Question

I’m aware of Quaternion methods of doing this. But ultimately these methods require us to transform all objects in question into the rotation ‘space’ of the Camera.

However, looking at the math, I’m certain there must be a simple way to get the XY, YZ and XZ equations for a line based on only the YAW (heading) and PITCH of a camera.

For instance, given the normals of the view frustrum such as (sqrt(2), sqrt(2), 0) you can easily construct the line (x+y=0) for the XY plane. But once the Z (in this case, Z is being used for depth, not GL’s Y coordinate scrambling) changes, the calculations become more complex.

Additionally, given the order of applying rotations: yaw, pitch, roll; roll does not affect the normals of the view frustrum at all.

So my question is very simple. How do I go from a 3-coordinate view normal (that is normalized, i.e the vector length is 1) or a yaw (in radians), pitch (in radians) pair to a set of three line equations that map the direction of the ‘eye’ through space?

NOTE:

Quaternions I have had success with in this, but the math is too complex for every entity in a simulation to do for visual checks, along with having to check against all visible objects, even with various checks to reduce the number of viewable objects.

Answer 1

 nx = (float)(-Math.cos(yawpos)*Math.cos(pitchpos));
 ny = (float)(Math.sin(yawpos)*Math.cos(pitchpos));
 nz = (float)(-Math.sin(pitchpos)));

That gets the normals of the camera. This assumes yaw and pitch are in radians.

If you have the position of the camera (px,py,pz) you can get the parametric equation thusly:

x = px + nx*t
y = py + ny*t
z = pz + nz*t

You can also construct the 2d projections of this line:

0 = ny(x-px) + nx(y-py)
0 = nz(y-px) + ny(z-pz)
0 = nx(z-pz) + nz(x-px)

I think this is correct. If someone notes an incorrect plus/minus let me know.