TIIEORY OF PERSPECTIVE.
THE theory of perspective may be divided into four parts or sections. In the first section is explained the method of drawing on a plane surface the exact representation or picture of any object, the positions of the eye and the pic ture, and also the position and magnitude of the object being given. In the second section is explained the method of determining the original objects, the repre sentation or pictures being given. The third section treats of the appearance of pictures when seen from a point which is not the proper point of sight. The fourth section treats of the delineation of shadows.
1. The plane on which the representation, projection, or picture of any object, is drawn, is called the perspective plane, and also the plane of the picture. It is supposed to be placed between the eye and the object.
2. The point of sight is that point from which the pic ture ought to be viewed. This point is also called the point of view, 3. If from the point of sight, a line be drawn at right angles to the picture or perspective plane, the point in which it meets that plane is called the centre of the pic ture; and the distance between that centre and the point of sight, or the perpendicular above mentioned, is called the distance of the picture.
4. By original object, is meant the real object placed in the situation it is represented to have by the picture.
5. By original plane, is meant the plane on which any original point, line, or plane figure, is situated.
6. The point in which any original line, or any original line produced, cuts the perspective plane, is called the in tersection of that line.
7. The line in which any original plane cuts the per spective plane, is called the intersection of that original plane. If the original plane be that of the horizon, its intersection with the picture, or the line above mentioned, is called the ground line.
8. The point in which a straight line drawn through the point of sight parallel to any original line cuts the picture, is called the vanishing point of that original line.
And the distance between that point and the point of sight, is called simply the distance of that vanishing point.
9. The line in which a plane drawn through the point of sight parallel to any original plane cuts the perspective plane, is called the vanishing line of that original plane. If from the point of sight there be drawn a line cutting that vanishing line at right angles, the point of intersec tion is called the centre of the vanishing line. And the distance between the point of sight and that point or cen tre is called simply the distance of the vanishing line.
10. If from a given point a straight line be drawn at right angles to any plane, the point of intersection is call ed the seat or orthographic projection of the given point on that plane. And if from all the points of any line or plane figure perpendiculars be drawn to any plane, the Iine or figure formed by their intersections with it, is call ed the seat or orthographic projection of the given line or figure on that plane.
That the definitions may be fully understood, let 0 (Plate CCCCLI X, Fig. 1.) represent the point of sight, ADKB the perspective plane, and A\V any original plane. If from 0, OC be drawn at right angles to the plane ADKB, C will be the centre of the picture, and OC will be its distance. If through 0 the plane QI be sup posed to be drawn parallel to the original plane A\V, HI, its intersection with the perspective plane will the va nishing line of A\V ; and if OG be drawn at right an gles to HI, G will he the centre and OG the distance of HI. If OV be supposed parallel to EF, V will be the vanishing point of EF, and OV will be its distance. AD, the line in which the plane A\V intersects the per spective plane, is the intersection of AW.
Postulate.
In treatises of perspective it is assumed that the rays of *light proceed in straight lines from the objects to the eye. This is only strictly true on the supposition that the air is of uniform density ; but for the purposes of painting its truth may be safely assumed in all cases.