Alberti's Construction
 The first written account of a method of constructing pictures in correct perspective is found in a treatise written by the learned humanist Leon Battista Alberti (1404 – 1472).  The first version, written in Latin, was entitled De pictura (On painting), and was Alberti’s effort to relate the development of painting in Florence with his own theories on art.  An Italian version (Della pittura) appeared the following year, and was dedicated to Filippo Brunelleschi.  We shall look at how to properly construct a tiled floor or pavement.  The details of construction are shown in Fig. 4, 5 and 6. Fig. 4 – Choosing the centric point C. First, the centric point C is chosen, and this is the point in the picture directly opposite the viewer’s eye.  It is also known as the “central vanishing point”, the “point of convergence”, or simply the “vanishing point”.  The ground plane AB in the picture is divided equally, and each division point is joined to C by a line.  These are lines that run perpendicular to the plane of the picture, and are known as “orthogonals”. Fig. 5 – Choosing the right diagonal vanishing point R. In Fig. 5, the point R is determined by setting NR as the “viewing distance”.  The “viewing distance” is how far the painter was from the picture.  This is then how far a viewer should stand from the picture.  R is known as the “right diagonal vanishing point”.  Fig. 6 – Alberti’s construction.  The line NB is intersected by the lines converging at R.  The final step is to draw lines perpendicular to the line NB from these intersection points.  These are called the “transversals”, and they run parallel to the ground line AB of the picture.  They are also known as “horizontals”.  Notice that the diagonal points of the squares in the grid can be joined by a straight line.  This is an indication that Alberti’s construction shows the ground plane of a picture in the correct perspective.  Such mathematically correct “floors” are known as pavimenti, since most of the first treatises on their constructions were written in Italian.  Notice that the spacing of the square grids gets smaller as the lines of the grid get farther away from the viewer.  This is known as foreshortening.  Intuitively, it feels as if the distance CR is the viewing distance, and not NR.  We can obtain a geometrical proof of why the correct viewing distance is NR by considering Fig. 7.   Fig. 7 – The plan and vertical section corresponding to Alberti’s construction. O and P are the positions of the eye and foot respectively, and are derived from the Italian words for eye and foot, namely occhio and piede.  MP is the viewing distance.  This is closely related to the HP, which is the distance from the viewer to the last transversal.  If one was to stand at R instead of P, one can easily see that the distances AR and HP are the same.  Hence, the viewing distances NR and MP are the same.