Comments on: Quaternions for Rotating, Scaling, and Translating Space

By: Peter L. Griffiths

Peter L. Griffiths — Mon, 30 Apr 2012 16:16:07 +0000

There is careless error in my comments of 29 April 2012. The third sentence should be A further clockwise 90 degree rotation can be achieved by making x=-5 and y=-2 which really is the negative of the first point on the complex plane, apologies.

By: Peter L. Griffiths

Peter L. Griffiths — Sun, 29 Apr 2012 16:36:26 +0000

Further to my comments of 19 April 2012, 90 degrees rotation of the complex plane is fairly easy if the correct procedure is followed. If the point on the complex plane is say x=+5 and y=+2 then a 90 degree clockwise rotation can be achieved by making x=2 and y=-5. A further clockwise 90 degree rotation can be achieved by making y=-5 and x=-2 which is the negative of the first point on the complex plane and is the same result as 180 degree angle of the Cotes format of the complex numbers. However this similarity is not shared by smaller angle rotations. Curiously enough this 90 degree rotation can also be achieved on a three dimensional solid such as a sphere where we have three coordinates say x=+5 y=+2 and z=+9. We also have 8 quadrants. Each 90 degree rotation involves one change of sign and one change of position of the coordinates. It seems that this cannot be achieved by smaller angle rotations.

By: Peter L. Griffiths

Peter L. Griffiths — Thu, 19 Apr 2012 16:34:01 +0000

The purpose of the angles is not for rotating but to identify the n roots of the complex number. These angles are only obtained by finding the arcotangent of the complex ratio. The example of costheta and sintheta which you mention works with theta equalling 90 degrees but this results in the same axes not a 90 degree rotation of the axes.

By: Clifford Algebras for Rotating, Scaling, and Translating Space :: nklein software

Mon, 06 Jul 2009 19:52:23 +0000

[...] using quaternions for rotating, translating, and scaling three-dimensional space. [...]