Re: [Algorithms] How to derive transformation matrices

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

Steve Wood  wrote:

>> From: ro...@do... [mailto:ro...@do...]
>> 
>> Having dealt with rotations, what about shear?  I'll leave that aside
>> until someone asks the question using an intrinsic geometric
>> definition of "shear" (And it does exist).  
>> 
>
>Which begs the question to Lorrimar...What did you mean by shear? 

Guilty of begging the question,  not because I didn't know the answer,
but because it was getting late.  I can't necessarily answer every
question in onepost or one evening.

> I'm not a
>matrix guy at all (well, except for the movie which rules) but I do know a
>few things about shear forces. 

There is no question of forces here, but just of affine mappings.
True, a shear force on a deformable object tends to produce a
deformation that would be described by a shear mapping.  I think the
engineers say "Stress is proportional to strain".  The stress is the
shear force, the strain is the deformation.  

But on a rigid body a shear just produces a force couple, which
results in rotation, not a shear deformation, so not a shear
transformation..  But all this is a digression from the issue of
transformations, i.e. mappings.
   
> 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.

> In engineering we need
>material that can withstand shear forces so things won't rip apart.  In 3D
>graphics I'm assuming that it will create a moment in the object receiving
>the force and instead of determining the deflection and deformation of the
>material or illustrating the breakage of the material I also assume you will
>use shear to cause the object to move or spin.
>

See above the comment on the difference between shear qua force and
shear qua mapping.