Perspective Projection - Transformations and Projections in Computer Graphics - page 77

spans a viewing angle of about 53 ◦ , and this is verified by Figure 3.13, which follows the
site plan given by [Sgrilli 33]. Finally, Manetti mentions that the diameter of the hole on
the painted side of the panel was about the thickness of a bean (6-7 mm). Figure 3.12d
illustrates how the same angle of 53 ◦ is obtained if the eye of the viewer is glued to the
back of the panel (where according to Manetti the hole was bigger, about the size of a
ducat, 20 mm) and the thickness of the panel is the same 6-7 mm.

Masaccio

Perhaps the first great Renaissance painter to use the ideas of Brunelleschi in a serious
work of art was Tommaso di ser Giovanni di Mone (or Tommaso di ser Giovanni cassai),
known to us as Masaccio, a nickname that can be translated as Big Thomas, Rough
Thomas, Clumsy Thomas, Sloppy Thomas, Bad Thomas, or even the Messy Thomas.
He died in 1428, at age 27, and in his last two years he painted a fresco, today titled
Trinity (or Holy Trinity ), in the church of Santa Maria della Novella in Florence. The
accurate execution of one-point perspective in this picture creates the illusion of a
sculpture placed in a cavity in the wall, although the picture is flat. This large picture
(approximately 6 . 7 3 . 2m,or21ft10 2 in by 10 ft 5 in) has a sad history of incompetent

restoration and a 19th century attempt to cut it off the wall and move it to another
wall in the same church. Figure C.2 (page 233) is a small replica showing how the single
vanishing point was placed by the artist at the viewer's position.

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The architectural setting of this fresco [the Trinity ] is so accurate in its perspective
and so Brunelleschian in style that some scholars have suggested Brunelleschi drew
the sinopia, or cartoon, on the wall for Masaccio to paint. This is certainly possible,
but it is also quite possible that Masaccio—a master draftsman as well as an inspired
painter—could have done the whole work himself. Perhaps it doesn't matter. The
important fact for the future of Western art is that Masaccio met Brunelleschi and
gained such a deep knowledge of perspective that he set a standard for every painter
to follow.

—Paul Robert Walker, The Feud that Sparked the Renaissance (2002)

Alberti

In 1435-36, Leon Battista Alberti wrote and published (in Latin and Italian) Il Trat-
tato della Pittura e I Cinque Ordini Archittonici (“On Painting”), where he describes
a simple geometric method for constructing a correct one-point perspective of a hori-
zontal grid on a vertical picture plane. This method was later simplified by Piero della
Francesca in his 1478 mathematical treatise De prospectiva pingendi and is illustrated
in Figure 3.14.
The left part of the figure shows a side view where the picture plane is intercepted
by a family of visual rays that emanate from the viewer's eye. Each ray connects the
eye to one of the transversals (or divisions) of the grid on the ground. The point where
the ray intercepts the picture plane is then transferred to the front view (on the right
part of the figure) to indicate where to place the particular transversal in the picture.
It is easy to see how the transversals, which are equally spaced on the ground, become