The method of projections is a basis of the theory of creation of drawing images in engineering graphics. Most often it is used when it is necessary to find the image of a body in the form of its projection to the planes or to obtain data on its position in space.
Instruction
1. In multidimensional space any image of an object on the plane can be received by means of projection. However you should not judge a geometrical shape of a body or of a form of the simplest images in geometry on the basis of one projection of a point. The most complete information on the image of a solid is given by several projections of points. For what use projections of points of a body at least in two planes.
2. For example, it is necessary to construct a projection of a point And. For this purpose arrange two planes perpendicularly each other. One - it is horizontal, calling it the horizontal plane and designating all projections of elements with index 1. The second - vertically. Call it, respectively, frontal plane, and appropriate to projections of elements index 2. Consider both of these planes infinite and opaque. The axis of coordinates OH becomes the line of their crossings.
3. Then accept as the fact that the space between the projection planes conditionally is divided into quarters. You are in the first quarter and see only those lines and points which are in this area of a dihedral angle.
4. The essence of process of projection consists in carrying out a beam through the set point until the beam meets the plane of projections. This method received the name of a method of orthogonal projection. According to it, lower from a point And a perpendicular on the horizontal and frontal plane. The horizontal projection of a point of A1 or a frontal projection of a point of A2 will also be the basis of this perpendicular just. Thus, you receive the provision of this point in space of the set planes of projections.