It is evident that the view of the scene as well as the apparent position of any vanishing point must change with every new position of the observer. There fore a perspective drawing can only attempt to represent the view as it will appear from one point of view. This is a limita tion inherent in every perspective drawing.
Instead of sighting along an actual element, the observer can look in a direction parallel to an element. The direction in which he looks may be considered as an imaginary element which will lead his eye to the desired vanishing point. In fig. 6, the observer is looking in a direction parallel to the two edges ab and cd of the roof plane. These two edges appear to him to converge towards a point infinitely distant from him in the direction of his gaze.
Rule A.—From the method of locating a vanishing point it follows that if a system is horizontal its vanishing point must appear to be on a level with the eye. If a system vanishes upward its vanishing point will be located above the eye ; if downward, below the eye ; if toward the right, to the right of the eye ; or if toward the left, to the left of the eye.
Theoretically every system of lines has two vanishing points, for, if the observer can locate one by looking along an element in one direction, he can also locate a second by looking along the same element in the opposite direction. For any given position of the observer one of these vanishing points will usually lie before and the other behind him. The one lying in the direction of his gaze is the only one considered, except in certain special problems. Systems of Planes.—Plane surfaces which are parallel appear to approach one another as they recede. This will be evident from fig. 7. Since the horizontal edges of the cube appear to converge, the top and bot tom planes must appear nearer together at cd and gh than at ab and ef, and must seem to approach one another as they extend into space. Parallel planes extended an in finite distance appear to meet in a straight line known as the vanishing trace of the planes. Each system of planes will have its own vanishing trace which can be lo cated by looking along any one of the planes. The plane will appear edgewise, as a line, and cover the vanishing trace which every plane of the system will appear to approach.
The method of locating a vanishing trace is illustrated in Plate I., figs. 5 and 7. The plane along which the observer looks is known as the visual plane of the system. It appears as a straight line and the other planes of the system seem to approach it. The vanishing trace of the system of horizontal planes will evidently be a horizontal line on a level with the observer's eye. To this vanishing trace is given the special name of horizon. The visual plane of a horizontal system is called the horizon plane.
If the observer while locating a vanishing trace should slowly turn completely around still looking along the visual plane, at every instant he would see the vanishing trace as a straight line directly in front of him. The vanishing trace therefore may be considered as a circle of infinite radius which is theoretically the same thing as a straight line. In practical work so small a field is usually visible that a vanishing trace is always treated as a straight line.
Axiom i. Parallel lines appear to converge as they vanish, and to meet at an infinite distance from the observer in an imaginary point called the vanishing point of the system.
Axiom 2. Parallel planes appear to approach one another as they recede from the eye, and to meet at an infinite distance from the observer in an imaginary straight line known as a vanishing trace.
Axiom 3. A line lying in a plane must have its vanishing point in the vanishing trace of the plane. This is evident from the man ner of locating the vanishing point of a line and the vanishing trace of a plane.
Axiom 4. The vanishing trace of a plane must contain the van ishing points of all lines which lie in the plane. This is the con verse of number 3.
Axiom 5. A line which forms the intersection of two planes, since it lies in both, must have its vanishing point at the inter section of the vanishing traces of the two planes.
Rule B. To locate the vanishing point of a system of lines, look along any real or imaginary line of the system.