# How to build a complex drawing

Image methods and their practical application is studying descriptive geometry. Any object has three dimensions. For the image of its spatial form of the plane you need to know the laws of the transition from two-dimensional to three-dimensional representation, ie, be able to read the drawing.

### You will need:

- pencil; - Line; - Compasses; - Meter; - Triangle.

## Instruction how to build an integrated drawing

Step 1:

The basis of these laws is a projection method. In the space are plane P ', the point S - center projections and an arbitrary point A (Figure 1). If through the point S and A draw a straight line to the intersection with the plane P ', you get the point A'. This projection of the point A in a plane projections of P '. Direct SA called projecting beam. Drawing, built with the help of the design, it is a projection.

Step 2:

If projecting rays are perpendicular to the plane of projection, such projections are called rectangular. When determining the position of a point in space by its projection of one plane of projection is not enough. Therefore introduced an additional second plane. The most suitable location is a projection planes in which one of them is vertical, and the other - horizontal.

Step 3:

The plane of projection is located horizontally is called the horizontal plane of projection, and is denoted P₁. The vertical plane is located in front of the observer, called the frontal plane of projection and is designated P₂. P₂ P₁ plane perpendicular to the plane (Figure 2). Direct mutual intersection of the two planes of projection is called the axis x₁₂ projections.

Step 4:

Assuming that the plane of the drawing coincides with the frontal plane of projection, the horizontal projection plane P₁ is perpendicular to the plane of the drawing.

Step 5:

The planes P₁ and P₂ should simultaneously coincide with the plane of the drawing. For this plane P₁ is rotated around the axis x₁₂ to align with the plane P₂ (figure 3).

Step 6:

The drawing is not designated P₂ and P₁ plane, and is carried out only horizontal line - coordinate axis x₁₂ (Figure 4).

Step 7:

Point A is located in the system of planes P₁ and P₂ (figure 5). To construct the projections of A held AA₂ projecting beams perpendicular P₂ and AA₁ - perpendicular to the plane P₁. A₂ - front view of a point A and A₁ - horizontal projection of the point A in the space.

Step 8:

Rectangular projections of two mutually perpendicular planes projections called orthogonal projections. AA₁ - the distance from point A to P₁ plane; AA₁ = A₂A₁₂. AA₂ - the distance from point A to P₂ plane; AA₂ = A₁A₁₂.

Step 9:

The drawing, which shows the projection of the point, combined with a plane called the complex drawing (course). In the drawing a horizontal and integrated front projection located at one point of the vertical link A₂A₁, x₁₂ perpendicular to the coordinate axis.

Step 10:

Example. Build a complex drawing point A remote from the plane P₁ to 30 mm and from the plane P₂ - 20 mm (Figure 6).

Step 11:

Spend x₁₂ axis. Perpendicular to the axis line build vertical ties. From the projection axis interval of 30 mm, - get a front projection of the point A₂. Similarly A₁₂A₁ set aside a segment of 20 mm - get a horizontal projection of the point A₁ imaging is the desired complex drawing and determines the position of the point A in the space.