Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!uunet!mcsun!ukc!slxsys!ibmpcug!peterl
From: peterl@ibmpcug.co.uk (Peter Leaback)
Newsgroups: comp.graphics,connect.audit
Subject: Errors in rotations
Summary: A problem with errors in rotations
Keywords: ROTATIONS
Message-ID: <1990Jan2.163405.24094@ibmpcug.co.uk>
Date: 2 Jan 90 16:34:05 GMT
Organization: The IBM PC User Group, UK.
Lines: 35


[this message has been re-posted because it did not reach some sites]

At the moment,I define my rotations as a 3x3 matrix containing 16 bit
fixed point numbers from 1 to -1. The problem I face is that after a few
thousand rotations,the errors that occur in combining rotations has
malformed the matrix. In fact, the matrix then becomes a scaling matrix
and reduces the size of the rotated object.

What I require is some method of keeping the errors from amplifying. I
have been told there are methods of reconstructing rotation matrices. But
I have also been told that reconstructing a rotation matrix is costly in
processor time,so microcomputer flight simulators that use this method
can only afford to reconstruct the rotation matrix every 500 or 1000
rotations. This method is undesirable because at the point where
reconstruction of the matrix occurs, the object visibly jolts back into
shape.

What I would prefer (and some flight simulators use) is a method that
after every rotation the matrix is nudged back into shape.

I did think of using a method where the rotation is defined as x,y,z
degrees from the axes. This would mean that any errors that occur would
only affect the angles through which to rotate and NOT malform into any
other geometrical transformation. The problem with this data structure is
that combining two rotations defined as x,y,z degrees is very costly on
processor power and requires 2 divisions.

*ANY* comments on how to solve my problem would be greatly appreciated.

Regards,Pete Leaback.
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