Derivation of Matrix to Quaternions conversion

sarah22 · 12-05-2009, 08:54 AM

How did the first matrix derived? Also the second one?

The picture came from here. Part Five: Quaternions

**Bubba** · 12-05-2009, 02:35 PM

I believe it comes from this:

(Q1 * Q2).w = (w1w2 - x1x2 - y1y2 - z1z2)
(Q1 * Q2).x = (w1x2 + x1w2 + y1z2 - z1y2)
(Q1 * Q2).y = (w1y2 - x1z2 + y1w2 + z1x2)
(Q1 * Q2).z = (w1z2 + x1y2 - y1x2 + z1w2)

12-05-2009, 08:54 AM	#1
sarah22 Registered User Join Date: May 2009 Posts: 58	Derivation of Matrix to Quaternions conversion How did the first matrix derived? Also the second one? The picture came from here. Part Five: Quaternions Attached Images
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12-05-2009, 02:35 PM	#2
Bubba Super Moderator Join Date: Aug 2001 Posts: 8,322	I believe it comes from this: (Q1 * Q2).w = (w1w2 - x1x2 - y1y2 - z1z2) (Q1 * Q2).x = (w1x2 + x1w2 + y1z2 - z1y2) (Q1 * Q2).y = (w1y2 - x1z2 + y1w2 + z1x2) (Q1 * Q2).z = (w1z2 + x1y2 - y1x2 + z1w2) __________________ I remember when The Weather Channel talked about weather, MTV played music videos, and the History Channel talked about history instead of conspiracy theories.
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