RE: [Algorithms] How to derive transformation matrices

[Steve W. <Ste...@im...>]

> -----Original Message-----
> From: Klaus Hartmann [mailto:k_h...@os...]
> 
> Okay, I know... I said I would exit the thread, but I did a 
> mistake in my last post.
> 

OMG!  :O

> > 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.
> 

I see your point and agree with you...I think it has finally dawned on me
why shear forces are described with reference to the shear plane.  Thanks.
Mostly what I remember about my statics class was the endless repository for
laughter called Mohr's circle, just barely edging out the slide rule...which
believe it or not was a required lesson the year before I took geometry (we
were the lucky class to be first to use a calculator), and our instructor's
slide show of when he was called off during 2 weeks of the class to help in
the assesment of the Loma Prieta earthquake of '89.

> 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 found the vector thing intuitive for me...I don't use matrices but that
might help others understand.

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

Well, I think we'll let it go this time...but one more time and...! ;)

R&R