Trinithis

10-05-2009, 11:09 PM

I was wondering if anyone knows to calculate any set of angles to rotate a plane with a normal n to a specified normal n' (or -n'). It does not matter at what point on the plane it gets rotated about.

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Trinithis

10-05-2009, 11:09 PM

I was wondering if anyone knows to calculate any set of angles to rotate a plane with a normal n to a specified normal n' (or -n'). It does not matter at what point on the plane it gets rotated about.

oesxyl

10-06-2009, 12:47 AM

I was wondering if anyone knows to calculate any set of angles to rotate a plane with a normal n to a specified normal n' (or -n'). It does not matter at what point on the plane it gets rotated about.

cos a = <n, n'> / (| n | . | n' |)

<a,b> - scalar product of a and b

| v | - must be probably 1 since n and n' are normals of the plane

best regards

cos a = <n, n'> / (| n | . | n' |)

<a,b> - scalar product of a and b

| v | - must be probably 1 since n and n' are normals of the plane

best regards

Trinithis

10-06-2009, 02:01 AM

Doesn't that only work in 2D? For 3D I would need (xRot, yRot, zRot) for each of the axes.

oesxyl

10-06-2009, 02:46 AM

Doesn't that only work in 2D? For 3D I would need (xRot, yRot, zRot) for each of the axes.

work for any dimension of the space because scalar product and vector size is redefined.( that if the space is liniar)

<x1, ..., xn> , <y1, ..., yn> = x1*y1 + ... + xn * yn

| <x1, ..., xn> | = sqrt(x1^2 + ...+ xn^2)

the angle is in the plane defined by vectors x and y.

best regards

work for any dimension of the space because scalar product and vector size is redefined.( that if the space is liniar)

<x1, ..., xn> , <y1, ..., yn> = x1*y1 + ... + xn * yn

| <x1, ..., xn> | = sqrt(x1^2 + ...+ xn^2)

the angle is in the plane defined by vectors x and y.

best regards

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