Whatever its degree of sophistication in antiquity, the knowledge of perspective was lost until the fifteenth century. From the Duecento to the Cinquecento, after which art academies formally introduced the teaching of perspective, painters explored various techniques to evoke spatial depth on a flat surface. Progress was relatively uneven because painters did not always work in close contact with each other. Moreover, medieval painting was essentially a representation of religious, rather than human, experience. The importance of the figures was fixed by canonical tradition so that the most significant figure in the painting was the largest and that all other figures were portrayed in diminishing in size regardless of their position within the pictorial space, similar in concept to Egyptian art. Important figures are often shown as the highest in a composition (fig. 2), also from hieratic motives, leading to the so-called "vertical perspective." Thus, for the medieval artist there was little impetus to devise a rational system by which the things of the world might be represented in scale on a two-dimensional surface, in obedience to the unvarying laws of geometry and optics. Painters experimented with what art historians refer to as "empirical perspective," ad hoc solutions devoid of consistent rules. Gothic painting slowly progressed in the naturalistic depiction of distance and volume, although these elements were never essential features of representation.
Infinite Space Artbook Pdf 11
Distance Points & Distance Lines:8 The two vanishing points on the horizon at which diagonal 45 degrees 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.
Horizon, Apparent Horizon, Visible Horizon, Skyline: The line at which the sky and Earth appear to meet. For observers near sea level the difference between the geometrical horizon (which assumes a perfectly flat, infinite ground plane) and the true horizon (which assumes a spherical Earth surface) is imperceptible to the naked eye (for someone on a 1000-meter hill looking out to sea the true horizon will be about a degree below a horizontal line).
Plane: In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. In colloquial language, any flat surface, such as a wall, floor, ceiling, or level field.
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. 3) opening up in front of the viewer, a single, fixed viewpoint would create an insurmountable obstacle, interfering with the spectator's freedom to wander about and engage himself with the vastness of nature.
Linear perspective initially arose from the desire to represent in a convincing manner the exteriors and interiors (fig. 7 & 8) of buildings, which are, perhaps, the most vital and inspiring of human products. 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. 9). "A paved floor, road or piazza, were all ideal grounds on which to lay out a grid of intersecting lines, to establish the base for the correct diminution of forms receding into the pictorial distance. Perspective, therefore, made paintings more architectura.l"3
Even though the Last Supper (fig. 11) and the Death of the Virgin by Duccio exhibit concerted attempts to create a realistic space, in which tangible objects occupy a space that continues beyond the picture, the orthogonals converge at different points. 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. 2ff7e9595c
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