Tim Nikias v2.0 wrote:
> Just kidding, though it is kinda weird how someone
> presents a nice thing he's just finished, and then
> one or another points out how someone else already
> did that, and how he made it better than what
> you've just created. I still like my algorithm,
> but it's kinda pointless now, I guess. :-(

The leaning experience was not pointless. Every time you make up some
algorithm on your own your programming skills improve a bit. That is not
the case if you just use someone else's algorithm from the beginning. :)

Rune
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Tim Nikias v2.0 wrote:
> With the technique you mentioned, and have to do
> some inbetween calculations to get the desired
> angles, like projecting the forward vector onto
> a plane with the sky-vector, thus getting vectors
> with which I can calculate the "internal" spin to
> get the up-vectors lined up...

I'm not sure I understand. Why do you need any sky-vector in the first
place? Why do you need to know anything about the spin of the tunnel?

> It's my perspective on things that stands in my
> way of finding efficient solutions for problems
> like these. Don't play around with vectors,
> matrix-transformations and angles enough, I guess...

Playing around with those have often proven to be very handy for me...
;)

Rune
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> Don't be sad. Look at it this way: if you haven't done
> it yourself, you are often not able to understand the
> solution of someone else. So keep posting your own
> solutions.

I'm not sad. I still think I can be pretty proud of myself, cause I do find
some sort of solution on my own most of the time, may they be pretty
unspectacular and round-about. And posting here keeps the newsgroups alive
and provides insight into techniques for others (even if the algorithm is
overly complicated, it might be useful for something else).

Regards,
Tim

-- 
"Tim Nikias v2.0"
Homepage: <http://www.nolights.de>
Email: tim.nikias (@) nolights.de

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> The leaning experience was not pointless. Every time you make up some
> algorithm on your own your programming skills improve a bit. That is not
> the case if you just use someone else's algorithm from the beginning. :)

Right. In this case, I guess my problem is more with the vector-arithmetic
than the programming, but I'll tackle that sooner or later as well.

Regards,
Tim

-- 
"Tim Nikias v2.0"
Homepage: <http://www.nolights.de>
Email: tim.nikias (@) nolights.de

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Rune wrote:
> Tim Nikias v2.0 wrote:
>> With the technique you mentioned, and have to do
>> some inbetween calculations to get the desired
>> angles, like projecting the forward vector onto
>> a plane with the sky-vector, thus getting vectors
>> with which I can calculate the "internal" spin to
>> get the up-vectors lined up...
>
> I'm not sure I understand. Why do you need any sky-vector in the first
> place? Why do you need to know anything about the spin of the tunnel?

Here's some crude and simple code to explain the basic idea. The
algorithm is simpler than I remembered. Just use the VPerp_Adjust()
macro to make the last up-vector perpendicular to the current
forward-vector and then use that as the current up-vector... The code
here just aligns boxes and does not create a tunnel out of a mesh, but
the basic idea is the same.

#include "transforms.inc"
#include "math.inc"
camera {location <-2,1,-3> look_at 0}
light_source {<-1,2,-3>*1000, color 1}
background {rgb 1}
#declare Spline = spline {
   cubic_spline
   -2, -x,
   -1, -x,

    0, -y,
    1, -z,
    2, y,
    3, z,
    4, x,
    5, x+y,

    6, y+z,
    7, y+z
}
#declare C = 0;
#declare Samples = 50;
#declare Range = 5;
#declare LastY = y;
#while (C<=Samples)
   #declare Val = C/Samples*Range;
   #declare P = Spline(Val);
   #declare Z = vnormalize(Spline(Val+0.001)-Spline(Val-0.001));
   #declare Y = VPerp_Adjust(LastY,Z);
   #declare X = vcross(Y,Z);
   #declare T = Matrix_Trans(X,Y,Z,P)
   #declare LastY = Y;
   superellipsoid {<0.2,0.2> scale 0.1 transform {T} pigment {rgb 1}}
   #declare C = C+1;
#end


Rune
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3D images and anims, include files, tutorials and more:
rune|vision:  http://runevision.com **updated Jan 29**
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> I'm not sure I understand. Why do you need any sky-vector in the first
> place? Why do you need to know anything about the spin of the tunnel?

You somehow have to put the two forward- and up-vectors into relation. I
thought that maybe projecting both forward vectors onto a plane, get the
angle, rotate the vectors and then calculate new angles for the up-vector
might be a way to go. You've probably got something faster up your sleeve,
the way you phrase it...

Regards,
Tim

-- 
"Tim Nikias v2.0"
Homepage: <http://www.nolights.de>
Email: tim.nikias (@) nolights.de

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> Here's some crude and simple code to explain the basic idea. The
> algorithm is simpler than I remembered. Just use the VPerp_Adjust()
> macro to make the last up-vector perpendicular to the current
> forward-vector and then use that as the current up-vector... The code
> here just aligns boxes and does not create a tunnel out of a mesh, but
> the basic idea is the same.

Hm. I can see that it works, but I don't understand why and how. I can't
visualize what that VPerp_Adjust actually does, and why it works for
generating a proper new matrix for the new box. Care to elaborate and
enlighten me? :-)

Regards,
Tim

-- 
"Tim Nikias v2.0"
Homepage: <http://www.nolights.de>
Email: tim.nikias (@) nolights.de

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Tim Nikias v2.0 wrote:
>> Here's some crude and simple code to explain the basic idea. The
>> algorithm is simpler than I remembered. Just use the VPerp_Adjust()
>> macro to make the last up-vector perpendicular to the current
>> forward-vector and then use that as the current up-vector... The code
>> here just aligns boxes and does not create a tunnel out of a mesh,
>> but the basic idea is the same.
>
> Hm. I can see that it works, but I don't understand why and how. I
> can't visualize what that VPerp_Adjust actually does

From the doc:
VPerp_Adjust(V1, Axis). Find a vector perpendicular to Axis and in the
plane of V1 and Axis. In other words, the new vector is a version of V1
adjusted to be perpendicular to Axis.

So the new Y vector is the same as the previous Y vector, except that it
is adjusted to be perpendicular with the new Z vector. Since the
previous and the new Y vectors are as close to each other as possible,
there is no twisting.

The Y and Z vectors are now perpendicular, and from those we can get the
X vector using the vcross-function. Now we have the local X, Y and Z
vector for the box as well as its origin P, and then we can create its
transformation matrix out of those four vectors.

That's all really.

Rune
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3D images and anims, include files, tutorials and more:
rune|vision:  http://runevision.com **updated Jan 29**
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> That's all really.

Hm, now that you've described it, I can actually build a visual
representation in my mind. You see, as long as I can't actually tell via
diagramm (even if its a complicated one that only fits into the mind, not on
paper) I don't really grasp the formula. I've read the doc, but I got
confused somewhere with that Last_Y and the actual Y etc. Now I can picture
it and understand it.

Now that I've understood it, I'll try to implement it, shouldn't be too much
of a problem. Once the tunnel is properly constructed, I'll get to the
actual tricky part: water simulation. I'm still wondering if I should make
something half-artistic and half-simulation, so that I can actually control
the effects, but still have some degree of realism... Ah well, I'll come to
that later. Maybe I'll ponder about it for a few days and tackle some other
stuff first.

Regards,
Tim

-- 
"Tim Nikias v2.0"
Homepage: <http://www.nolights.de>
Email: tim.nikias (@) nolights.de

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Tim Nikias v2.0 wrote:
> Hm, now that you've described it, I can actually
> build a visual representation in my mind. You see, as
> long as I can't actually tell via diagramm (even if
> its a complicated one that only fits into the mind,
> not on paper) I don't really grasp the formula.

My mind works the same way... :)

> Once the tunnel is properly constructed, I'll get to
> the actual tricky part: water simulation.

I'm looking forward to see what you'll come up with!

Rune
--
3D images and anims, include files, tutorials and more:
rune|vision:  http://runevision.com **updated Jan 29**
POV-Ray Ring: http://webring.povray.co.uk

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