[ODE] Mapping to OpenGL axis system: not convinced

[Ruud van Gaal]

Hi Norman,

> I am surprised no one jumped in with an explanation here, since a reversal
> of coordinate systems would be a rather important issue, if it indeed were
> the case in ODE. So, I attempted to reproduce your error. I was unable to.
...
> Starting with the following orientation:
>
> -0.000000 0.000000 1.000000
> 0.000000 1.000000 0.000000
> -1.000000 0.000000 -0.000000
...
> I obtain after one frame the following orientation
>
> 0.000000 0.071051 0.997473
> -0.000000 0.997473 -0.071051
> -1.000000 -0.000000 0.000000
...
> This is NOT in agreement with your results. You got a slightly positive
> y component for the z axis. I got a slightly negative component for the
> y component of the z axis (as it should be, and as you expected).

That's weird. Thanks for testing this out; I'll have to invest more time, 
perhaps create a small test program derived from test_boxstack.cpp for example 
to see what's going on.

> Is it possible that your torque is so large that you are causing a
> rotation more than 360 degrees, causing an apparent rotation in the
> wrong direction?

I don't think so. Using smaller torque I hardly get any movement (say, 10), so 
I upped that to 1000. I use timesteps inbetween 0.001 and 0.004 seconds in my 
sim.

...
> If the body's rotation matrix is represented by R, then the matrix R
> converts FROM coordinates expressed in frame R *TO* world coordinates -
> which is indeed the correct behavior.

Weird, I had always thought it was the opposite way. Could it have anything to 
do with a premultiply vs. postmultiply thing (have read about that, but don't 
know exactly what the implications are)?
Couldn't you also think of it the other way? I mean, take a world vector 
(1,0,0), multiply that with R (which is a projection onto the axes in R), and 
you end up with the (1,0,0) vector in R's coordinates (body coordinates). This 
would give a body->world conversion. Or would you be multiplying with the 
transpose of R to achieve that? (whoever invented the row vs column matrix form 
to make things so confusing! ;-)).

> Consider the vector (1,0,0). Assuming
> this vector is in R coordinates, this means it is one unit along R's local
> X axis. Multiplying this vector by R gives you the first column of R -
> which is R's local X axis, in WORLD coordinates. So, R converts from
> body coordinates to world coordinates.

You're right, I can follow that. Strangely though, with the tranpose, I get 
everything working. I added contact points and the car behaves reasonably well 
(although on some kerbs it gets way too much impulse when hitting that (I use 
an OBB-plane intersection to generate the contact points with ODE itself).

> Are you sure you don't have a mixup in your code?

I might, but then my *whole* program would have been built in reverse thinking. 
:) Amazing that it could still work that way, lol. I must do some more testing 
and see where I go wrong. Too bad I've got 30hr/day workdays coming up. :(

Thanks very much for the help,
Ruud