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Subject: Re: [geda-user] Apollon
From: John Doty <jpd AT noqsi DOT com>
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Date: Sun, 13 Sep 2015 17:22:29 -0600
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On Sep 13, 2015, at 4:47 PM, John Doty <jpd AT noqsi DOT com> wrote:

>> 
>> I bring it up only because it's been an issue before, before the
>> nanometers switch.  Rotating by X then -X did not result in the
>> original.
> 
> In the Pythagorean/rational system, if you make the rotation matrix for -X the transpose of the rotation matrix for X, you get the original back. That’s mathematically the natural way to do it. You would want to compose rotations by matrix multiplication rather than angle addition. Not hard in a decent high level language.

Upon further reflection, I note that if you choose (x, y) as the pair representing the rotation approximating angle t, and (y, x) as the pair representing the rotation approximating u = 90 - t, the composed rotations tu and ut will be *exactly* 90 degrees. So a rotation of 30 degrees followed by a rotation of 60 degrees will accumulate no error at all, even with respect to the external system.

Pun intended.

John Doty              Noqsi Aerospace, Ltd.
http://www.noqsi.com/
jpd AT noqsi DOT com