where none exist in the object, and it excludes some parts of the surface while
displaying others. An art student, drawing from the model, grapples with the
problem of how to convey the continuity of roundness. He is tempted to take
the arbitrary contour literally and to produce the image of a shield rather than
108 P O R M
a volume. William Hogarth, in his
Analysis of Beauty,
describes the dilemma eloquently: "But in the common way of taking the view of any opaque object, that part of its surface which fronts the eye is apt to occupy the mind alone, and the opposite, nay even every other part of it whatever is left unthought of at that time; and the least motion we make to reconnoiter any other side of the object confounds our first idea, for want of the connexion of the two ideas, which the complete knowledge of the whole would naturally have given us, if we had considered it in the other way before."How arbitrarily any view selects the portions visible in the projective image becomes most evident when we learn how much trouble the "hidden surface problem" gives the practitioners of computer graphics. The image of
a wire frame model of a solid can be rotated and distorted by the computer with relative case. If the solid's transparent body is given in a certain position, the computer can show it from the back or from the top, thus saving today's architects much labor. But when it comes to simulating the actual look of the opaque solid from a given viewpoint, it is no longer sufficient to manipulate the properties of the solid itself. Arbitrary effects are always hard to calculate. The computer must determine the interaction between the spatial system of the object and the projective system imposed upon it-an expensive, timc consuming operation.
Once we put up with reducing a volume to one of its aspects, we must decide which view to select for any particular purpose. For some objects all aspects are equal or equally good-for example, a sphere or an irregularly shaped piece of rock. Usually, however, there are definite distinctions. In a cube the orthogonal projection of any surface dominates. In fact, oblique as pects of the surface are seen as mere deviations from the square-shaped one. This distinction is based on the law of simplicity. The dominant projections are those which produce patterns of the simplest shape.
Arc these simplest and perceptually preferred aspects best suited to convey the visual concept of the three-dimensional object? Some of them are. Our visual concepts of many objects are characterized by structural symmetries, which arc brought out most directly by certain aspects of the object. Thus a straight front view of a human figure displays this striking feature. But an undistorted sidcfacc of a cube can be shown only at the price of hiding all the others. Or consider Figure
82.
It is surely the simplest possible representation of a Mexican wearing a large sombrero. Yet such a view would be used only as a joke, which results precisely from the contradiction between the repre sentation's indisputable correctness and its patent inadequacy. The picture isF O R M
certainly faithful-a similar view can be obtained photographically from a third-floor hotel window-but it is inadequate for most purposes because it does not distinguish a Mexican from a millstone or a doughnut. The structural skeleton of Figure
82
is too slightly related to the structure of the visual concept to be conveyed; instead it creates other, misleading associations.The example reminds us that for some special purpose, the draftsman may deliberately choose a view that misleads and hides rather than informs. Early stages of pictorial representation avoid any such concealment. They aim for the dearest and most direct sight, and so do all illustrations aimed at straight instruction. At levels of higher sophistication, back views, tilted heads, and the like are admitted for the enrichment they bring to the spatial conception.
The elementary task of depicting on a surface the main properties of an object's shape is a difficult one. Should the portrait of a given person show the front-face view or the profile?
G.
K. Chesterton speaks of "one of those women whom one always thinks of in profile, as of the clean-cut edge of some weapon." Police records require both views, as do anthropometric studies, because important characteristics often show up in one view and not in the other. Alberto Giacometti once said jokingly to a man whose portrait he was painting: "Full face you go to jail, and in profile you go to the asylum." A further complication is introduced when some parts of an object show best from one angle whereas others do so from another. The typical shape of a bull is con:veyed by a side view, which, however, hides the characteristic lyre pattern of the horns. The wingspread of a flying duck does not show in profile. The angle that must be chosen to identify the goblet and stem of a wineglass destroys the circularity of the mouth and foot. The problems multiply with combinations of objects: how can a pond, whose undistorted outline is revealed110 F O R M