An automated system and method of geometric 3D point location. The invention teaches a system design for translating a CAD model into real spatial locations at a construction site, interior environment, or other workspace. Specified points are materialized by intersecting two visible pencil light beams there, each beam under the control of its own robotic ray-steering beam source. Practicability requires each beam source to know its precise location and rotational orientation in the CAD-based coordinate system. As an enabling sub-invention, therefore, an automated system and method for self-location and self-orientation of a polar-angle-sensing device is specified, based on its observation of three (3) known reference points. Two such devices, under the control of a handheld unit downloaded with the CAD model or pointlist, are sufficient to orchestrate the arbitrary point location of the invention, by the following method: Three CAD-specified reference points are optically defined by emplacing a spot retroreflector at each. The user then situates the two beam source devices at unspecified locations and orientations. The user then trains each beam source on each reference point, enabling the beam source to compute its location and orientation, using the algorithm of the sub-invention. The user then may select a CAD-specified design point using the handheld controller, and in response, the handheld instructs the two beam sources to radiate toward the currently selected point P. Each beam source independently transforms P into a direction vector from self, applies a 3×3 matrix rotator that corrects for its arbitrary rotational orientation, and instructs its robotics to assume the resultant beam direction. In consummation of the inventive thread, the pair of light beams form an intersection at the specified point P, giving the worker visual cues to precisely position materials there. This design posits significant ease-of-use advantages over construction point location using a single-beam total station. The invention locates the point effortlessly and with dispatch compared to the total station method of iterative manual search maneuvering a prism into place. Speed enables building features on top of point location, such as metered plumb and edge traversal, and graphical point selection. The invention eliminates the need for a receiving device to occupy space at the specified point, leaving it free to be occupied by building materials. The invention's beam intersection creates a pattern of instantaneous visual feedback signifying correct emplacement of such building materials. Unlike surveying instruments, the invention's freedom to situate its two ray-steering devices at arbitrary locations and orientations, and its reliance instead on the staking of 3 reference points, eliminates the need for specialized surveying skill to set up and operate the system, widening access to builders, engineers, and craftspeople.