Perspective of a Point, Visual Rays, &c.
We perceive objects by means of the visual rays, which are imaginary straight lines drawn from the eye to the various points of the thing we are looking at. As those rays proceed from the pupil of the eye, which is a circular opening, they form themselves into a cone called the Optic Cone, the base of which increases in proportion to its distance from the eye, so that the larger the view which we wish to take in, the farther must we be removed from it. The diameter of the base of this cone, with the visual rays drawn from each of its extremities to the eye, form the angle of vision, which is wider or narrower according to the distance of this diameter.
| Fig. 17. |
Now let us suppose a visual ray EA to be directed to some small object on the floor, say the head of a nail, A (Fig. 17). If we interpose between this nail and our eye a sheet of glass, K, placed vertically on the floor, we continue to see the nail through the glass, and it is easily understood that its perspective appearance thereon is the point a, where the visual ray passes through it. If now we trace on the floor a line AB from the nail to the spot B, just under the eye, and from the point o, where this line passes through or under the glass, we raise a perpendicular oS, that perpendicular passes through the precise point that the visual ray
passes through. The line AB traced on the floor is the horizontal trace of the visual ray, and it will be seen that the point a is situated on the vertical raised from this horizontal trace.
[ V]
Trace and Projection
If from any line A or B or C (Fig. 18), &c., we drop perpendiculars from different points of those lines on to a horizontal plane, the intersections of those verticals with the plane will be on a line called the horizontal trace or projection of the original line. We may liken these projections to sun-shadows when the sun is in the meridian, for it will be remarked that the trace does not represent the length of the original line, but only so much of it as would be embraced by the verticals dropped from each end of it, and although line A is the same length as line B its horizontal
trace is longer than that of the other; that the projection of a curve (C) in this upright position is a straight line, that of a horizontal line (D) is equal to it, and the projection of a perpendicular or vertical (E) is a point only. The projections of lines or points can likewise be shown on a vertical plane, but in that case we draw lines parallel to the horizontal plane, and by this means we can get the position of a point in space; and by the assistance of perspective, as will be shown farther on, we can carry out the most difficult propositions of descriptive geometry and of the geometry of planes and solids.