Richard Talbot63 Bedford Street North Shields Tyne and Wear NE29 0AR UK
Briefly, I propose that an explanation for the unique compositions
and the apparent inconsistencies of many paintings is that their
spatial structures have not been generated purely using the logic
of linear perspective. I would argue that their distinctive characteristics
are not the result of making a projection from a ground plan
or constructing a
My research has also been fuelled by reading James Elkins's
I will now set out the broad areas that are particularly relevant for my thesis, and then show how they are relevant to the construction of certain paintings. I will look at Alberti's construction, the orthodox history of perspective and some of its assumptions, and the various geometric patterns found in paintings, the significance of which I believe has been overlooked.
Figure 1. The general principle of linear perspective For a painter, this surface is usually, but not necessarily
flat, and is known as the 'picture plane'. The discovery of perspective
is attributed to the architect Brunelleschi, and it has been
suggested that it originated in his desire to understand the
mechanism that governs the apparent diminution of architectural
elements according to their position and distance from the eye.[4] This knowledge
would then have enabled him to control the relationship between
the real space within a building and the projected image of that
space. The subsequent adoption of linear perspective as a tool
by artists/painters appears to have its roots in a general desire
to represent or depict the third dimension more accurately or
convincingly. The assumption is that artists wanted to solve
the problem of creating a more logical, measurable, naturalistic
and unified space and that Brunelleschi's discovery provided
the solution. However, the precise nature of that solution and
the mechanism and date of its discovery remain unclear.[5] Reliefs by Donatello are the earliest
works to show a relatively consistent approach to diminution
in space, but Masaccio's In 1435, some eight years after Masaccio's Figure 2. He described it as a projection and explained the relationship
between the position of the eye, the cone of vision and its intersection
with the picture plane. He described two separate constructions,
the information from which is combined to give a receding perspectival
grid. Consequently, most analyses of the perspective constructions
of Renaissance paintings post 1435, are based on the tacit assumption
that the artists would be using Alberti's method in one form
or another, or would be aware of the principles underlying Alberti's
theory.[8]
It is assumed that the artist would initially have created a
perspectival grid on the ground ( In reality, however, there are paintings that show an approach that could not be considered to be purely Albertian. Many paintings show a floor grid with a recession that appears to be governed solely by the 45° diagonals of the grid squares being drawn towards a point at eye level, often placed at the edge of the painting. This approach is often referred to as the 'distance point' method and these points are known as 'distance points' simply because the distance between them and the central vanishing point is the same as the distance between the viewer and the picture plane.[9] It follows that if the vanishing point for the orthogonals is placed centrally, and the edge of the painting is used as a distance point, then the 'correct' viewing distance is half the width of the painting. It also follows that the angle of view is 90°. It has been generally assumed that these points have been placed at the edge of the paintings for completely practical reasons. However, Alberti's description of the mechanics of the perspective construction is, in fact, slightly ambiguous and open to various interpretations. Samuel Y. Edgerton demonstrated that Alberti's description could imply that the viewing point should be placed at the edge of the painting, and that the artist subsequently decides the position of the picture plane [Edgerton 1975: 40-49]. The two diagrams described by Alberti are, in effect, overlaid, and under certain circumstances, when the picture plane is placed down the centre of the painting, would result in the distance point and the viewer's position coinciding. The particular properties and wider implications of this construction, however, appear to have gone unnoticed. The following two figures show two of many possibilities. In Figure 3 the viewer's distance from the picture plane is half the width of the picture, making the angle of view 90°. The resulting transversals are found to be placed at 1/3 and 1/2 the height of the rectangle. Figure 3. In Figure 4, the viewer is 1/4 the width of the picture from the picture plane, and the resulting transversals are found to be placed at 1/2, 2/3, and 3/4 the height of the rectangle. Figure 4. These forms of the Albertian construction, where the viewer, the picture plane and grid units along the base are in a defined relationship to each other, are particularly important. Under normal circumstances regular surface grids and perspective diminution do not mix, but in this particular case they do. The resulting divisions within the rectangles follow simple ratios, creating simple harmonic grids based on the reciprocals of whole numbers. It is known that both Piero della Francesca and Leonardo da Vinci were interested in and researched these specific relationships [Wittkower 1953]. For these relationships to hold, the distance from the eye to the picture plane must be the same as the length of the grid units along the base (Figure 5). Figure 5. Figure 6 shows another way of developing the same divisions, and Figure 7 shows that the transversals of a perspectival grid drawn within such a rectangle divide along their length into 4, 5, 6, 7 etc, equal parts. Figure 6. Figure 7. Alberti's text can be interpreted as describing a general principle of projection, with no predetermined measured relationship between the plan, the picture plane and the viewer. The construction that results lends itself to the drawing of a simple rectangular space, based on a rectangular floor subdivided into squares. Edgerton's interpretation is more specific and results in
a construction which contains very particular geometric and number
properties. Additional orthogonals are easily inserted where
the transversals touch the sides of the rectangle, resulting
in a space that is not confined by two dominant orthogonals from
the two lower corners of the rectangle (see Figure 7). The construction
fills the whole rectangle and is consequently more evocative
of larger and more open spaces, a quality that can be seen in
the under-drawing of Uccello's Equally important is the fact that it is a construction that can be developed without any regard for the concepts of 'projection' and the 'picture plane'. I suspect, for reasons that will become apparent, that it is this type of construction and the simple harmonic relationships within it that are the key to Brunelleschi's architecture and his involvement with the development of the geometry of perspective.
Flagellation
see [Wittkower and Carter 1953]; For Masaccio's Trinity
see [Field 1997], [Field, Lunardi and Settle 1988], [Aiken 1995],
[Kern 1913], [Schlegel 1963], [Janson 1967], [Coolidge 1966],
[Polzer 1971], [Sanpaolesi 1962: 42-53] and [Cristiani-Testi
1984]. return to text[2]
Kemp writes: 'In the Flagellation, the artful ambiguity is less
developed, but there is no question that Piero is sharply aware
of surface interplays such as those between the sharply silhouetted
light and dark forms inside and outside the praetorium. I think
it is true in general to say that the greatest perspectivists
- we may think of Masaccio, Piero, Leonardo and Saenredam as
among such - have not only exhibited complete mastery of the
construction of space, but have also shown a heightened awareness
of the shapes of forms when projected on to the flat surface
of the painting' [Kemp 1992: 32]. Speaking of Domenico Veneziano,
Kemp writes: 'His St Lucy Altarpiece not only contains a virtuoso
display of advanced perspective but also exploits a marvellously
cunning series of visual conjunctions which compress elements
at different depths into an interlocked composition' [Kemp 1992:
35]. [3]
The date for its discovery is suggested by different authors
to be anywhere between 1409 and 1425. It is complicated by the
fact that the term 'perspective' was originally linked to the
general area of optics, and only later took on its more specific
meaning. [4]
Wittkower acknowledges that '…he had to invent painters'
perspective since the two-dimensional projection was the only
mathematical way of determining the relation between distance
and diminution' [1953: 288]. However, any building containing regular intervals
and a fixed height throughout would achieve some of the qualities
that Wittkower is claiming for Brunelleschi's buildings, but
he goes on to say that 'it was only during the Renaissance that
everything was done to make the perception of a harmonically
diminishing series a vividly felt experience'. The elevation
of a building is parallel to the picture plane and so is unaffected
by perspective. There must be something else that distinguishes
the image formed by a Brunelleschi interior, from the image formed
by any other set of objects placed at regular intervals in space.
This is an area that was originally dealt with earlier in Argan
[1946]. [5]
Manetti, thought to be the author of the biography The Life of
Brunelleschi, describes Brunelleschi as the inventor of perspective.
Manetti claims to have first hand knowledge of the painted panels
that were used by Brunelleschi to show perspective It is from
Manetti's description that numerous attempts have been made to
understand the precise nature of these panels which no longer
exist. The main problems are understanding exactly what Brunelleschi
did or did not know at the time, what it was he was actually
demonstrating, the exact nature of these panels, and how he made
them. These problems have generated a multitude of explanations
ranging from the panels being made from measured plans and elevations,
through to the idea that Brunelleschi was in fact demonstrating
paintings made using a camera obscura. See [Manetti 1970]; [Tsuji
1990]. [6]
The suggested collaboration between Masaccio and Brunelleschi
is usually on the grounds of the style of the architecture depicted
in the painting. [7]
[Alberti 1972]; [Alberti 1966]. The original Latin version, [8]
A reconstruction of the perspective structure of a painting makes
certain assumptions, the most important being that the painting
actually contains a rational space. Working backwards, a rational
ground plan can then be reclaimed from the painting, and it is
often assumed that the artist must have started with such a ground
plan. The most well known reconstruction of this type is Wittkower
and Carter's analysis of Piero's [9]
The two vanishing points on the horizon at which diagonal 45°
lines in the horizontal plane meet, are known as distance points.
They are the same distance from the central vanishing point as
the viewer is from the picture plane. If within a picture, a
horizontal square parallel to the picture plane can be identified,
extending the diagonals to the horizon will give the distance
points. The distance of the viewer to the picture plane is then
known, and it becomes possible, by working backwards, to create
a plan of the space within the picture. It is debatable whether
the correct viewing distance was of any importance to the early
users of perspective. It becomes more important when the game
playing potential of perspective is realised. There can also
be a conflict between this 'ideal' viewing distance, the physical
distance that the artist is from the surface while working, and
the distance from which the painting is normally seen. For instance,
I think that within Piero's Baptism of Christ in the National
Gallery, London, Piero may have generated a perspectival grid
using a diagonal to the edge of the painting, making the 'correct'
viewing distance half the width of the painting. Standing very
close to the painting, one eye shut, level with the horizon,
the space within the painting alters dramatically, making sense
of the proportions of the figures in the background.
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