TinCanMan wrote:
> 
> > > 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)
> 

I agree, I was replying after to Thorsten but my target was the original
poster in the previous post.

Internal mental note: Learn to reply correctly!->

I mainly agree with Thorsten that building a sphere with this idea is worthless
and conter-productive.
And more over, it will introduced another 2D object which cannot be used in CSG
either. Meshes are a pleague, once you start with them, you stop thinging about
volume.

> 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.

Me too, but is there such complex objects that could be done by hand ?
(it was the reason of the initial idea...) 

Now, where is the original poster ?
Because (s)he has some answers to provide if (s)he really wants some work to be
done...

-- 
Non Sine Numine
http://grimbert.cjb.net/
Etiquette is for those with no breeding;
fashion for those with no taste.

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"Majukatur" <maj### [at] hotmailcom> wrote in message
news:3d2b4e76@news.povray.org...
> 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.

Check out my curvetri.inc, posted in p.b.s-f (I think :)

...Chambers

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On Thu, 11 Jul 2002 18:58:32 -0700, "Ben Chambers" <bdc### [at] yahoocom> wrote:
> 
> "Majukatur" <maj### [at] hotmailcom> wrote in message
> news:3d2b4e76@news.povray.org...
> > 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.
> 
> Check out my curvetri.inc, posted in p.b.s-f (I think :)
> 
> ....Chambers
> 

Been thinking about this... This idea may be very mathimatically intensive, but lets
say you did
the folowing... Use the three points on the triangle and there relationship to the
normal provided
(assuming you can) and find an area of a real sphere defined by those points and with
same
real curvature, then use the math for generating spheres to produce those points
within the
that triangle. This assumes you can calculate based on those point and a curve what
the radius
would need to be for the sphere, but would in theory produce a true curve, without the
need to
tessilate the object further. I haven't a clue how myself, but geometrically it should
work. Or so
I assume...

Post a reply to this message

> Been thinking about this... This idea may be very mathimatically
intensive, but lets say you did
> the folowing... Use the three points on the triangle and there
relationship to the normal provided
> (assuming you can) and find an area of a real sphere defined by those
points and with same
> real curvature, then use the math for generating spheres to produce those
points within the
> that triangle. This assumes you can calculate based on those point and a
curve what the radius
> would need to be for the sphere, but would in theory produce a true curve,
without the need to
> tessilate the object further. I haven't a clue how myself, but
geometrically it should work. Or so
> I assume...
>

At first thought on this, I don't think it will work.

First of all, the three points and three normals will, in most cases, not be
able to realize a sphere. Any sized sphere large enough to contain all three
points (i.e., can 'rest' on the three points without falling through) can be
defined by these three points, but unless the patch has a spherical
curvature, it can never match all 3 normals.

Secondly, you want each triangle to run smoothly into the next.  Simple
analysis of spheres will tell you that no two spheres of different radii can
be intersected in such a way that their surfaces intersect smoothly.

I don't mean to rain on your parade but I just wanted to point this out
before someone puts a lot of time into trying this only to find it won't
work.  In reality, I don't think there are any simple POV primitives (blobs
and isosurfaces notwithstanding, but I don't even want to think about the
complexity of that) that can define every possible curved triangle.

-tgq

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On Fri, 12 Jul 2002 19:08:54 -0400, "TinCanMan" <Tin### [at] hotmailcom> wrote:
> At first thought on this, I don't think it will work.
> 
> First of all, the three points and three normals will, in most cases, not be
> able to realize a sphere. Any sized sphere large enough to contain all three
> points (i.e., can 'rest' on the three points without falling through) can be
> defined by these three points, but unless the patch has a spherical
> curvature, it can never match all 3 normals.
> 
> Secondly, you want each triangle to run smoothly into the next.  Simple
> analysis of spheres will tell you that no two spheres of different radii can
> be intersected in such a way that their surfaces intersect smoothly.
> 
> I don't mean to rain on your parade but I just wanted to point this out
> before someone puts a lot of time into trying this only to find it won't
> work.  In reality, I don't think there are any simple POV primitives (blobs
> and isosurfaces notwithstanding, but I don't even want to think about the
> complexity of that) that can define every possible curved triangle.
> 
> -tgq


Hadn't thought of that.. I was thinking of a single normal definiing the center of the
triangle and
therefor the curve of the whole thing.. Forgot there where 3. lol However.. What about
an
ellipsoid? That I think would, but kind of creates and even bigger mess figuring it
out. lol May still
not work, but it may be worth the try anyway since if it wasn't possible it should
produce a very
interesting shape, which itself would be very difficult to produce correctly.

Though I agree that in most cases it probably isn't needed, but I kind of get tired of
supposedly
'high-end' models that when rendered require you go back and photoshop the edges
because
you can't smooth out obvious surfaces on the line parallel to the camera view. I don't
care how
good you are with photoshop you miss some and for people like me that are horrible at
it... lol
Additional tessalation is a very poor answer imho. There has got to be a better way
and this one
could produce interesting results in the attempt for anyone with the knowledge to make
the attempt.

First step I think would be to figure out how much to move the points to make them
match a true
sphere, then use that displacement to scale that part to an ellipsiod. Since the
normals would still
be pointing the right way for both that section of the ellipsiod and the intended
curve... Hard to say
without trying, at least for me. Hmm. Though... there may be problems there too, but
only in the sense
of rotation, the needed curve will occure someplace at the right angles on an
ellipsoid, but finding it is
the rub. :p

Post a reply to this message

TinCanMan wrote:
> 
> > Been thinking about this... This idea may be very mathimatically
> intensive, but lets say you did
> > the folowing... Use the three points on the triangle and there
> relationship to the normal provided
> > (assuming you can) and find an area of a real sphere defined by those
> points and with same
> > real curvature, then use the math for generating spheres to produce those
> points within the
> > that triangle. This assumes you can calculate based on those point and a
> curve what the radius
> > would need to be for the sphere, but would in theory produce a true curve,
> without the need to
> > tessilate the object further. I haven't a clue how myself, but
> geometrically it should work. Or so
> > I assume...
> >
> 
> At first thought on this, I don't think it will work.
> 
> First of all, the three points and three normals will, in most cases, not be
> able to realize a sphere. Any sized sphere large enough to contain all three
> points (i.e., can 'rest' on the three points without falling through) can be
> defined by these three points, but unless the patch has a spherical
> curvature, it can never match all 3 normals.

It's even worth than that, but you did not seem to have read my previous posts
on the subject.

> Secondly, you want each triangle to run smoothly into the next.  Simple
> analysis of spheres will tell you that no two spheres of different radii can
> be intersected in such a way that their surfaces intersect smoothly.

Where did you get this second point ?
It was never implied, at least from the explanation.
But it's interesting... and might be expected 

> 
> I don't mean to rain on your parade but I just wanted to point this out
> before someone puts a lot of time into trying this only to find it won't
> work.  In reality, I don't think there are any simple POV primitives (blobs
> and isosurfaces notwithstanding, but I don't even want to think about the
> complexity of that) that can define every possible curved triangle.

There is many cases to study, according to the 4 normals.
(the three explicit ones and the one of the triangle)

If they all meet at one point, you get a part of a sphere,
where the intersection is the center of the sphere.

But what is most interesting, is when one of the explicit normal is
heading outward of the triangle while the two others are inward 
(or vice-versa), the surface need to be subdivided in more curves.

Similarly, when the three normals do not meet (most of the time!),
it might be wise to subdivide.

I ended up trying to generate a spherical triangle from the initial data, 
only to find out that the mapping is far too difficult (for me, at least).
So I only implemented a cleaner object to which you only provide the 
simple data:

The hull is just a triangle on a sphere:
 the first vertex is fixed (<1,0,0>,
 the second one evolves on nearly a circle (*),
 and the third and last one evolves on the remaining sphere.

*: excepted that the second vertex cannot be identical or opposite to
the first vertex.

Syntax is currently like the superellipsoid & torus, 
except it take a 3D vector instead of 2D.

hull { <elevation of second, phi of third, elevation of third> ....

The used sphere is the unit sphere, but you can of course scale/translate/rotate/...
it.
See a quick movie with a hull in p.b.a

-- 
Non Sine Numine
http://grimbert.cjb.net/
Etiquette is for those with no breeding;
fashion for those with no taste.

Post a reply to this message

Patrick Elliott wrote:

> Hadn't thought of that.. I was thinking of a single normal definiing the center of
the triangle and
> therefor the curve of the whole thing.. Forgot there where 3. lol However.. What
about an
> ellipsoid? That I think would, but kind of creates and even bigger mess figuring it
out. lol May still
> not work, but it may be worth the try anyway since if it wasn't possible it should
produce a very
> interesting shape, which itself would be very difficult to produce correctly.

Ellipsoid is only a linear transformation of a sphere, so it won't help when the
normals
do not meet.

> 
> Though I agree that in most cases it probably isn't needed, but I kind of get tired
of supposedly
> 'high-end' models that when rendered require you go back and photoshop the edges
because
> you can't smooth out obvious surfaces on the line parallel to the camera view. I
don't care how
> good you are with photoshop you miss some and for people like me that are horrible
at it... lol
> Additional tessalation is a very poor answer imho. There has got to be a better way
and this one
> could produce interesting results in the attempt for anyone with the knowledge to
make the attempt.
> 
> First step I think would be to figure out how much to move the points to make them
match a true
> sphere,

If you keep insisting on getting both vertices and normales, you have too much
constraint
for the
general case to work.

> then use that displacement to scale that part to an ellipsiod. Since the normals
would still
> be pointing the right way for both that section of the ellipsiod and the intended
curve... 

A linear transformation would help you to make convergent the normale!

> Hard to say
> without trying, at least for me. Hmm. Though... there may be problems there too, but
only in the sense
> of rotation, the needed curve will occure someplace at the right angles on an
ellipsoid, but finding it is
> the rub. :p

Consider when a normal is turned toward the center of the triangle and an other is 
turning away of that center. You won't find that surface on a sphere, or even on
ellipsoid.


-- 
Non Sine Numine
http://grimbert.cjb.net/
Etiquette is for those with no breeding;
fashion for those with no taste.

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On Sun, 14 Jul 2002 17:55:54 +0200, Le Forgeron <jgr### [at] freefr> wrote:
> Patrick Elliott wrote:
> 
> Consider when a normal is turned toward the center of the triangle and an other is 
> turning away of that center. You won't find that surface on a sphere, or even on
> ellipsoid.
> 

Hmm.. Ok that is true. :p It does make for some limited utility. Oh, well just
throwing
out ideas. I never claimed to actually have a clue what I was doing. lol

Post a reply to this message

Le Forgeron wrote:
> Ellipsoid is only a linear transformation of a
> sphere, so it won't help when the normals do not meet.

Does that logic apply?

Three normals of a sphere will always meet in the same point. But three
normals of a ellipsoid will not always meet in the same point. I'm not
saying that an ellipsoid is a solution, but just questioning this
particular argument.

Rune
--
3D images and anims, include files, tutorials and more:
rune|vision:  http://runevision.com (updated July 12)
POV-Ray Ring: http://webring.povray.co.uk

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On Sun, 14 Jul 2002 22:13:32 +0200, "Rune" <run### [at] mobilixnetdk> wrote:
> Le Forgeron wrote:
> > Ellipsoid is only a linear transformation of a
> > sphere, so it won't help when the normals do not meet.
> 
> Does that logic apply?
> 
> Three normals of a sphere will always meet in the same point. But three
> normals of a ellipsoid will not always meet in the same point. I'm not
> saying that an ellipsoid is a solution, but just questioning this
> particular argument.
> 
> Rune

I believe he is refering to trangles that bend two directions. i.e. the triangle
itself looks
like:

____
        \
          \
            \______

According to the normals provided. And he is correct that under such circumstances
you can never find any primitive that has such a shape. It does occure to me that
in such instances one may be able to find two curves on an ellipsoid that may conform
to such a shape, but you end up tracing the interior of one and the exterior of
another,
not to mention it maybe not working at all, since all three corners could be distorted
in
ways that make it impossible to find any combination that would match. :p There has
got to be a better way of doing this, but... A method that used ellipsoid matching
could
probably 'fix' about 90% of the triangles in the average mesh, but that last 10% are a
problem. And in some objects the percentages could end up drastically shifting the
other way. Oh, well.. Hopefully someone will come up with a decent solution, probably
about the same time someone gets rid of coincident surfaces that are the true bane
of my existance. lol

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