RE: [Algorithms] How to derive transformation matrices

[Robert D. <RD...@ac...>]

I think most people in this case take shear to mean a transformation in
which there is an invariant plane, but everything outside that plane is
moved within its own parallel plane, so viewing through the said invariant
plane, you would see this :


  pre-shear            post-shear

  +------+             +------+
  |      |            /      /
--+------+----- -----+------+-------- invariant plane
  |      |          /      /
  +------+         +------+

Useful for certain effects, but in general not a good thing because unlike a
rotation matrix it doesn't preserve your normals.

Robert

-----Original Message-----
From: Steve Wood [mailto:Ste...@im...]
Sent: 24 July 2000 17:49
To: 'gda...@li...'
Subject: RE: [Algorithms] How to derive transformation matrices


> 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?  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.  If that is what you meant then a shear is
the perpendicular component of force on a surface.  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.

R&R

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