To get an idea of the subject, use its image on paper or screen. Usually the image of an object from one of the sides does not give a full picture of its shape; it is required to obtain its projection on two or three planes. In order to streamline the projection process, the planes onto which the projection takes place are arranged perpendicular to each other. Consider what kind of planes exist. There are three of them, and they form a trihedral right angle in space.
Each of the projection planes has its own name and letter designation. The frontal plane is the projection plane vertically located in front of our gaze. For clarity, this is the plane to which we are facing, that is, the plane of the picture we are considering. The frontal plane is denoted by the Latin letter V.
The horizontal plane is perpendicular to the frontal. Figuratively speaking, the horizontal plane is that plane that lies “under our feet”. It is customary to denote the letter H.
The third of the main planes of projections is called profile. Like the frontal plane, it is located vertically and forms a right angle with the two previous ones. Designate the profile plane with the Latin letter W.
At the pairwise intersection of these three planes, the projection axes x, y, z are formed. These are mutually perpendicular rays with a common vertex at the intersection of all three projection planes, denoted by the letter O.
To obtain a detailed image of an object, it is required to combine its images obtained on three mutually perpendicular faces. To do this, two faces of the corner are deployed and combined with the third. The frontal plane remains in place, the horizontal plane rotates downward 90 ° along the x axis, the profile plane rotates 90 ° to the right along the z axis. Thus, the last two planes are combined with the front (the horizontal is located under it, the profile on the right).
In descriptive geometry, any arbitrarily located plane in a drawing can be defined in different ways: projections of three points not lying on one straight line, projection of a line and a point located outside it, as well as projections of parallel or intersecting straight lines or planar figures.
With respect to the main projection planes, the considered plane can occupy the following positions:
1. It can be non-perpendicular to any of them. Then this is the so-called. general position plane.
2. It can be perpendicular to one of the three projection planes. In this case, it is called a horizontal projection, profile projection or frontal projection, respectively, of the plane to which it is perpendicular.
3. The plane may be perpendicular to two of them and parallel to the third. Then it is called frontal, horizontal or profile, respectively.
A straight line can occupy the following positions with respect to the plane:
1. Belong to her.
2. To be parallel to it.
3. Cross the plane (a special case - in the form of a perpendicular)
The plane has the main lines, which are called horizontals and frontals. These are straight lines lying in the plane and parallel to the corresponding projection planes.
Any plane can be represented as a so-called. traces of the plane, that is, the lines along which it intersects with the projection planes. Traces of the plane are also called horizontal, frontal and profile. At the points of intersection of the projection axes with the plane on the axes, points of mutual intersection of the traces of the given plane arise, which are commonly called vanishing points of traces of the plane.
The horizontal and frontal traces of the plane on the projection planes coincide with their projections of the same name. It should also be mentioned that any horizontals of the same plane are mutually parallel and parallel to its horizontal footprint, and any of its frontals are also mutually parallel and parallel to its frontal footprint.