Question

I have a point in 3D space and two angles, I want to calculate the resulting line from this information. I have found how to do this with 2D lines, but not 3D. How can this be calculated?

If it helps: I’m using C++ & OpenGL and have the location of the user’s mouse click and the angle of the camera, I want to trace this line for intersections.

Answer 1

In trig terms two angles and a point are required to define a line in 3d space. Converting that to (x,y,z) is just polar coordinates to cartesian coordinates the equations are:

x = r sin(q) cos(f)

y = r sin(q) sin(f)

z = r cos(q)

Where r is the distance from the point P to the origin; the angle q (zenith) between the line OP and the positive polar axis (can be thought of as the z-axis); and the angle f (azimuth) between the initial ray and the projection of OP onto the equatorial plane(usually measured from the x-axis).

Edit:

Okay that was the first part of what you ask. The rest of it, the real question after the updates to the question, is much more complicated than just creating a line from 2 angles and a point in 3d space. This involves using a camera-to-world transformation matrix and was covered in other SO questions. For convenience here’s one: How does one convert world coordinates to camera coordinates? The answers cover converting from world-to-camera and camera-to-world.