CURVILINEAR PERSPECTIVE DRAWING LESSONS : A Guide to drawing in curvilinear, cylindrical, panoramic perspective

How to Draw in Curvilinear Perspective

It is sometimes urged that in nature even straight lines look curved, tending as they do to meet their parallels in a vanishing point at each end. This is true provided they are long enough. We see it in the rays of light that stretch across the whole sky at sunrise or sunset. It is equally true of the lines of a perspective drawing. lf they are extended far enough, they too will look curved. But the vanishing points of a straight line are at opposite ends of the world, and cannot be put in the same plane-picture, nor can enough of any line to display the apparent curvature ordinarily be included in a drawing. If it were, the drawn line would also look curved. Yet the fact that as we turn the eye successively toward the opposite ends 'of a series of parallel lines, the cornices that border a long street for instance, we see them converge both ways, has led some men to insist that they should be drawn so in one and the same picture, and to devise ways of doing this. It is done as in panoramas, by projecting the view as on a vertical cylinder with the Station Point in its axis, which cylinder is unrolled into a flat picture.

In the plan, Fig. 81, the two equal circles A and A' representing towers or shafts of columns, are projected from the same Station Point S on the picture plane and on the cylindrical surface, the first in ab, which is practically the same on both surfaces, the second in a"b" on the plane and a'b' on the cylinder. The Centre C is here taken as the common tangent point of plane and cylinder, and it is clear that while the projection a"b" is larger than ab, or even than the width of the object A', being made obliquely on PP, a'b' is considerably less than the diameter of A' or even than ab, as would be the natural appearance, A' being farther than A from the eye at S. C may for comparison be taken for a Center on the cylindrical surface ab'1, but properly the Center may be anywhere on its horizon line, or nowhere, for any radius, being normal to the cylinder, may be called the Axis, and no point in its horizon line has different properties from any other. There being no Center, there are no Diagonals, and no distance points, and though there are vanishing points, for these are phenomena of vision, and not of the picture, the whole apparatus of measuring is done away with, and the picture must be constructed by conical projection in the manner described above as the natural system, the horizontal projections being taken from a plan, as in Fig. 81, and the heights from a side projection or elevation.

Straight lines projected on the cylinder look straight from the Station Point, of course, but are really hoops centred on that point, as the horizon is in space; and all but the Horizon Line are ellipses, being sections of the cylinder by oblique visual planes, while the vanishing points are the points where these ellipses intersect the Horizon Line on opposite sides of the cylinder. When the cylinder is developed,-unrolled, that is,these sections become elongated curves, like all oblique plane sections of a cylinder, except the Horizon Line, which, being a right section, becomes a straight line. The extreme possible length of such a picture unrolled, taking in the whole horizon and returning into itself, is only the circumference of the cylinder, and the distance between vanishing points of any straight line is half the circumference, corresponding to the
theoretical but impossible projection of half the horizon on a plane surface, so that the picture is narrowed within convenient limits, instead of being extended enormously when it assumes to take in a wide area. Fig. 82 shows the projections of Fig. 81 on the picture surfaces, at B the regular plane perspective construction, at D the cylinder developed. It will be seen how the projections widen in the first as they withdraw from the Center, and how any limit narrows the width of the cylindrical picture when it is unrolled. This is a considerable advantage, the only resource, in truth, when one takes in a very
wide area; but the fact that all but vertical lines come out conspicuously curved makes it impossible to represent the straightness of a long building or street, bringing distortions that no change of position by the spectator will cure, and that often are as offensive as those that are amended. This fact, with the labor and difficulty of making large drawings in which all the lines but the verticals are curves to be constructed point by point, like circles in ordinary perspective, makes curvilinear perspective too laborious, and after all too unsatisfying, to find much use in ordinary pictures.

Plate XIX shows part of a panoramic view of Paris, photographed on a cylinder with a revolving camera, and then unrolled, so that it is in true cylindrical perspective. It will be seen that the only straight horizontal line in it is the Horizon Line. The lines of the principal building, the Hotel de Ville, which are really as straight as they can be built, are conspicuously curved in the picture, and those of the adjoining buildings, which are parallel to them, are warped into a crescent. The main proportions of the building are preserved as they would not have been in a plane photograph, but at the cost of very unflattering distortion. If, however, the picture were rolled up into a cylinder of the right diameter, and viewed from the axis of the cylinder at the height of the Horizon Line, the curves would straighten to the eye, and the distortion disappear.