What would the angles be for a 3D vector?

Question

Nathan 2013-12-6

回答： Roger Stafford 2013-12-6

Hi, I've got a vector with components, x, y and z. I need to know the x, y and z angles for that vector.

I assume that the x-angle would be atand(max(y)/max(x))) and I also assume that the y-angle is 90-x.

Would those be correct for a 3D vectors definition of a x and y angle? Also, how do I calculate the z-angle?

Answer 1

Roger Stafford 2013-12-6

Let x, y, and z be the vectors' three components. The angle the vector makes relative to the positive x-axis can be computed as:

ax = atan2(sqrt(y^2+z^2),x);

Similarly ay and az, the angles with respect to the y and z axes, are given by:

 ay = atan2(sqrt(z^2+x^2),y);
 az = atan2(sqrt(x^2+y^2),z);

These are somewhat more accurate than using the ax = acos(x/sqrt(x^2+y^2+z^2)) type formula. Note that the resulting angles are in radians.