Re: [Algorithms] How to derive transformation matrices

[Klaus H. <k_h...@os...>]

Okay, I know... I said I would exit the thread, but I did a mistake in my
last post.

> With this I don't agree. Certainly, in the case of your box, the shear
force
> is perpendicular to the surface of contact. But that's not necessarily
true
> for other primitives. What about spheres for example? Imagine a sphere
that
> is centered at the origin. The fixed plane is the x/z plane of the world
> coordinate system, and we shear along the x-axis (y, and z are fixed). So
> our shear force could be represented as a vector H = <h 0 0>, where h is
the
> magnitude of the force in x-direction. Would you still say, that the shear
> force if perpendicular to the surface of contact? Maybe I just
misunderstand
> you, but for me it's not perpendicular to the surface of contact.

Forget the vector H thing, which is quite incorrect, because shearing
depends on another coordinate. Examples:

Hxy is a shear matrix that changes x depending on y.
Hxz is a shear matrix that changes x depending on z.
Hyx is a shear matrix that changes y depending on x.
Hyz is a shear matrix that changes y depending on z.
Hzx is a shear matrix that changes z depending on x.
Hzy is a shear matrix that changes z depending on y.

I hope that at least this time I was faster to correct myself than others ;)
Niki