This paper presents a novel system for reconstructing the 3D structure of free-form objects using three 2D images acquired simultaneously. The approach is to first describe the 3D-from-2D problem in projective space in which structure is defined relative to some virtual plane. The projective approach allows combining the two families of parameters into one set that can be recovered linearly in a straightforward manner. The linearity of the process also ensures a unique and stable solution, which is a key factor for obtaining automation of the measurement process. Moreover, the geometric and algebraic constraints of the 3D-from-2D problem, including the combination with photometric constraints, are described by a unique family of multi-linear equations whose coefficients form a tensor, known as the "tri-linear tensor". One of the key features of the tensor is that it describes the 3D-from-2D constraints under all possible situations, i.e., it is not subject to any form of singularities. The system has been implemented as a portable non-contact 3D-measurement device, which is capable of measuring objects with accuracy levels ranging from 30-100 microns for the entire object. Being a robust and portable system that can be placed close to the measured objects, it covers large areas with single digital images. The outputs provided by the system can be surfaces, edges, holes, cross-sections and other reports as requested by users. The system can be used for numerous applications such as design (digitization of clay models), die and mold correction, parts measurement, prototype assembly, quality control and reverse engineering. The benefits over previous techniques, such as contact measurement ones, are the portability, capability of operating in uncontrolled environments such as production lines and the much higher throughput.