Whats the 3d rotation matrix?

Question

one last thing don't link me to wikipedia, its useless to.

Answer 1

You're awfully picky for someone who's asking for free help.

Answer 2

rotate around the x-axis [ ]x

'Edit: basis: (1,0,0), (0,cosa,sina), (0,-sina,cosa)

1*********0****************0

0******Cos(A)*******-Sin(A)

0****** Sin(A)********Cos(A)

rotate around the y-axis [ ]y

basis: (cosa,0,sina), (0,1,0), (-sina,0,cosa)

Cos(A)******0*********-Sin(A)  

0************1***********0    

Sin(A)*******0*********Cos(A)

rotate around the z-axis [ ]z

'basis: (cosa,sina,0), (-sina,cosa,0), (0,0,1)

Cos(A)*****-Sin(A)*****0    

Sin(A)******Cos(A)*****0

0*************0***********1

The order of matrix multiplication

is important! Visualize your rotation

in 3D and choose: [ ]z [ ]x for example

If you know matrix multiplication, the correct

combination of these will result in the 3D

rotation you want. I wrote a Visual basic program

using these to produce any rotation in space.

You may have been looking at a combined

matrix using any combination of the above.

Your chosen matrix combination "above" needs to

be multiplied by a column vector for each point you're

rotating:

|x|

|y|

|z|

Answer 3

I don't understand what you mean by "the 3d rotation matrix." There are many 3d rotation matrices and different ways to represent them.

Generally speaking any matrix in the group SO(3) represents a rotation in 3d. SO(3) is the group of orthogonal matrices with determinant 1. An orthogonal matrix is one that satisfies:

A^T A = I

where T means transpose and I is the identity matrix. This is the same as saying A^T is A inverse.

If you are more specific about what you want I might be able to help more ... .

Edit:

AI P's matrices are correct for rotation about the y and z axes. He appears to have a typo on the first one. It should be

1******0********0

0******Cos(A)********-Sin(A)

0******Sin(A)*********Cos(A).

Can you describe what you want geometrically. For example you could ask:

What is the matrix for clockwise rotation of theta about the x axis followed by clockwise rotation of gamma about the y axis?

or

How do I find the matrix which gives a rotation of theta clockwise about the axis spanned by a vector v?

or

How do I find the matrix that rotates the standard basis into another orthonormal basis {E1,E2,E3}?