Raphael, part 1
Master of the Renaissance Perspective
The great master of the Italian Renaissance Raffaello Sanzio (1483-1520), also known by his anglicized name Raphael, showed his gift as early as a young boy. His father, himself a painter, soon recognized his son's talent and took him to Perugia, where the young Raphael became an apprentice in the Perugino's studio.4 From Perugino he learned his feeling for harmony; the use of color and most importantly - basics of perspective.
At that time the perspective system was a valuable "know how" and was kept secret. Those who theorized about it did not know the whole deal and those theoreticians who knew the whole deal omitted the fundamentals. Raphael was not a theoretician, he was, first of all, a painter. Later on his superior knowledge of the geometry and his skills as a draughtsman would led him to the position of the papal architect. Today we can say that he was not only an outstanding executor of perspective, but also an innovative applied scientist. Fortunately, he left behind many hints referring to the Renaissance perspective system and his legacy is coded in his work.
The Marriage of the Virgin (1504)
The simplified analysis of The Marriage of the Virgin shows how Raphael coped with perspective in one of his earlier works. Raphael is so kind to informs us, although implicitly, about the presence of the Golden ratio triangle ABV, also known as Kepler triangle (green line), and points to the basic ratios of the Renaissance perspective system.
There are couple of steps, necessary for the viewer, to arrive at the foreshortened square, which provides us with the exact measurements to work within the three dimensional space of the picture. The first step in the system's sequence is to transfer the rectangular area of the picture plane into the same square area with center in the vanishing point. From the base square (purple line) all other proportions unwind.
The subsequent construction of the circles, which geometrically sets the correct proportions in the system, are achievable only with a use of a compass. From φ circle we construct √φ circle at the base square bottom line. Thus the hypotenuse AV of the golden ratio triangle defines the radius of the upper φ circle with the center at the vanishing point and the cathetus AB defines the radius of the smaller √φ circle with the center in the middle of the square's bottom side. Therefore radius of the smaller circle (BA) to half side of the square (BC) equals √1.618 to 1. The radius of the lower circle (BF) equals to the upper, but more importantly defines the focal length distance.(fig.1)
This brings us to a new element that has been overlooked or rather confused with the distance point. Let us call it focal point - F point. F point is the apex of the visual pyramid with the focusing effect of a concave lens, which Jean Pelerin refers to in his book De Artificiali perspectiva (1505).
Raphael placed the focal point or F point at the distance based on the golden ratio proportion. The distance from the base line to the focal point BF is to half side of the base square BC at the ratio of 1.618 to 1. The focal point's main role is to generate the lateral points.
The whole geometrical structure has to be shifted down of the picture itself as if we were standing in front of it. From the 1.618 circle we proceed to construct another circle with the radius of √1.618, whose ratio Raphael used to a paved white path between the tiles. Central white paths run to the stairs and to the vanishing point at the 38.2 degree slope.
The lateral points on the horizon equal the distance of the F point and can be reached either via a compass transfer or geometrically (will be shown in The Annunciation).
Once we determine the lateral points we can easily find out that a single tile is proportioned 2:1.
Notice how Raphael creatively used Mary's suitors to highlight important points in the constructional scheme. Each of them holds in his hand a wooden stick (red lines). Joseph's flowered stick aims to the bottom of inceptive circle, which ratio of its radius to half of the base square is 1.618 to 1. It is a circle from which all other geometry, especially the circular one, unfolds.
Next stick points to the bottom of the circle of the same radius, but with the center at the base square's bottom side. It is the F point or focal point, the one which generates the lateral points. Although the lateral points (L points) are commonly called the distance points, they are not the same as the viewing distance. The distance point is the distance from which the picture was taken and from which the whole scheme unwinds. The term distance point comes from a misunderstanding of its function and should not be called as such.
The third stick aims to the point of coordinate importance - D point or the distance point. And the fourth rod passes through the corner of the frame and aims to right corner of the bottom square. One of the suitors, a boy, has decided to break the stick over his knee. One end of his stick aims to the horizon and 1.618 circle crossing and the other aims to the bottom line and √1.618 circle crossing. Although they can now be considered as hints, these lines could have functioned as a tool for the painter himself during the geometrical process and to speed up his work.
A single tile measures 12 x 6 Roman palmi, so from the edge of the picture plane to the bottom of the stairs of a hexadecagonal building it is 99 Roman palmi. The distance point is from the bottom of the stairs 26 meters or 85 feet.
It is worth mentioning that the purple line (generated by the diagonals) passes right through the wedding ring. Raphael set the size of the base square, basic building unit, to 20 Roman palmi (purple line). With this issue of the base square, basic building unit, we move on to the next chapter.
to be continued...