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Hugo <hua### [at] post3 teledk> wrote in message
news:3cc08cf7$1@news.povray.org...
>
> Sort of ... boundaries acting like a skeleton, that gives away the basic
> shape, and those control points that are within the boundary are then
> connected...? Or, I'm not sure I understood what you meant.. But this was
> another idea. ;o) I don't know if it would work.
>
That is exactly what I meant. In fact, the averaging could easily be used to
create a NxN mesh which could then be subdivided with the macro I have
already written. This would be like cheating. The user would only need to
put in a boundary and then some group of points. No edge or triangle
information would be required.
-Shay
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Shay wrote:
>
> Jide <jid### [at] kotisoonfi> wrote in message
> news:3cc03cf7@news.povray.org...
> >
> > On a sidenote: After 3.5 is finalized I'm gonna start bugging people
about
> > programming subdivision surfaces for POV (You are now on that list of
> people
> > ;)
> > ). I've already approached J. Vansickle about this matter.
> >
>
> Someone has already done this. I can't remember who or where, however. The
> file was called "Surface Subdivision Suite" and is probably still around.
My
> macro isn't true mesh subdivision, just surface subdivision. It could
easily
> be adapted to subdivide entire meshes, but I think most modelers work with
> triangles and not quads. I am considering learning a computer language and
> writing my own modeler which works mainly with scripting, but also
supports
> mouse point selection, dragging, etc.
>
The Surface Subdivision Suite is Vansickles AFAIK :)
And actually he's making a modeller of his own as well :P
so there... hehe
--
-Jide
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Shay wrote:
>
>...
> What do y'all think of this?
I like the results Shay !
Have you tried to make recursive subdivision algorithms ?
Tor Olav
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"Tor Olav Kristensen" <tor### [at] hotmailcom> wrote in message
news:3CC15D49.9FFB7AC0@hotmail.com...
>
> I like the results Shay !
>
Thank you.
> Have you tried to make recursive subdivision
> algorithms ?
>
I'm not 100% sure what you mean, but I'm guessing that you mean an algorithm
which only adds triangles where they are "necessary." If this is the case, I
think that splitting each edge as many times as necessary in one pass might
be simpler and faster than finding the edges and dividing them with multiple
passes. This was my intention at first, but I decided against it.
The main reason is that doing so destroys the appearance of the mesh
approximation. I believe after a *lot* of consideration and experimentation
that in most cases the number of vertices saved is not worth the sacrifice
in appearance. An algorithm which splits edges when the angle is over a
certain threshold attempts to place vertices where they are most needed. It
fails, however, to take into account viewing angle and the places on the
shape where a person's eye will generally check for accuracy.
As an experiment, I created three spheres. One sphere was made up of 24
quads (48 triangles), a second was made by splitting latitude and longitude
lines into quads in the middle and a pie on the top and bottom, the third
was made by dividing a buckey into "pies" one time. All of the spheres had a
reasonably similar number of triangles (really the buckey had a lot more),
and the buckey was probably the closest to what a recursive algorithm would
produce. Without normals, the best looking sphere was the quad sphere. The
quad and the buckey also had the advantage that the faces could be divided
over and over again and the triangles would all remain about the same size
as each other. When I also considered that a buckey was much slower to add
on to the end of a cylinder or come, quad was the obvious winner, despite
whatever disadvantages it may have.
The second reason was that I wanted to make a macro which worked one pass at
a time. I found that by changing the weights by a multiplier for each pass,
some useful "special-effects" could be created (see attached pic.)
Despite all of this, I can see times where using triangles may be necessary.
In those cases, I will still reduce as far as possible with quads to
preserve the look of the mesh.
I am very interested in your or anyone else's opinions about my conclusions.
If anyone is really interested, I can reproduce the experiment.
-Shay
Post a reply to this message
Attachments:
Download 'seJPG.jpg' (11 KB)
Preview of image 'seJPG.jpg'
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Shay, when you say 'dividing a buckey into "pies"
one time', do you mean that you start with a
Buckyball (i.e. a Buckminsterfullerene) ?
If so, then I think that this is a quite interesting
test, as I am quite fond of those.
The pentagons and the hexagons of a Buckyballs are
easily dividable into "pies". So such a sphere mesh
would consist of 12*5 + 20*6 = 180 triangles,
wouldn't it ?
Can you please post images that shows the results
of this test ?
Tor Olav
Btw.:
How did the initial grid for the shape to the right
in your attached image look like (before subdivision) ?
24 "quads" ?
Shay wrote:
>...
> > Have you tried to make recursive subdivision
> > algorithms ?
> >
>
> I'm not 100% sure what you mean, but I'm guessing that you mean an algorithm
> which only adds triangles where they are "necessary." If this is the case, I
> think that splitting each edge as many times as necessary in one pass might
> be simpler and faster than finding the edges and dividing them with multiple
> passes. This was my intention at first, but I decided against it.
>
> The main reason is that doing so destroys the appearance of the mesh
> approximation. I believe after a *lot* of consideration and experimentation
> that in most cases the number of vertices saved is not worth the sacrifice
> in appearance. An algorithm which splits edges when the angle is over a
> certain threshold attempts to place vertices where they are most needed. It
> fails, however, to take into account viewing angle and the places on the
> shape where a person's eye will generally check for accuracy.
>
> As an experiment, I created three spheres. One sphere was made up of 24
> quads (48 triangles), a second was made by splitting latitude and longitude
> lines into quads in the middle and a pie on the top and bottom, the third
> was made by dividing a buckey into "pies" one time. All of the spheres had a
> reasonably similar number of triangles (really the buckey had a lot more),
> and the buckey was probably the closest to what a recursive algorithm would
> produce. Without normals, the best looking sphere was the quad sphere. The
> quad and the buckey also had the advantage that the faces could be divided
> over and over again and the triangles would all remain about the same size
> as each other. When I also considered that a buckey was much slower to add
> on to the end of a cylinder or come, quad was the obvious winner, despite
> whatever disadvantages it may have.
>
> The second reason was that I wanted to make a macro which worked one pass at
> a time. I found that by changing the weights by a multiplier for each pass,
> some useful "special-effects" could be created (see attached pic.)
>
> Despite all of this, I can see times where using triangles may be necessary.
> In those cases, I will still reduce as far as possible with quads to
> preserve the look of the mesh.
>
> I am very interested in your or anyone else's opinions about my conclusions.
> If anyone is really interested, I can reproduce the experiment.
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Tor Olav Kristensen <tor### [at] hotmailcom> wrote in message
news:3CC5AFE2.4EEF7D51@hotmail.com...
>
> Shay, when you say 'dividing a buckey into "pies"
> one time', do you mean that you start with a
> Buckyball (i.e. a Buckminsterfullerene) ?
>
Well, I cheated really. I started with an icosahedron and split each
triangle into four. This gives an itentical result with less math.
>
> Can you please post images that shows the results
> of this test ?
>
Yes, I will rebuild the test Wednesday night.
>
> How did the initial grid for the shape to the right
> in your attached image look like (before subdivision) ?
>
> 24 "quads" ?
>
started with 9 quads and divided a few times with a different abuse of the
equation each time. The shape on the left is the original shape.
-Shay
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Shay <sah### [at] simcopartscom> wrote in message news:3cc5b867@news.povray.org...
>
>
> started with 9 quads and divided a few times with a different abuse of the
> equation each time. The shape on the left is the original shape.
>
> -Shay
>
Nope, you were right. I looked at it again and it was 24 quads.
-Shay
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Shay wrote:
>
> Tor Olav Kristensen <tor### [at] hotmailcom> wrote in message
> news:3CC5AFE2.4EEF7D51@hotmail.com...
> >
> > Shay, when you say 'dividing a buckey into "pies"
> > one time', do you mean that you start with a
> > Buckyball (i.e. a Buckminsterfullerene) ?
> >
>
> Well, I cheated really. I started with an icosahedron and split each
> triangle into four. This gives an itentical result with less math.
I've been staring on the icosahedrons on this page;
http://mathworld.wolfram.com/Icosahedron.html
for several minutes now, but I cannot see how such
an icosahedron can be transformed into a buckyball
by dividing each of its triangles into 4 smaller
triangles.
I can see though, how it can be be done if each of
its triangles are divided into 3 smaller triangles
and 1 hexagon.
Do the results become the same after 1 or 2 further
triangle subdivisions ?
(Assuming that one normalizes and then scales each
vertex vector equally.)
Tor Olav
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The triangles do not form a buckeyball, they only form a shape from which a
buckeyball could be selected. If the proper sides were removed, then a
buckeyball would be present. Actually, I'm not even sure if the shaped
formed would be a true Buckminsterfullerene, but it is a fullerene.
-Shay
Tor Olav Kristensen <tor### [at] hotmailcom> wrote in message
news:3CC### [at] hotmailcom...
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Shay wrote:
>
> The triangles do not form a buckeyball, they only form a shape from which a
> buckeyball could be selected. If the proper sides were removed, then a
> buckeyball would be present. Actually, I'm not even sure if the shaped
> formed would be a true Buckminsterfullerene, but it is a fullerene.
OK, I see.
Tor Olav
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