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Re: Rotate3D bug solution

• To: mathgroup@smc.vnet.net
• Subject: [mg10311] Re: Rotate3D bug solution
• From: Robert Beretta <beretta@callamer.com>
• Date: Mon, 5 Jan 1998 03:47:27 -0500
• Organization: Conix Enterprises
• References: <68l33o$mej@smc.vnet.net>

Addendum:

My previous statement that "it is not generally possible to represent
large spatial rotations with three sequential rotations about each of
the fixed coordinate axes" is silly.  It certainly is possible to
represent large rotations in this way.

It is the inverse of this parameterization - converting a rotation
matrix into a unique sequence of three rotations - that is troublesome.
A family of sequential rotations exist that result in the same spatial
orientation when the magnitude of the "middle" rotation is +-Pi/2.

This difficulty is no different than the polar singularity that exists
with Euler's angles when theta = 0 or Pi.  It is primarily this
singularity that motivates the use of Euler parameters in some
applications.

Bob Beretta
Conix Enterprises
beretta@callamer.com