*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