3D point from two angles and a distance

Question

I want to be able to calculate the coordinates of a 3D point, based on its distance from the origin, and two angles: "yaw" around Y-axis, and "pitch" around the X-axis.

In the example, distance from the origin would be 50 units, yaw 10 degrees, and pitch 10 degrees.

Is there a formula to retrieve the 3D result point?

Answer 1

If you have a point which is defined by an azimuth angle (yaw), an altitude angle (pitch) and a distance along this direction vector, then you have to transform the azimuth angle (yaw) and altitude angle (pitch) to a unit direction vector first .
See Solar zenith angle, Azimuth or Euler angles.

In an coordinate system, where the x axis points to the left and the z axis to the front and the y axis is the up vector (Lefthanded coordiante system), this can be calculated as follows:

x = sin(yaw) * cos(pitch)
y = sin(pitch) 
z = cos(yaw) * cos(pitch)

where yaw is the clockwise angle between the z axis and the vector to the point (projected to the XZ plane).

This direction has to be multiplied b the distance to the origin:

P = distance * (x, y, z); 

or

Px = distance * sin(yaw) * cos(pitch) 
Py = distance * sin(pitch) 
Pz = distance * cos(yaw) * cos(pitch)