Origine e sviluppi degli algoritmi per l'intersezione in avanti nel rilievo di architettura

The algorithm AP (Migliari 1985), used in the photogrammetry laboratories of Rome and Chieti universities, renders the coordinates of a point P in space observed by two topographic stations A and B. The algorithm thus constructs the segment of minimum distance between the two straight lines which collimate at the observed point, and are assumed to be oblique. Recently, however, efforts have been made to find a more general method to overcome the limits derived from the use of only two stations. The new algorithm APn, presented here, constructs the point which is at the minimum distance possible from the n collimation radii from n stations; this point, of course, is the median point of the segment of minimum distance when there are only two radii of collimation. To demonstrate the effectiveness of this approach, the study considers the case of three stations and compares the theoretical limits of the old algorithm with those of the new one. The results of the theoretical discussion are then compared with the first application of the new algorithm used in the photogrammetric representation of the frescoes of Giovanni and Cherubino Alberti in the Vatican s Sala Clementina.