Organized by Istituto e Museo di Storia della Scienza

VOLKER HOFFMANN

The Trinity of Masaccio: perspective construction - isometric transformation - coordinate system

Masaccio's Trinity fresco is known as the first picture constructed with the help of linear perspective. The correctness of this statement has not been proven by Art Science up today: since Kern's fundamental perspectival analysis (1913) with its (wrong) determination of the vanishing point and distance point, more than at least 13 other distance point statements have been published. All differ from each other and are in a range of 894,2 and 211 cm. Furthermore, according to each author the ground plan of the barrel vaulted hall is estimated being either square, crossways or lengthwise rectangular, the position of the cross either in the front, in the middle or in the back. There are only two explanations for such a chaotic scientific situation: or the fresco has not been constructed with the help of linear perspective or the methods of analyzing the perspective are not worth anything.
To solve the problem we are herewith introducing the hypothesis, the Trinity's perspective has been developed after the geometrical principles of the costruzione legittima (viewing beam method, distance point method) discovered in the 15^th century. To prove the hypothesis we have to pick up first 3 and then 4 points from a photogrammetrical reproduction (therefore not distorted), as well as the horizontal line. From there, we have to reconstruct the perspective as a graphic model and expect the construction lines of this model and of the fresco (represented by the photogrammetrical picture) being congruent. The congruency can be obtained, indeed, and thus, we are having the evidence that the perspective of the Trinity has been constructed after the principles of the costruzione legittima. The "distance" of the perspective construction of the painting can now be precisely determined: 452 cm. The investigation is revealing, that the fresco was based on a draft which had been slightly changed during its execution. Furthermore, we are demonstrating, that, and how the perspectival room can be transformed in an isometrical one. Thus, an exact or at least an almost exact location of the figures and objects of the fresco is possible.
We are investigating Brunelleschi's part in the invention of the costruzione legittima (simulation of the optical view) and finally describe the system of measurement: it bases on the division of the basic measure in the sense of a geometrical progression: 1, 1/2, 1/4, 1/8 and so on.

The costruzione legittima, in principle, is always the foreshortening of a square, therefore, of an isometrical basis. At any time, we are able to retransform a foreshortened square into a normal square. Putting on a square a hollow body, a cube or a rectangular, this body can also be foreshortened by the rules of the costruzione legittima, in other words, perspectivly represented - and being retransformed into an isometrical representation after, from which the exact ground-plan, the elevation and the sides can be figured out. Regarding the 'Trinity', this means, that its perspective has obviously been constructed from the ground-plan and the elevation with the help of the 'viewing beam'.
For the first time in documented history there is the possibility to transform an isometrical representation in to a perspectival one - and vice versa.
The vedutas Brunelleschi had created with the help of the perspective instrument are range-finder images. Analog to the them, the 'Trinity' is an arithmetically measured picture due to the possibility of transformation of its perspective into an isometrical representation. The costruzione legittima allows to take the represented room as a coordinate system. All points of the picture are defined by points of the coordinate x, y und z. The position of Christ's omphalos can be defined arithmetically in centimeters like: x211, y105, z84.

Literature:

Volker Hoffmann: Filippo Brunelleschi: Kuppelbau und Perspektive. In: Quaderni dell'Istituto di Storia dell'Architettura, nuova serie, fasc. 2 15-20, 1990, S. 317-326.

Volker Hoffmann: Masaccios Trinitätsfresko: Die Perspektivkonstruktion und ihr Entwurfsverfahren. In: Mitteilungen des Kunsthistorischen Institutes in Florenz, XL Band, 1996, Heft 1/2, S. 42-77.