Rotation Matrix about a Point Other Than the OriginDate: 12/18/2006 at 19:53:19 From: Jon Subject: Rotation Matrices about points, not origin I know that in order to rotate a point around the origin you use the rotation matrix [cos x -sin x] [sin x cos x] I was wondering how you rotate a point around a point other than the origin? I thought that you'd have to place a value in front of the sine and cosine (3sin x or 5cos x, for example), or add to the sine or cosine value (3+sin x or 7+cos x). I don't know what to add to where, I get very inconsistent results. Date: 12/19/2006 at 06:38:42 From: Doctor Schwa Subject: Re: Rotation Matrices about points, not origin Hi Jon, I think the idea you're looking for is called "conjugation", which means to do something, then do something else, then undo the first thing. For instance, to leave a room when the door is shut, you open the door, leave the room, then un-open the door (that is, close it). Now you have magically gotten out of a room with a closed door! Similarly, to rotate about a point that is not the origin, first you move all the points so the center is the origin, use the usual rotation matrix, and then move all the points back to where you found them. For instance, if the center is (3,5) you first subtract (3,5) from all the coordinates, then use your matrix, then add the (3,5) back to everything. Does that help clear things up? - Doctor Schwa, The Math Forum http://mathforum.org/dr.math/ Date: 12/19/2006 at 15:04:56 From: Jon Subject: Thank you (Rotation Matrices about points, not origin) You guys make it look so easy! Thank you a TON for your help, it makes sense now! |
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