Rotating coordinates

No don''t use the dot product. Use the cross product to discover angles between vectors.

(My Wisdom) + (My Courage) + (My Will) > God''s Power - (ytilaerlariv) = [My] laissez faire [for] Liberatis

I don''t understand. The cross product will return a vector. But I think I need a scalar value for rotation. Or am I wrong? Thank you,

JVFF

You can create a matrix that transforms object coordinates into world coordinates very easily. Assuming that your X, Y, and Z vectors are unit vectors that specify the object''s coordinate system in world coordinates and the object''s origin is at [ T_x,T_y,T_z ] (in world coordinates), then the transformation matrix, A is this:

Xx  Yx  Zx  Tx
Xy  Yy  Zy  Ty
Xz  Yz  Zz  Tz
0   0   0   1

 

Use it like this: W = AO, where W is the point in world coordinates, and O is the point in object coordinates.


Finally, to answer your question, the matrix that transforms world coordinates into object coordinates in the inverse of A -- A^-1.

Actually you''ll want to use the dot product right?

A*B = |A||B|cos(theta)


well, once you have the angles, you use rotation matrixes abouy X, Y , and Z. Or you could convert to quaternians, but the matrix should be fine. There are a lot of good explinations of this once you have the angles.

http://vered.rose.utoronto.ca/people/david_dir/GEMS/GEMS.html

theres one. Its a combination of the three matrices. And if you just have the matrix, but not the angles, you can extract them by things like Beta = arcsin(-R13) and Gamma = arctan(R12/R11) and Alpha = arctan(R23/R33)

where alph, beta, gam are rotation about x,y,z.