Vector and Matrix - Rotation3D

Syntax:
= Rotation3D(Alpha, Beta, Gamma[, RadDeg])

Description:
Returns the rotation matrix for a rotation of the three angles Alpha (x-axis rotation; rotation in the yz plane), Beta (y-axis rotation; rotation in the xz plane), Gamma (z-axis rotation; rotation in the xy plane). The optional parameter RadDeg can be used to enter the angles in degrees (RadDeg=1) instead of radians (RadDeg= 0; default).

Rotation3D is an array function. Select the 3 by 3 block of cells to which you want to add the formula and type the formula in the formula box. Then press Ctrl-Shift-Enter.

The rotation matrix can be used to rotate any set of x,y,z coordinates by multiplying it with the rotation matrix. Consider a point A in 3D space with coordinates x, y and z. The vector OA (from the origin to A) can be rotated by multiplying it by the rotation matrix. Suppose the rotation matrix is in A1:C3 and the coordinates of A are in E1:G1 then the formula =MMult(E1:G1,A1:C3) will rotate the x,y,z coordinates of A to x',b',c', the coordinates of A', the point after the rotation was done.

Example:
=Rotation3D(10,20,30,1)  'Rotate 10, 20 and 30 degrees across the x-axis, y-axis and z-axis respectively.