the
surface in question. There could only be one normal per pixel, which I supposed
could create quite a few limitations. Ah well, just a thought.
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There is a plugin for MAX called DirtyReyes which does just this, and very
realistically. Unfortunately it uses mapping coordinates of the mesh and
thus I don't think could be implimented easily with POV-Ray.
--
Lance.
The Zone - http://come.to/the.zone
Ken <tyl### [at] pacbell net> wrote in message
news:38158BD5.F0F02B93@pacbell.net...
>
>
> 2. (Fine Arts) The color or incrustation which age gives to works of art;
> especially, the green rust which covers ancient bronzes, coins, and
medals.
>
> It is quite common to see a patina discoloration inside the cracks,
> crevices, and deep folds on sculpture while it's surface maintains
> more of the original material's coloration.
>
> How would one apply this affect to a 3d object with proceedural methods
> rather than relying upon complicated image maps ?
>
>
> --
> Ken Tyler - 1100+ Povray, Graphics, 3D Rendering, and Raytracing Links:
> http://home.pacbell.net/tylereng/index.html http://www.povray.org/links/
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On Fri, 29 Oct 1999 18:56:14 -0500, Mike wrote:
>> But with mirrors etc. the number of normals to be stored would become HUGE,
>> requiring massive amounts of memory. Monte Carlo sampling around the curent
>> intersection would give nearly the same result.
>
>Shouldn't be if you just store the normal at the intersection point of the
>surface in question. There could only be one normal per pixel, which I supposed
>could create quite a few limitations. Ah well, just a thought.
It's not true that there'd be just one normal per pixel. It wouldn't be easy to
come up with a scene to demonstrate this, but it could be done. Basically,
because of partial reflection, a single eye ray can spawn a couple dozen rays
inside the scene, any or all of which could hit the object in question.
--
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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