Methods for specifying a plane in a drawing
The position of the plane in space is determined by three points that do not lie on one line, a straight line and a point taken outside the line, two intersecting lines and two parallel lines. Accordingly, the plane in the drawing (Figure 3.1) can be given by the projections of three points not lying on one straight line (a), a straight line and a point taken outside the line (b), of two intersecting straight lines ( c), of two parallel lines (r). Projections of any planar figure can also serve as a reference to the plane in the drawing; for example, see Fig. 3.10 image of the plane by the projections of a triangle.
Position of the plane relative to the planes of the projections
The plane relative to the planes of projections can occupy the following positions: 1) not perpendicular to the planes of projections; 2) perpendicular to one plane of projections; 3) perpendicular to the two projection planes.
A plane that is not perpendicular to any of the projection planes is called the general position plane (see Figure 3.1).
The second and third positions of the planes are particular cases. The planes in these positions are called projecting planes.
A plane perpendicular to one plane of the projections. A visual representation of the plane a given by the triangle ABC and perpendicular to the plane Π! is shown in Fig. 3.2, its drawing is in Fig. 3.3. This plane is called horizontally projecting .
A visual representation of the plane β given by the parallelogram ABCD , perpendicular to the frontal plane of the projections, is shown in Fig. 3.4, its drawing is in Fig. 3.5. Such a plane is called front-projecting .
A drawing of a plane in the form of a triangle with projections A "C 'A' B'C ', A' B tn C ', perpendicular profile plane of projections is shown in Fig. 3.6. Such a plane is called profile-projecting.
Traces of planes. The intersection line of a plane with a plane of projections is called track . The line of intersection of some plane -
a, defined by the triangle ABC, with the plane π, is denoted by a ', and with the plane π2 - a (see Figure 3.2).
The line of intersection of the plane with the plane π is called the horizontal trace, with the plane π2 - the front track, with the plane π, - the profile trace.
For a plane perpendicular to the π plane, the horizontal trace a '(see Figure 220.127.116.11) lies at an angle to the x-axis corresponding to the angle of inclination of this plane to the frontal plane of the projections, and the frontal track a' - perpendicular to the x-axis.
Similarly, for a plane β perpendicular to the π2 plane (see Figure 18.104.22.168), the front track β is located at an angle to the axis x, corresponding to the slope of this plane to the plane Π), and the horizontal trace β 'is perpendicular to the axis x.
In the drawings, the trace that is perpendicular to the axis of projection, usually when it does not participate in the constructions, is not represented.
The property of the projections of geometric elements lying in projecting planes (see § 1.1, Π. 1, c). The projecting plane is represented by a straight line
line in the plane of projection to which it is perpendicular. Consequently, any closed geometric figure lying in the projecting plane is projected onto this plane of projections into a straight line segment.
The planes perpendicular to the two planes of projections. If the plane is perpendicular to the two planes of projections, then it is parallel to the third plane of projections. This plane is called horizontal (parallel to plane π,), front (parallel to plane π2) and profile (parallel to plane π3).
Examples of their visual images and drawings are shown in Fig. 3.7, a, b (the front plane y and the point ( A), belonging to it in Fig. 3.8, a, b (the horizontal plane β and the point ( B) belonging to it, in Fig. 3.9, a, b (the profile plane a and the point Q belonging to it.
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