By using three, or more, electronic distance measurement (EDM) instruments, such as commercially available laser trackers, in an unconventional trilateration architecture, 3-D coordinates of specialized retroreflector targets attached to cardinal points on a structure can be measured with absolute uncertainty of less than one part-permillion. For example, 3-D coordinates of a structure within a 100 meter cube can be measured within a volume of a 0.1 mm cube (the thickness of a sheet of paper). Relative dynamic movements, such as vibrations at 30 Hz, are typically measured 10 times better, i.e., within a 0.01 mm cube. Measurements of such accuracy open new areas for nondestructive testing and finite element model confirmation of stiff, large-scale structures, such as: buildings, bridges, cranes, boilers, tank cars, nuclear power plant containment buildings, post-tensioned concrete, and the like by measuring the response to applied loads, changes over the life of the structure, or changes following an accident, fire, earthquake, modification, etc. The sensitivity of these measurements makes it possible to measure parameters such as: linearity, hysteresis, creep, symmetry, damping coefficient, and the like. For example, cracks exhibit a highly non-linear response when strains are reversed from compression to tension. Due to the measurements being 3-D, unexpected movements, such as transverse motion produced by an axial load, could give an indication of an anomaly–such as an asymmetric crack or materials property in a beam, delamination of concrete, or other asymmetry due to failures. Details of the specialized retroreflector are included.