Re: [Algorithms] How to derive transformation matrices

[Ron L. <ro...@do...>]

----- Original Message -----
From: "Steve Wood" <Ste...@im...>
To: <gda...@li...>
Sent: Tuesday, July 25, 2000 10:58 AM
Subject: RE: [Algorithms] How to derive transformation matrices


> > From: ro...@do... [mailto:ro...@do...]
>
> [snip]
> >
> > > If that is what you meant then a shear is
> > >the perpendicular component of force on a surface.
> >
> > Although incompletely stated,  I believe you have this wrong.  The
> > shear comes from the force component parallel to the surface, not
> > perpendicular.
> >
>
> uh...no, it's the perpendicular.  Forces parallel to a surface do not
> interact with the surface (actually, there would be no resulting force for
> any actions parallel to a surface) unless the perpendicular force causes
> penetration so the parallel component then has something to "grab onto".
>

Not in the classical picture (as opposed to the quantum mechanical picture).
Consider the force of friction of a flat table on a rectangular block being
pushed along it.  That frictional force is parallel to the interface, not
perpendicular.  True, in the quantum mechanical detail of the intersurface
forces at the molecular level , there is some interpenetration of the outer
layers of the electromagnetic fields of the surface molecules of the two
interacting materials, but at that level of detail, the notion of "surface"
becomes fuzzy.  Also true that, in the classical picture,  the magnitude of
that frictional force (parallel to the interface) does depend on the normal
force.

Now,  if the force pushing the block along is applied above the level of the
interface, then it is the couple of the pushing force and the frictional
resistance, both parallel to the table, that produces the shear force, and
the shear deformation if the body is deformable.  The perpendicular force is
simply equal and opposite to the weight of the block and produces no shear
deformation.

But again, this is a huge digression from the issue of deriving
transformation matrices. although the ideas are certainly important in the
sort of physical modeling that people are now doing in games.  In those
models, frictional force is parallel to the interface.