I think about a genaral problem: if I have a freeform-surface and I want
to devide it up into small faces, I often have the possibility to make
polygons (most faces then are quads) or triangles. Which way is the
better one ?

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In article <3A3804A6.36A052CC@gmx.de>, chris <chr### [at] gmxde> 
wrote:

> I think about a genaral problem: if I have a freeform-surface and I want
> to devide it up into small faces, I often have the possibility to make
> polygons (most faces then are quads) or triangles. Which way is the
> better one ?

You can put triangles in a mesh, which can be much more efficient in 
memory usage. Also, if you have more than one copy of the object, a copy 
of a mesh will use the same data, saving even more memory, while a copy 
of a union of polygons will copy *all* the data.

-- 
Christopher James Huff
Personal: chr### [at] maccom, http://homepage.mac.com/chrishuff/
TAG: chr### [at] tagpovrayorg, http://tag.povray.org/

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Chris Huff wrote:

> 
> You can put triangles in a mesh, which can be much more efficient in
> memory usage. Also, if you have more than one copy of the object, a copy
> of a mesh will use the same data, saving even more memory, while a copy
> of a union of polygons will copy *all* the data.

Thanks, but I thought of another problem. 
If I devide my complex freeform-surface up into polygons (quads) or
trinangles and I want to render it (pov or another highquality
renderer), there is the problem of defining a "smooth" transition from
one element to the next, which is done with "spline"-patches, first (and
second?) derivative at the boundaries the same (I'm not a
math-expert..). I think, that both types (patches from quads or
triangles) give a little different aproximation of the
free-form-surface, but which one is the better one ?

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In article <3A386840.67044BB7@gmx.de>, chris <chr### [at] gmxde> 
wrote:

> If I devide my complex freeform-surface up into polygons (quads) or
> trinangles and I want to render it (pov or another highquality
> renderer), there is the problem of defining a "smooth" transition from
> one element to the next, which is done with "spline"-patches, first (and
> second?) derivative at the boundaries the same (I'm not a
> math-expert..). I think, that both types (patches from quads or
> triangles) give a little different aproximation of the
> free-form-surface, but which one is the better one ?

I don't know what you are looking for...
Well, to start with, POV-Ray doesn't have a "quad" primitive, you will 
have to approximate them with triangles or use polygons, so you can stop 
talking in terms of quads.
You can use smooth_triangles, where you specify the normal of each 
vertex of the triangle, and it is interpolated across the surface of the 
triangle, but it doesn't actually do anything to the surface, it is 
still perfectly flat.
Polygons don't allow you to specify vertex normals, and can not be used 
in meshes.
You might be looking for bicubic patches (also called Bezier patches)...
In these, you specify a 4*4 grid of 16 points, and POV creates a curved 
surface from this information. The surface really is curved, sort of 
like a sheet of rubber, it doesn't just fake it with the normal(though 
it is actually a triangle mesh internally). However, you can't use 
bicubic_patch objects in meshes either, so your memory requirements will 
go up, possibly *way* up, depending on what you are doing.

-- 
Christopher James Huff
Personal: chr### [at] maccom, http://homepage.mac.com/chrishuff/
TAG: chr### [at] tagpovrayorg, http://tag.povray.org/

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