3D Vector defined by 2 angles

Question

So basically I'm looking for a way to calculate the x, y and z component of a vector using 2 angles as shown: Where alpha is the 2D angle and beta is the y angle. What I've been using uptill now for 2D vectors was:

x = Math.sin(alpha);
z = Math.cos(alpha);

After searching on stackexchange math I've found this forumula doesn't really work correctly:

 x = Math.sin(alpha)*Math.cos(beta);
 z = Math.sin(alpha)*Math.sin(beta);
 y = Math.cos(beta);

Note: when approaching 90 degrees with the beta angle the x and z components should approach zero. All help would be appreciated.

Fagaceous

Answer 1

The proper formulas would be

x = Math.cos(alpha) * Math.cos(beta);
z = Math.sin(alpha) * Math.cos(beta);
y = Math.sin(beta);

Village

Thanks, that works and makes a lot more sense. (i had to switch the x and z but that's just how my enviroment is set) – Fagaceous

@MoffKalast Two angles on perpendicular planes are sufficient to define a vector in 3D space. You could calculate the angle of the projection on the third plane (in this example, XY) using the first two angles. – Substitute

Any idea on how to compute it, if the used x,y,z directions were relative to a plane of a model, and not relative to the coordinate-system the model sits within? – Limburger

I took a stab at doing this in 4D, I came up with: a = Math.cos(gamma); x = Math.cos(alpha)*Math.cos(beta)*a; z = Math.sin(alpha)*Math.cos(beta)*a; y = Math.sin(beta)*a; w = Math.sin(gamma); How close was I? – Baelbeer

Given alpha and beta, what is the angle between red and green lines. – Gottuard

Answer 2

That formula just come from the transformation of Spherical coordinates (r, theta, phi) -> (x, y, z) to Cartesian coordinates.

Hitch

The angle beta shown by OP is not the same as the polar angle in spherical coordinates – Tedda