Hi all.

Well, this is an idea that I had, is about the meshes, I was thinking, the
smooth triangle have a simulated normal that seems to be smooth, but it

smooth_triangle really smoothed?, if the syntax of the smooth_triangle is
conserved we can use the new shape with old mesh objects without problem,
but with better quality.

This object have another characteristics, for example, the amount of
triangles needed to create a model are very few, compared with the normal
mesh, this is because the mesh is an aproximation of the real model, you
need a lot of triangles to seem to be a curve, in this case, it is a curve,
and you save a lot of triangles, this allow you make your models even
manually, with a good quality, and it also save allocation memory and disk
space, this is good if you want to share your models in internet, for
example.

There are another object similar, the bicubic patch, but it is too difficult
to use manually, and is difficult to transform a mesh model into bicubic
patchs, that's the reason of the idea of a mesh-like object.




Fernando Correa.

excuse my english.

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Majukatur <maj### [at] hotmailcom> wrote:
> Well, this is an idea that I had, is about the meshes, I was thinking, the
> smooth triangle have a simulated normal that seems to be smooth, but it

> smooth_triangle really smoothed?

  How? By subdividing it into more triangles?

> There are another object similar, the bicubic patch, but it is too difficult
> to use manually

  You are implicating that writing meshes manually is not difficult. I would
like to see you writing a bigger mesh by hand. ;)

-- 
#macro M(A,N,D,L)plane{-z,-9pigment{mandel L*9translate N color_map{[0rgb x]
[1rgb 9]}scale<D,D*3D>*1e3}rotate y*A*8}#end M(-3<1.206434.28623>70,7)M(
-1<.7438.1795>1,20)M(1<.77595.13699>30,20)M(3<.75923.07145>80,99)// - Warp -

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Warp wrote:
>   You are implicating that writing meshes manually is
> not difficult. I would like to see you writing a bigger
> mesh by hand. ;)

Well, bicubic patches are just plain difficult to use in general.
Because of their four corners, it's very difficult to make advanced
shapes where the patches are joined up smoothly. Some 3d programs which
also use patch-like shapes come about this problem by offering special
patches with 3 or 5 corners to supplement the regular ones with 4
corners. Not POV-Ray though.

Rune
--
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POV-Ray Users: http://rsj.mobilixnet.dk/povrayusers/
POV-Ray Ring:  http://webring.povray.co.uk

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...

Majukatur <maj### [at] hotmailcom> wrote:
> Well, this is an idea that I had, is about the meshes, I was thinking, the
> smooth triangle have a simulated normal that seems to be smooth, but it

> smooth_triangle really smoothed?

  How? By subdividing it into more triangles?

> There are another object similar, the bicubic patch, but it is too
difficult
> to use manually

  You are implicating that writing meshes manually is not difficult. I would
like to see you writing a bigger mesh by hand. ;)


Well, this object not is a mesh of triangles, is a curve defined by 3 points
and its normal vectors, it is not an aproximation. There is an equation that
have all this characteristics, not is a mesh of triangles, is a mesh of
patchs, and it is easy to write this kind of meshes MANUALLY, for example,
you need only 4 "triangles" to describe an sphere, with normal meshes you
need hundreds of triangles. For describe ANY ellipse you need only 12
"triangles".

Imagine this, cut a sphere in 3 equal areas, each of this areas is the shape
of one of these "triangles", is defined by 3 points and 3 normal vectors, of
course, this is not a triangle, but you can use it like one.

If you want to use a modeler, like Rhinoceros for example, you can use very
few triangles in your model (when you export it to POV syntax) without any
lost of quality, it allow you to share your model because the file is too
small.

Well, I'm looking for the equation (formula) that describes this shape, I
know that is difficult to imagine, I need to prepare a better description of
this in order to explain my idea. May be a image can show you what I am
talking about, I'm going to prepare one.

Thanks for your attention



Fernando Correa

excuse my english

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In article <3d2bca3e$1@news.povray.org> , "Majukatur" 
<maj### [at] hotmailcom> wrote:

> Well, this object not is a mesh of triangles, is a curve defined by 3 points
> and its normal vectors, it is not an aproximation. There is an equation that
> have all this characteristics, not is a mesh of triangles, is a mesh of
> patchs, and it is easy to write this kind of meshes MANUALLY, for example,
> you need only 4 "triangles" to describe an sphere, with normal meshes you
> need hundreds of triangles. For describe ANY ellipse you need only 12
> "triangles".

Why build a sphere out of triangles if you can just use the sphere object in
POV-Ray?  Sounds like reinventing the wheel to me...

    Thorsten

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By the way, I strongly suggest that you either use the actual reply
functionality of your newsreader or configure it to quote articles properly.
In that format it's extremely difficult to see what is a quote and what is
a reply.

-- 
#macro M(A,N,D,L)plane{-z,-9pigment{mandel L*9translate N color_map{[0rgb x]
[1rgb 9]}scale<D,D*3D>*1e3}rotate y*A*8}#end M(-3<1.206434.28623>70,7)M(
-1<.7438.1795>1,20)M(1<.77595.13699>30,20)M(3<.75923.07145>80,99)// - Warp -

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In article <3d2b4e76@news.povray.org>,
 "Majukatur" <maj### [at] hotmailcom> wrote:

> Well, this is an idea that I had, is about the meshes, I was thinking, the
> smooth triangle have a simulated normal that seems to be smooth, but it

> smooth_triangle really smoothed?, if the syntax of the smooth_triangle is
> conserved we can use the new shape with old mesh objects without problem,
> but with better quality.

There have been a couple people working on macros to produce "curved" 
smooth triangles. The only good way to do that seems to be to divide 
each triangle into more triangles on a curved surface...trying to solve 
directly for the surface would probably be too slow for a mesh with a 
fair number of triangles. Their macros are probably in the scene file 
groups on this server. You might also want to look for information on 
subdivision surfaces.

-- 
Christopher James Huff <chr### [at] maccom>
POV-Ray TAG e-mail: chr### [at] tagpovrayorg
TAG web site: http://tag.povray.org/

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Thorsten Froehlich wrote:
> 
> In article <3d2bca3e$1@news.povray.org> , "Majukatur"
> <maj### [at] hotmailcom> wrote:
> 
> > Well, this object not is a mesh of triangles, is a curve defined by 3 points
> > and its normal vectors, it is not an aproximation. There is an equation that
> > have all this characteristics, not is a mesh of triangles, is a mesh of
> > patchs, and it is easy to write this kind of meshes MANUALLY, for example,
> > you need only 4 "triangles" to describe an sphere, with normal meshes you
> > need hundreds of triangles. For describe ANY ellipse you need only 12
> > "triangles".
> 
> Why build a sphere out of triangles if you can just use the sphere object in
> POV-Ray?  Sounds like reinventing the wheel to me...
> 
>     Thorsten

By 3 points and 3 normals (only direction, with the same constraints that
is now on smooth_triangle (normals go to the same side)), how many spheres go through
?
If you are lucky, one; else none.
Problem is that most of the time, you will be unlucky (at least due to computational
errors but not only). 
This is because the center of the sphere should be at the intersection
of the three lines made by the normals and points. and there is no reason for theses
lines to intersect, even two by two. There is in fact no reason that two of them be
in any common plane.

Another approach with a sphere might be to use a mapping from the first point&normal
to always be a well know point on the sphere (such as the intersection of x axis with
the unit sphere) and then, using only the normals informations, placing the second and
third points of a geodesic triangle (additional contrainte for the second point should
be added also, so that it lies in the xOy plane for instance).
Then you will need to compute a transformation matrix (3 points give 3 points, so that
should be easy) and perform the intersection test against the geodesic triangle on
the unit sphere (as well as the normal computation).

Problems are:
Any two normals should not even be parallel (whereas currently it is possible with
smooth_triangle)
The three normals must ABSOLUTELY define a free base of 3D space 
And of course, the triangle must not be degenerated (or flat)

So it's not that easy to do by hand! At least the parser must be very strict.

Additional caveat: 
- the matrix found may be dependent on the order of the points,
which might end up that an ABC triangle is not identical to a ACB, 
or even a BCA triangle!!! [I need a mathematician here !!]
- Computation of the intersection with the geodesic triangle is not
straight ahead. The third point has far too much freedom, from a programmer
point of view! The hit on the sphere is easy (copy&paste from current sphere object)
but then the only hope I could see is to express the normal in the base of the 
three triangle normales, if any coefficient is negative, it's outside of the geodesic
triangle.

Rendering time (per triangle) is probably fine, but I'm afraid of optimisation,
because bounding the curved_triangle is probably not easy to do exactly
(bounding of unit sphere transformed by the inverse matrix is the best I can imagine,
and it leaves a lot of false positives).

I'm not sure, given the additional contraints and all the trouble,
 that this new object is forth its developpement. 
Could you come with some (basic) scenes/objects, which are not already covered
by the existings objects ? (the sphere was a bad example !)
-- 
Non Sine Numine
http://grimbert.cjb.net/
Etiquette is for those with no breeding;
fashion for those with no taste.

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> > Why build a sphere out of triangles if you can just use the sphere
object in
> > POV-Ray?  Sounds like reinventing the wheel to me...
> >
> >     Thorsten

> By 3 points and 3 normals (only direction, with the same constraints that
<snip>
> Non Sine Numine
> http://grimbert.cjb.net/
> Etiquette is for those with no breeding;
> fashion for those with no taste.

That's one heck of a reply, but I think you misunderstood what Thorsten was
implying. He was talking about building a sphere using meshes not building
meshes out of spheres (though that is very interesting and you gave quite a
thorough answer)

BTW to Thorsten: I think the original reference to building a sphere out of
meshes was just a simple analogy, not meant to be taken literally but meant
to be extended to more complex objects.

-tgq

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Thorsten


example to show you a comparative between this shape and the mesh of
triangles.

FC

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