PS: If you need an explanation about the math used, just ask.

-- 
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):_;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/

Post a reply to this message

"Warp" wrote:
> PS: If you need an explanation about the math used, just ask.

Thanks, I understand it well with two vectors, but I don't quite grasp how
to handle n vectors... It hasn't really anything to do with the clock like
in the example; it was just easier for me to explain what I meant that way.
What I need is a weighted average on n vectors V[N], each with their own
weight W[N].

How can that be done?

Rune
--
\ Include files, tutorials, 3D images, raytracing jokes,
/ The POV Desktop Theme, and The POV-Ray Logo Contest can
\ all be found at http://rsj.mobilixnet.dk (updated January 6)
/ Also visit http://www.povrayusers.org

Post a reply to this message

"Rune" wrote:
> What I need is a weighted average on n vectors V[N], each
> with their own weight W[N].

Well, let me just reveal that what I ultimately want to do is to take an
average of multiple matrixes. Got any ideas?

Rune
--
\ Include files, tutorials, 3D images, raytracing jokes,
/ The POV Desktop Theme, and The POV-Ray Logo Contest can
\ all be found at http://rsj.mobilixnet.dk (updated January 6)
/ Also visit http://www.povrayusers.org

Post a reply to this message

Rune <run### [at] inamecom> wrote:
: Thanks, I understand it well with two vectors, but I don't quite grasp how
: to handle n vectors... It hasn't really anything to do with the clock like
: in the example; it was just easier for me to explain what I meant that way.
: What I need is a weighted average on n vectors V[N], each with their own
: weight W[N].

  Perhaps something like this:

#declare C = <0,0,0>;
#declare Clen = 0;
#declare TotalW = 0;
#declare Ind = 0;
#while(Ind<Amount)
  #declare C = C+vnormalize(V[Ind])*W[Ind];
  #declare Clen = Clen+vlength(V[Ind])*W[Ind];
  #declare TotalW = TotalW+W[Ind];
  #declare Ind=Ind+1;
#end
#declare C = vnormalize(C/TotalW)*(Clen/TotalW);

-- 
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):_;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/

Post a reply to this message

Rune wrote:

> Imagine two vectors, A and B.
> C is a regular weighted average of the two vectors, say clock*A +
> (1-clock)*B.
>
> With this type of average the vector-point is linearly "interpolated", but
> the rotation and length of the vector is not.
>
> To make the length of C linearly interpolated is easy, but how do I linearly
> interpolate the "rotation"?
>
> I need a general method that can average not just two, but multiple vectors.
> How can I do this?

Make normalized copies of the two vectors, a and b.
Find the angle, A, between them: 2*asin(vlength(b-a)/2).
The vector you want is (a+b)/2 + tan(-A/2+A*clock)*vlength((a+b)/2)*vnorm(b-a)
Where clock goes from 0 to 1 from vector a to vector b.

--
David Fontaine  <dav### [at] faricynet>  ICQ 55354965
My raytracing gallery:  http://davidf.faricy.net/

Post a reply to this message

David Fontaine wrote:

> Make normalized copies of the two vectors, a and b.
> Find the angle, A, between them: 2*asin(vlength(b-a)/2).
> The vector you want is (a+b)/2 + tan(-A/2+A*clock)*vlength((a+b)/2)*vnorm(b-a)
> Where clock goes from 0 to 1 from vector a to vector b.

This math is untested BTW.

--
David Fontaine  <dav### [at] faricynet>  ICQ 55354965
My raytracing gallery:  http://davidf.faricy.net/

Post a reply to this message

Btw, the code I posted probably doesn't make what you want. Sorry.

-- 
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):_;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/

Post a reply to this message

I just tackled this problem myself:

given vectors v0, v1 (I assume they are at the origin)
#declare vn = vnormalize(vcross(v0,v1));
#declare v2 =
vaxis_rotate(v0,vn,clock*degrees(acos(vdot(vo,v1)/(vlength(v0)*vlength(v1)))));

v2 is in the right direction, so normalize it and adjust the length normally.

Josh

Rune wrote:

> Imagine two vectors, A and B.
> C is a regular weighted average of the two vectors, say clock*A +
> (1-clock)*B.
>
> With this type of average the vector-point is linearly "interpolated", but
> the rotation and length of the vector is not.
>
> To make the length of C linearly interpolated is easy, but how do I linearly
> interpolate the "rotation"?
>
> I need a general method that can average not just two, but multiple vectors.
> How can I do this?
>
> Rune
> --
> \ Include files, tutorials, 3D images, raytracing jokes,
> / The POV Desktop Theme, and The POV-Ray Logo Contest can
> \ all be found at http://rsj.mobilixnet.dk (updated January 6)
> / Also visit http://www.povrayusers.org

--
Josh English -- Lexiphanic Lethomaniac
eng### [at] spiritonecom
The POV-Ray Cyclopedia http://www.spiritone.com/~english/cyclopedia/

Post a reply to this message

"Warp" wrote:
> Btw, the code I posted probably doesn't make what you want. Sorry.

Thanks anyway!

Maybe it'll be good enough if the vector lengths are linearly interpolated,
but not the rotations, and linearly interpolating the lengths isn't a
problem.

Rune
--
\ Include files, tutorials, 3D images, raytracing jokes,
/ The POV Desktop Theme, and The POV-Ray Logo Contest can
\ all be found at http://rsj.mobilixnet.dk (updated January 6)
/ Also visit http://www.povrayusers.org

Post a reply to this message

Rune wrote:
>... 
> Well, let me just reveal that what I ultimately want to do is to take an
> average of multiple matrixes. Got any ideas?

"The Matrix and Quaternions FAQ" has an answer to this question:

"How do I use quaternions to perform linear interpolation 
between matrices?"

http://www.cs.ualberta.ca/~andreas/math/matrfaq_latest.html#Q61


Regards,

Tor Olav
-- 
mailto:tor### [at] hotmailcom
http://www.crosswinds.net/~tok/tokrays.html

Post a reply to this message