Thread: linear algebra, rotation matrix

hello,

i'm wondering if it is possible to find a rotation matrix that does not rotate about the origin.


A and B shows the standard rotation of a square about the origin. C is a square not about the origin, if i apply the rotation matrix, i end up with D, however I'd like to end up with E.

If C had the coordinates c1 (-1,1) c2 (-1, 3), c3 (-3, 3), c4 (-3, 1). It would be a rotation about (-2, 2). Is this possible?

thanks

Hello closetnerd

Originally Posted by closetnerd

hello,

i'm wondering if it is possible to find a rotation matrix that does not rotate about the origin.


A and B shows the standard rotation of a square about the origin. C is a square not about the origin, if i apply the rotation matrix, i end up with D, however I'd like to end up with E.

If C had the coordinates c1 (-1,1) c2 (-1, 3), c3 (-3, 3), c4 (-3, 1). It would be a rotation about (-2, 2). Is this possible?

thanks

I'm afraid not, because every 2 x 2 matrix will map (0, 0) onto itself, and you'll want (-2, 2) to map onto itself, it that is to be the centre of rotation.

Grandad

hello,

i'm wondering if it is possible to find a rotation matrix that does not rotate about the origin.


A and B shows the standard rotation of a square about the origin. C is a square not about the origin, if i apply the rotation matrix, i end up with D, however I'd like to end up with E.

If C had the coordinates c1 (-1,1) c2 (-1, 3), c3 (-3, 3), c4 (-3, 1). It would be a rotation about (-2, 2). Is this possible?

thanks

hi
first you shift your point to the origin by using translation matrix
then apply rotation matrix and finally apply inverse of translation matrix

Hello -

My answer assumes that you are using matrix multiplication only. Matrix addition will allow you to shift the origin, of course.

Grandad