I've read and searched, can anyone help me?

Given 4 unique and non-coplanar points (A, B, C, & D) in space (3D) what is the
simplest way of defining the surface that would result from a film being
stretched over a frame composed of four sides (AB, BC, CD, & DA), or that frame
being immersed and removed from a suitable liquid for bubble making?

I think a hyperbolic paraboloid would be about the right shape, but that hasn't
yielded a reasonable result thus far.

Post a reply to this message

Le 01/10/2010 16:02, Graham a écrit :
> I've read and searched, can anyone help me?
> 
> Given 4 unique and non-coplanar points (A, B, C, & D) in space (3D) what is the
> simplest way of defining the surface that would result from a film being
> stretched over a frame composed of four sides (AB, BC, CD, & DA), or that frame
> being immersed and removed from a suitable liquid for bubble making?
> 
> I think a hyperbolic paraboloid would be about the right shape, but that hasn't
> yielded a reasonable result thus far.
> 
> 
Looks for minimal surface tension.

3 points defining a plane, it's only a matter of positioning the fourth
one in regard to the open triangle.

case #1: ABCD is a tetraedron. The film is likely to be two-fold, each
fold as two faces.

case #2: ABCD is flat, the film is flat too.

case #3: you can hope for a HyperbolicParaboloid

Hint: transition from #2 to #3 seems easy. But How do you evolve from #1
to #3 ?



-- 
A good Manager will take you
through the forest, no mater what.
A Leader will take time to climb on a
Tree and say 'This is the wrong forest'.

Post a reply to this message

On 10/1/2010 10:02 AM, Graham wrote:
> I've read and searched, can anyone help me?
>
> Given 4 unique and non-coplanar points (A, B, C,&  D) in space (3D) what is the
> simplest way of defining the surface that would result from a film being
> stretched over a frame composed of four sides (AB, BC, CD,&  DA), or that frame
> being immersed and removed from a suitable liquid for bubble making?
>
> I think a hyperbolic paraboloid would be about the right shape, but that hasn't
> yielded a reasonable result thus far.

Yes, it is a portion of a hyperbolic paraboloid.  What exactly are you 
trying to accomplish?

Regards,
John

Post a reply to this message

Le_Forgeron <lef### [at] freefr> wrote:
> > Given 4 unique and non-coplanar points (A, B, C, & D) in space (3D) what is
> > the simplest way of defining the surface that would result from a film
> > being stretched over a frame composed of four sides (AB, BC, CD, & DA), or
> > that frame being immersed and removed from a suitable liquid for bubble
> > making?
> >
> > I think a hyperbolic paraboloid would be about the right shape, but that
> > hasn't yielded a reasonable result thus far.
> >
> >
> Looks for minimal surface tension.
Looks like the phrase that was eluding me.
>
> 3 points defining a plane, it's only a matter of positioning the fourth
> one in regard to the open triangle.
>
> case #1: ABCD is a tetraedron. The film is likely to be two-fold, each
> fold as two faces.
True. Given the two edges of the tetrahedron that aren't a part of our
frame are effectively the hinge of a pair of triangles each, it would make
some sense that the angles of the faces meeting at the hinges would both
contribute to the final equation, and they can be determined easily enough
from the normals to the faces determined by their two used vector sides.
>
> case #2: ABCD is flat, the film is flat too.
The case I had originally filtered out (because it didn't matter
much which pair of triangles I used to make the quadrilateral - as one
angle approaches pi so does the other. This is interesting if not relevant
given that our four points set the angles in stone.) I had also filtered
out (most of) the degenerate faces by capturing (separately) consecutive
and non-consecutive co-located points.
>
> case #3: you can hope for a HyperbolicParaboloid
I'm confident, but I'd really be hoping for an existing include file with
a macro that takes the four points as input variables and returns the
section of surface in position (but that might be asking too much). Failing
that, pointers in the right direction. I'm happy writing macros - I'd
written my own "Conic Frustrum Tangentially Connecting Two Spheres" macro
before running across the included one.
>
> Hint: transition from #2 to #3 seems easy. But How do you evolve from #1
> to #3 ?
I'm guessing the best answer would involve Mesh2(to preserve CSG, and given
what I'm already thinking about the surface it would be relatively simple to
generate a number of points), but is there a better non-Mesh solution?

Post a reply to this message

John VanSickle <evi### [at] hotmailcom> wrote:
> Yes, it is a portion of a hyperbolic paraboloid.  What exactly are you
> trying to accomplish?
>
Thanks John,
The simple answer* is that I'm attempting to have PovRAY develop a
horn-like shape.** It starts with the points defining a basic shape for
iteration. The points of the basic shape is Transmogrified (scaled,
rotated and translated) to yield the positions of the other end of the
basic unit. The shape of the (many) sides of the comprises two consecutive
points on the basic shape and their equivalent points on the T'd shape.
The triangles I have been using on the sides look to mechanical, and I
thought the curved nature of the HP might give it a more organic feel.
In any case, once the first unit is declared, then the spiral is built
by T'ing the unit and unioning another unit to it over several iterations.

*Proof only that there is no simple answer.
**This was originally going to read "I'm attempting to evolve a pair of
horns.", but on a second parse it was revised.

Post a reply to this message

Le 04/10/2010 15:05, Graham a écrit :
> Le_Forgeron <lef### [at] freefr> wrote:

>> case #3: you can hope for a HyperbolicParaboloid
> I'm confident, but I'd really be hoping for an existing include file with
> a macro that takes the four points as input variables and returns the
> section of surface in position (but that might be asking too much). Failing
> that, pointers in the right direction. I'm happy writing macros - I'd
> written my own "Conic Frustrum Tangentially Connecting Two Spheres" macro
> before running across the included one.

The problem is solving the equation of a hyperbolic paraboloid with ABCD.
Notice that the points A, B, C & D are not enough (4 non-coplanar points
do not fix an hyperbolic paraboloid), but you can add that each points
in AB, BC, CD & DA must also be on the surface.

>>
>> Hint: transition from #2 to #3 seems easy. But How do you evolve from #1
>> to #3 ?
> I'm guessing the best answer would involve Mesh2(to preserve CSG, and given
> what I'm already thinking about the surface it would be relatively simple to
> generate a number of points), but is there a better non-Mesh solution?
> 

I was not speaking from the POV point of view, but from the mathematical
surface point of view.
The case #3 to #2 is a degeneration of the HP into a plane. no real
discontinuity, as both are conic with 1 fold.
But I believe you have to sacrifice a fold when coming from #1.

Have you look at

http://mathworld.wolfram.com/SkewQuadrilateral.html

?


-- 
A: Because it messes up the order in which people normally read text.<br/>
Q: Why is it such a bad thing?<br/>
A: Top-posting.<br/>
Q: What is the most annoying thing on usenet and in e-mail?

Post a reply to this message

Okay, this is just weird. The group says there are six (probably now 7) messages
in this group, but when I go to read them I only get my original post and the
two responses - Message 1 - 3 of 3.

Post a reply to this message

Graham wrote:
> Okay, this is just weird. The group says there are six (probably now 7) messages
> in this group, but when I go to read them I only get my original post and the
> two responses - Message 1 - 3 of 3.

This can happen if posts have been deleted. If you have a "rc" file for the 
server (i.e., you're not using the web interface), check for discontinuous 
ranges of message numbers and fix that.

-- 
Darren New, San Diego CA, USA (PST)
   Serving Suggestion:
     "Don't serve this any more. It's awful."

Post a reply to this message

On 05.10.10 02:26, Graham wrote:
> Okay, this is just weird. The group says there are six (probably now 7) messages
> in this group, but when I go to read them I only get my original post and the
> two responses - Message 1 - 3 of 3.

As you are using the web interface, this most likely is a browser cache 
issue. Try clearing your browser cache and fully restarting your browser.

	Thorsten, POV-Team

Post a reply to this message

First, thanks Darren and Thorsten. No sooner had I posted the message saying
how weird it was then the problem resolved of its own accord. Go figure.

Le_Forgeron <lef### [at] freefr> wrote:
> Le 04/10/2010 15:05, Graham a écrit :
>
> The problem is solving the equation of a hyperbolic paraboloid with ABCD.
> Notice that the points A, B, C & D are not enough (4 non-coplanar points
> do not fix an hyperbolic paraboloid), but you can add that each points
> in AB, BC, CD & DA must also be on the surface.
So, if three non-collinear points determine a plane, then how many for a HP?
Surely this isn't new ground.
>
> >>
> >> Hint: transition from #2 to #3 seems easy. But How do you evolve from #1
> >> to #3 ?
> > I'm guessing the best answer would involve Mesh2(to preserve CSG, and given
> > what I'm already thinking about the surface it would be relatively simple to
> > generate a number of points), but is there a better non-Mesh solution?
> I was not speaking from the POV point of view, but from the mathematical
> surface point of view.
> The case #3 to #2 is a degeneration of the HP into a plane. no real
> discontinuity, as both are conic with 1 fold.
> But I believe you have to sacrifice a fold when coming from #1.
>
> Have you look at
>
> http://mathworld.wolfram.com/SkewQuadrilateral.html
>
Yes. I mocked up this based on the alternative z=xy,
where (-1,-1)<=(x,y)<=(1,1)
http://www.youtube.com/watch?v=ik6Kty1HSUw
The protrusions of the tips through the two triangular sides should
give an indication as to how this SQ was constructed.

I enjoy math, and from memory my maths of a surface got as far as grad,
div and curl, but I have no experience with Abelian Integrals. That was
half a lifetime ago...

I'm prepared to learn, but I thought you should be aware of my starting point.

Post a reply to this message