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Projection : From Latin proicere , "to throw ahead. Station Point SP or S : The position of the artist's eye relative to the object he or she is drawing. Sometiems referred to as "eyepoint," "point of veiw," or "viewpoint. Transversal : Transversal lines are lines that are parallel to the picture plane and to one another.

They are always at right angles to the orthogonal lines. Two-point Perspective : A drawing has two-point perspective when it contains two vanishing points on the horizon line. In an illustration, these vanishing points can be placed arbitrarily along the horizon. Two-point perspective can be used to draw the same objects as one-point perspective, rotated: looking at the corner of a house, or at two forked roads shrinking into the distance, for example.

One point represents one set of parallel lines, the other point represents the other. Seen from the corner, one wall of a house would recede towards one vanishing point while the other wall recedes towards the opposite vanishing point. Two-point perspective exists when the painting plate is parallel to a Cartesian scene in one axis usually the z-axis but not to the other two axes. If the scene being viewed consists solely of a cylinder sitting on a horizontal plane, no difference exists in the image of the cylinder between a one-point and two-point perspective.

Two-point perspective has one set of lines parallel to the picture plane and two sets oblique to it. Parallel lines oblique to the picture plane converge to a vanishing point, which means that this set-up will require two vanishing points.

Vanishing Point VP : Imaginary points on the horizon line in one- and two-point perspective. A point at which orthogonal lines receding into space appear to converge. The vanishing point acts on the visual field as a point of attraction, somewhat like an open drain of a water basin which draws all the water to it. He even anticipated the geometrical drawing technique, from descriptive geometry proper, by introducing the simultaneous use of plan and elevation to originate a detailed solution to architectural ornamentation of the classical orders.

Until Dutch traders began commercing in Western artworks in the seventeenth century, Oriental painters had not discovered, and therefore made no use of, linear perspective, because, as Erwin Panofsky 1 would point out, perspective is not only a direct transcription of the visual reality but a form of representation that originates within broader cultural needs.

Methods used by Chinese landscape painters to express the sensation of distance and three-dimensionality were uniquely suited to their artistic priorities, which were profoundly divergent from those of Western artists. The principal motifs of Chinese painters offered little impetus for devising a system of mathematically-based perspective. Rocks, mountains, mythical and human figures have no consistent straight lines to represent, and spatial depth could be effectively achieved by other means.

Moreover, a perspectival system that hinges on a single view point is both technically and expressively antithetical to the extended scroll form, which was one of the dominant artistic mediums. Chinese paintings might be as much as 10 meters long by one meter high, designed to be viewed one section at a time in the manner of reading a book.

Given that Chinese landscape painters strove above all to create an impression of infinite space fig. In Oriental art spatial depth was attained via overlap and what might be called "planar" perspective, consisting essentially of distributing subject matter on three spatial planes fig.

The foreground plane was associated with "earthly bound" objects like people, animals, buildings and forests. The middle plane often suggested emptiness i. The background plane generally represents "heavenly" elements such as hills, mountains and sky. The distance between each plane was accentuated by gradating hue, detail and tone aerial perspective creating extraordinary effects of atmosphere rarely achieved in Western painting.

Architecture and geometric objects fig. The complete book about 17th-century painting techniques and materials with particular focus on the painting of Johannes Vermeer.

Looking Over Vermeer's Shoulder is a comprehensive study of the materials and painting techniques that made Vermeer one of the greatest masters of European art. Bolstered by the author's qualifications as a professional painter and a Vermeer connoisseur, every facet of 17th-century and Vermeer's painting practices—including canvas preparation, underdrawing, underpainting, glazing, palette, brushes, pigments and composition—is laid out in clear, comprehensible language.

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While not written as a "how-to" manual, realist painters will find a true treasure trove of technical information that can be apapted to almost any style of figurative painting.

The more elementary procedures for representing pictorial space, the two-dimensional 'Egyptian' method as well as isometric perspective [i. Central perspective, however, is so violent and intricate a deformation of the normal shape of things that it came about only as the final result of prolonged exploration and in response to very particular cultural needs.

Despite the fact that each of the black and white floor tiles in Vermeer's The Art of Painting was perfectly square and identical in dimension, on the surface of the painting each tile has a measurably different shape and different dimension with respect to all the others—no two are equal. And yet, the illusion of geometric regularity and spatial recession that these deformations create is nearly impossible to perceptually override.

Linear perspective initially arose from the desire to represent in a convincing manner the exteriors and interiors fig. Objects were thought of not only a single entities, but as occupants of a spatial arena. Before it was employed to portray actual buildings, perspective was used to create architectural fictions on which to stage narratives.

Perspective could be used to create more interesting compositions and scale figures among themselves: the viewer could sense space almost fiscally. One of the prime building blocks of perspectival construction was the geometric pavement fig.

Perspective, therefore, made paintings more architectura. The birth of a true, geometrically based perspective is unique to the Italian Renaissance , and its development spans over the fourteenth and fifteenth centuries. Various trecento artists, such as Duccio di Buoninsegna c. Although the rafters in the ceiling do not converge perfectly at a single vanishing point they are too organized to be the result judgment by eye, as Martin Kemp would point out.

Giotto's perspectival understanding was essentially that "lines and planes situated above eye-level should appear to incline downwards as they move away from the spectator; those below eye-level should incline upwards; those to the left should incline inwards to the right; those to the right should incline inwards to the left; there should be some sense of the horizontal division and the vertical division which mark the boundaries between the zones; and along those divisions the lines should be inclined little if at all.

Even though the Last Supper fig. In The Last Supper the recession of the rafters is designed with a wishbone system and the table is titled at a bizarre angle inconsistent with anything else in the image. Despite these errors, Duccio's approach constitutes a fundamental step forward toward the representation of space of a flat surface. In its mathematical form, linear perspective is generally believed to have been devised about by the architect Filippo Brunelleschi — and codified in writing by the architect and writer Leon Battista Alberti — , in De pictura [ On Painting ].

The construction worked out by Alberti became was based on the belief that no picture can resemble nature unless it is seen from a definite distance and location, and the diminution in size as a function of distance. It was not until the mids that paintings fully designed according to the principles of perspective science began to appear. One of the first accurate employments of precise central convergence was in The H ealing of the Cripple and Raising of Tabitha — fig.

In contrast with contemporary empirical attempts to use convergent lines, the orthogonals of the foreground buildings on both sides of the street converge accurately at a single vanishing point. This work contains more than 20 horizontals that converge to an accurate vanishing point, although 4 other lines deviate from this center by a small amount.

As other early quattrocento works show, the probability of finding this degree of convergence on the basis of intuitive construction alone is so small as to be negligible.

While Italian paintings following the s display a sense of enthusiastic engagement with perspective construction fig. Artists of the fifteenth and sixteenth centuries rarely broke away from simple perspective systems. Despite the rapid diffusion of perspective among painters, the perspective of individual objects or figures was generally omitted from the procedure.

With few exceptions such as Mantegna, Correggio and Tintoretto , painters throughout the early Renaissance handled figure perspective much more freely or clumsily than architectural perspective. In Filippo Lippi's Adoration of the Magii c. Even architectural features could be represented with multiple vanishing points. Sandro Botticelli seems sometimes to have done this for dramatic effect, and even emphasized the perspective disparities with strongly foreshortened walls or platforms.

One of the most consummate examples of the one-point perspective system is Raphael's School of Athens fig. Raphael — , who himself made no contribution to the theory of perspective. Nonetheless, he brought the practice to its full potential as an artistic tool, and seems to have been one few artists of the time to intuit two-point perspective, in which the horizontals of objects set obliquely to the viewer recede to vanishing points in both directions.

Peter's Cathedral under construction at the time, 'instructed Raphael of Urbino in many points of architecture and sketched for him the buildings which he later drew in the perspective in the Pope's chamber, representing Mount Parnassus [i. Here Raphael drew Bramante measuring with a compass. It falls just below the outstretched right hand of the central figure, the aging Plato.

Although comprehending the idea of a uniform space, Northern European painters did not formulate a mathematically based concept of space independently. They began to apply the linear perspective to their pictures only after it was introduced by painters who had traveled to Italy, such as Jan Goessart c. Goessart's St Luke Drawing the Virgin fig.

Previously, Flemish Primitives had used optically based space privileging the physical and sensual representation of man and his environment. The technique of convergence was employed empirically, rather than rationally.

This approach is typified by the Arnolfini Portrait by Jan van Eyck c. Although he made no innovations, he was the first Northern European to treat visual representation in a scientific way. For almost four hundred years after , one-point perspective served as the standard technique for any painter who wished to create a systematic illusion of receding forms on a flat surface, be it canvas, wall or ceiling, although in many cases, perspective remained one of many strands woven into pictures of the time.

It was no accident that Gian Paolo Lomazzo — , best remembered for his writings on art theory, once asserted that he would rather die than disregard perspective. The elaboration of two-point perspective, necessary to render objects set at an oblique angle to the viewer, took another century to evolve. His most important statements are that the "central point" vanishing point and the two "tier points" distance points are located on a line at the level of the eye horizon line fig.

The major theorist of perspective in sixteenth-century France, Jean Cousin , perfected Viator's "tier point" technique Livre de Perspective , and offered an accurate method for foreshortening solid bodies by means of perspective and simple methods to create foreshortening and anamorphic images. It is possible that Raphael was inspired by one of Viator's two-point perspective illustrations to elaborate his Coronation of Charlemagne —; see image right.

But in Raphaels' work there are a total eight different horizontal positions of the vanishing points where there should be two had the whole composition been based on a uniform oblique grid.

It would appear that Raphael adopted Viator's particular construction for each part of the scene without understanding how they should be modified to form a coherent perspective projection. Aside from two paintings of doubtful attribution painted around , the first successful use of full angular perspective was by Dutch artist Gerard Houckgeest c.

There was limited use of the angular construction in floor tiling throughout the period, but this could easily be achieved by connecting the corners of a one-point perspective grid, and did not require an understanding of the rules of two-point construction.



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