Three dimensional angles in general are a tougher concept altogether. You are now talking about a single vector in x,y,z and not a comparison between two. To be perfectly honest, I myself am not completely comfortable with this notion. From what I can remember though, this type of interpretation does rely on breaking down the xyz vector into two vectors in xy and xz. After this is done then the angle of separation between these two vectors is calculated.

Not too long ago we had an ongoing thread trying to detail the intracacies of steradians which are another interpretation of three dimensional angles. (They are strictly speaking square radians.) They are used by those who deal with three dimensional projections regularly. Perhaps this would be an informative study for you. I know it left me scratching my head for a while. I will mention that I did not find a direct relationship between steradians and normal two dimentional angles other than the strict definition of a steradian itself. Briefly, I know how they calculate the steradian, but I do not see the connection to two dimensional angles. Type steradian into your browser and do some reading on the subject and you will see what I mean.

Perhaps one of the more knowledgable members here can help you out more. Good luck.

]]>So with that in mind, how do you consider a projection in 3D? Say you have an xyz, and you want to project off of that point a magnitude, bearing, and pitch. What role does pitch play in the 3D projection? Deep waters... Thanks for shedding some light already!]]>

The easiest way of imagining this is like this. If you have any two vectors with x, y, and z components then there will exist some plane, say w, that they both share. The angle that you compute is thus just the angle between the two on this plane.

Does that make more sense?

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