Description

The direction cosines, A, B, and C, are simply the cosines of the angles, a, b, and g, between a given vector, V = ( v_x, v_y, v_z), and the positive local X, Y, and Z axes.

Note that if V is a unit vector, i.e. |V| = Sqrt[ v_x² + v_y² + v_z² ] = 1, then the direction cosines, A, B, and C, are simply equal to the vector elements, v_x, v_y, and v_z, respectively.

Mathematically, the direction cosines are given by:

Once two direction cosines have been defined, the third is known through the following relationships.

A² + B² + C² = 1

cos²( a ) + cos²( b ) + cos²( g ) = 1

In these two relationships, the direction cosines have been normalized to 1.  FRED does not require that the direction cosines be normalized when they are entered in a dialog or macro command, but FRED will normalize them according to these relationships.