It is evident that the perspective of a straight line will always be a straight line, the extreme points of which are the perspec tives of the extremities of the given line.
24. Thus, the five axioms of perspective may be applied to Perspective Projection as follows :— (a) Parallel lines do converge and meet at the vanishing point of their system.
(b) Parallel planes do converge and meet at the vanishing trace of their system.
(c) The vanishing point of any line lying in a plane will be found in the vanishing trace of the plane.
Therefore, the vanishing points of all horizontal lines will be found in the horizon (§ 20).
(d) The vanishing trace of any plane will be determined by the vanishing points of any two lines that lie in it, and must con tain the vanishing points of all lines that lie in it.
(e) The vanishing point of the intersection of two planes will be found at the intersections of the vanishing traces of the two planes.
To the five axioms of perspective projection already stated may be added the following three truths concerning the construc tion of the perspective projection :— (f) The perspective of any point in space is where the visual ray through the point pierces that picture plane (§ 7).
(g) The perspective of the vanishing point of any system of lines is where the visual element of that system pierces the pic ture plane.
Rule for finding the perspective of the vanishing point of any system of lines :—Draw an element of the system through the ob server's eye, and find where it pierces the picture plane.
(h) Any point, line, or surface which lies in the picture plane will be its own perspective, and show in its trim size and shape.
25. Knowing how to find the perspective of any point, and how to find the vanishing point of any system of lines, any prob lem in perspective may be solved. Therefore, it may be said that the whole process of making a perspective projection reduces itself to the problem of finding where a line pierces a plane.
Before proceeding farther, the student should review the first twenty-five paragraphs by answering carefully the following questions : (1) What does a perspective projection represent? (2) What is a visual ray? (3) How is a perspective projection formed? (4) How does a perspective projection differ from an ortho graphic projection ? (5) What is the plane called on which the perspective pro jection is made? (6) What is meant by the term Station Point? (7) What is the most important phenomenon of perspective (8) What is meant by a system of lines? (9) What is meant by a system of planes? (10) What is a visual element ? (11) Define vanishing point.
(12) Define vanishing trace.
(13) Describe the position of the vanishing point of any sy8 tern of lines.
(14) Give the five axioms of perspective.
(15) Do parallel lines in space really converge? (16) Do the perspective projections of parallel lines really converge? (17) Where will the perspective projections of parallel lines meet? (18) How is the perspective of any point found? (19) How is the perspective of the vanishing point of any system of lines found? (20) What will be the perspective of a straight line? (21) What is meant by the horizon? (22) What is meant by the plane of the horizon ?