There are 8 points in space, each at the corners of a cube.  Each point has  
associated with it a velocity vector and a position in space.  Now, if I were  
to place a weightless particle in this cube and have it's direction and  
magnitude of movement determined by weighting each of the corner of the cube,  
depending how close to each corner this particle is, would there be a more  
efficient way mathimatically for weighting the eight corners of this cube? 

---

Request for Question Clarification by drdavid-ga on 27 Apr 2002 12:57 PDT

I'm having trouble understanding exactly what you want to know. As I
understand your task, you start out with position and velocity for the
8 corners of a cube. That's 48 variables (8 points x [3 position
components + 3 velocity components]). Since the dimensions of the cube
are fixed, and you assume zero mass (no gravity, and, I guess, no
other forces on the cube either?). It would appear to be more memory-
and computation-efficient to represent and compute the motion of the
cube with a set of parameters for the cube as a whole. Since the cube
is not a point, you would have to add angular velocity to the
description. Then you would track 9 variables (3 components each of
position, velocity and angular velocity) instead of 48 and compute the
48 from the 9 for rendering. Furthermore, if there are no forces on
the cube, the velocity and angular velocity would not change; only the
position would. There would be only three real variables. Sounds good,
and likely to be more efficient than calculating the motion of the 8
corners separately (plus you run no risk of having your corners move
relative to one another due to cumulative round-off error. So what's
your question? What are you comparing to when you want a "more
efficient way"? Or do you just need to know how to map back and forth
between the 48-variable description and the 9-variable description?
I'm not sure which part of the problem you're having difficulty with. 

You are describing an interesting problem! 

Can you provide more details about the mathemathical way you do it now? 

(For formulas you can post it in Latex format, so that I can compile it.)

I believe that your question, whilst interesting, is not novel - and therefore 
the most fruitful avenues for your quest involve researching EXISTING 
documented theory about 3D-modelling, rather than trying to deduce or derive a 
solution.

How strong is your maths?  I have checked out a few sites, and in most 
instances, the mathematics gets pretty heavy, pretty quickly.

This site has an extensive list of links that may prove useful, although 
unfortunately, the site is quite old, so some of the more promising links were 
broken.  You still might find something of interest, though:

http://www.geocities.com/SiliconValley/Park/9784/tut.html

This seems a very specialist area, so I wonder whether you would be willing to 
invest in a book, or even a short course, to cover the theory you need?  If so, 
there are other sites I might suggest.

If, however, you are not willing or able to pay for expert advice, you will be 
largely dependent on the input of unpaid enthusiasts in the field, which may 
vary very considerabley in quality.  I did find the following site, which 
includes some forums, where you might be able to pose your question, and get 
more specialised advice than I am able to offer:

http://www.flipcode.com/

I hope this provides some interesting leads......


Louise

It sounds like an application of bilinear interpolation but in 3D (no, I'm 
pretty sure trilinear interpolation is something involving interpolating 
between mipmaps) so you could probably utilise 3D acceleration hardware :)

Utilising 3D hardware would be especially beneficial if your application 
doesn't just have 8 points, but a whole lattice of cubes formed from points.

Otherwise, look for documentation of fast bilinear interpolation, you should be 
able to extrapolate from that.  3 colours can be changed to 3 direction 
components, and you'll just need to add the 3rd dimension, which should be 
relatively easy.