I have a unique problem that I'm struggling with with regards to surveying. Because my surveying equipment is much more accurate at measuring angles than distances I'd like to find an analytic solution using only the angular measurements. Let the surveyor sit at the origin of the coordinate system and represent the known vertex of the tetrahedron (or greater polygon if necessary.) I can then measure azimuth and pitch to each of the 3 (or up to 6) survey prisms allowing me to construct a unit vector pointing from the origin towards that prism (but magnitude remains unknown.) I also have precision CMM measurements of the relative geometry of the prisms, although not it the surveyors reference frame. Thus, if A, B and C are the prisms I know the lengths of AB, BC, and AC along with the angles between them. Again, I also know the unit vectors that points from the Origin "D" to A, B and C, - Va, Vb, and Vc respectively. I'd like to calculate the position (x, y, z) of points A, B, and C in the surveyor reference frame. It's understood that the solution will not be unique in some cases but that surveyor location can be chosen to eliminate many multiple solutions. Also, the surveyors less accurate distance measurement can be used to select the proper solution if multiples exist. Any help to a first time poster would be greatly appreciated.