What i had been doing, was taking the rz rotation matix for 45^ and the the Rx rotation matrix for 45^ (these are the two axes the scanner is rotated around) and multiplying them Rx45 x Rz45 x Ry0 which was giving me the matrices ive mentioned.
If its the first column of this matrix, which is x,y and z? Is it read in that order?
Am i doing it correctly?
Sorry guys, still kind of stuck with this simple part.
Imagine this matrix
0.8660 \\ -0.5 \\ 0
0.5 \\ 0.866 \\ 0
0 \\ 0 \\ 1
What is n_x, what is n_y and whats is n_z?
(Sorry, no matter how many spaces/dashes i put in i cant seperate the numbers any more)
(use [ code ] blocks without the spaces to preserve formatting)
A transformation matrix is different from a vector, you try to mix things.
When you multiply the 3D vector n (with [nx,ny,nz]) by a 3x3 rotation matrix, you get a new 3D vector, m, with [mx,my,mz].
There is no magic in this, either you use already working code for vector*matrix multiplication, or read this for an example of a 2x2 rotation matrix that multiplies coordinates, and shows the result :
http://en.wikipedia.org/wiki/Rotation_matrix#Rotations_in_two_dimensions
Thanks for the reply, ZBuffer. i know this isn’t magic, im not confused, just missing a piece of the puzzle.
To clarify, what i had been doing was, as it is a 3D rotation, substituting 45^ (or whatever angles I choose for a test) into two rotation matrices, depending on what two axis i am rotating around.
I then multiply Rx x Ry x Rz, as it mentions further down for matrix multiplication.
For the 45^ multiplication, I got
0.7071 -0.7071 0
0.5000 0.5000 -0.7071
0.5000 0.5000 0.7071
The normals you identifed for 45^ earlier were 0.5, and 0.7071. I assumed (wrongly) that was where you got it from, reading positions from those matrices.
So what i actually should be doing is multiplying some 3x3 matrix by a 3x1 matrix comprising 45,45,0?
What is the 3x3 matrix?
Ignore my attempt at
:confused:
Thanks again for all your help.[ code ] to properly close the block, you need / slash [ /code ]
V1= original vector, 3 components
M= a matrix with 3 columns and 3 lines, like the one you wrote above
V2= a new vector, which is V1 transformed by M
V1*M=V2
If V1 is aligned to an axis, it can be for example [1 0 0], so in V2 you will directly see the first line of the matrix.
For [0 1 0] it will be the second line, etc.
OK, see if I have this right.
I want to find the surface normals in x,y and z of a plane after a rotation.
Step 1: I take the three rotation matrices, and rotate them around different axes, by a set number of degrees. This means substituting 45^ for theta in each. I then multiply Rx by Ry by Rz. This gives me a 3 x 3 matrix.
Step 2: I then take the surface normals of the plane before I rotated it, 1,0,0 for vertical, or 0,0,1 for horizontal, and multiply this 3x1 matrix by a 3x3, giving me a 3x1 matrix.
This 3x1 matrix is n_x,n_y,n_z reading from top to bottom. Always.
?