1 Early theories of shape and the first experiments on shape constancy -- 2 The cognitive revolution leads to neo-gestaltism and neo-empiricism -- 3 Machine vision -- 4 Formalisms enter into the study of shape perception -- 5 A new paradigm for studying shape perception -- App. A 2D perspective and projective transformation -- App. B Perkins' Laws -- App. C Projective geometry in computational models -- App. D Shape constraints in reconstruction of polyhedra.