According to the invention, a set of sensors (4a) is placed on this shape (curve or surface), each sensor outputting signals representative of the orientation of the curve or the surface at the location of this sensor; a model of the curve or the surface is chosen; model parameters are determined from the signals; and the spatial distribution of the points on the geometric shape are determined using these parameters. The invention particularly applies to machining, joinery, masonry, and building domains.