A graphical representation method commonly used in engineering drawings and architectural design that shows the shape and size of three-dimensional objects by projecting them onto a two-dimensional plane. The main purpose of a projection drawing is to accurately express the geometry of a three-dimensional object on a plane for manufacturing, construction, or analysis.

Parallel projection method: If the projection center of the central projection method is moved to infinity, all projection lines can be regarded as parallel to each other. This projection method is called parallel projection method. Parallel projection method can be divided into oblique projection method and orthographic projection method.

Center projection method: The projection method in which all projection lines start from the same projection center is called the center projection method. The object projection graphics obtained by this method do not match the actual size of the object and cannot truly reflect the size of the object. The central projection method is mainly used to draw perspective drawings of buildings. It has a strong three-dimensional effect, but has poor metric and complicated drawing, so it is not often used in general engineering drawings.

Two straight lines that are parallel in space must be parallel if the projection image on the same projection surface is parallel.

If a straight line and a plane are parallel to the projection surface, the projection on the projection surface reflects the real length of the straight line or the real shape of the plane.

If a point is on a straight line or plane, the projection of the point must be on the same projection surface of the straight line or plane.

If a straight line or plane is perpendicular to the projection surface, then the projection of the straight line on the projection surface gathers into a point, and the projection of the plane gathers into a straight line

The ratio of point-to-line segments remains unchanged on the projection surface, and the length of two parallel line segments in space remains unchanged after projection.

If the plane is inclined to the projection surface, the area of ​​the projection on the projection surface becomes smaller, but the projection shape is similar.

Elevation projection plane (V plane): reflects the shape of the object's elevation, the height and length of the object, and its up-down, left-right positional relationship.

Horizontal projection plane (H plane): reflects the horizontal shape of the object, the length and width of the object, and its front-to-back, left-to-right positional relationship.

Side projection plane (W plane): reflects the side elevation shape of the object, the height and width of the object, and its up-down, front-to-back positional relationship

The length of the elevation is equal to the length of the plan.

The height of the front elevation is equal to the height of the side elevation.

The width of the plan is equal to the width of the elevation

The three-dimensional projection of a point refers to the figure obtained by projecting a point in space onto these projection surfaces through projection lines on three mutually perpendicular projection surfaces. The three projection planes are the horizontal projection plane (H plane), the vertical projection plane (V plane) and the side projection plane (W plane).

1. Verticality:

2. Isometric:

Upward straight line: vice versa

Descending straight line: A point on a straight line that is closer to the observer is higher than another point

characteristic

1. Principle: The real length of a straight line at a general position can be obtained by using the right triangle method. Assume straight line AB, its projection on the horizontal projection plane H is ab, and its projection on the upright projection plane V is a'b'.

In the three-plane projection system, the inclination angle of the straight line to the H plane is the α angle, and the size of the α angle is equal to the angle between the straight line and its horizontal projection; the inclination angle of the straight line to the V plane is the β angle, and the size of the β angle is equal to the straight line and its front projection. The angle between them; the inclination angle of the straight line to the W surface is the γ angle, and the size of the γ angle is equal to the angle between the straight line and its side projection.

1. Horizontal line: a straight line parallel to the H surface and inclined to the V and W surfaces. 2. Straight line: a straight line parallel to the V surface and inclined to the H and W surfaces. 3. Side horizontal line: a straight line parallel to the W surface and inclined to the H and V surfaces. The projection characteristics of a parallel line on a projection plane are: the projection on the projection plane parallel to it reflects the real length of the line segment, while the projections on the other two projection planes are parallel to the corresponding projection axes and shorter than the real length of the line segment.

1. Plumb line: a straight line perpendicular to the H plane (horizontal projection plane). 2. Ordinary vertical line: a straight line perpendicular to the V plane (erect projection plane). 3. Side vertical line: a straight line perpendicular to the W plane (side projection plane). The projection characteristics of vertical lines on the projection surface are: the projections on the vertical projection surface are gathered into a point, while the projections on the other two projection surfaces are parallel to the corresponding projection axes and reflect the real length of the line segment.

1. Let ∠AOB be a right angle, its side OB is parallel to the plane P, and its projection on this plane is ∠aob. Since the straight line ob parallel to OB is perpendicular to the two intersecting lines OA and Oo, it is perpendicular to the plane OAao and therefore perpendicular to oa.

2. Converse theorem:

Projection plane parallel plane

A plane parallel to the projection plane refers to a plane that is parallel to one projection plane and perpendicular to the other two projection planes. According to different parallel projection planes, it can be divided into horizontal plane, front plane and side plane.

1. Horizontal plane: parallel to the H plane (horizontal projection plane), perpendicular to the V plane (vertical projection plane) and W plane (side elevation projection plane). Its projection characteristics are that the projection on the H surface reflects the real shape, and the projections on the V and W surfaces are accumulated into straight lines and are parallel to the corresponding projection axis.

2. Front plane: parallel to the V surface, perpendicular to the H and W surfaces. Its projection characteristics are that the projection on the V surface reflects the real shape, and the projections on the H and W surfaces are accumulated into straight lines and are parallel to the corresponding projection axis.

3. Side plane: parallel to W surface, perpendicular to V surface and H surface. Its projection characteristics are that the projection on the W surface reflects the real shape, and the projections on the V and H surfaces are accumulated into straight lines and are parallel to the corresponding projection axis.

The vertical plane of the projection plane refers to a plane that is perpendicular to one projection plane and inclined to the other two projection planes. According to different vertical projection planes, it can be divided into plumb plane, front vertical plane and side vertical plane.

1. Vertical plane: perpendicular to the H plane and inclined to the V and W planes. Its projection characteristics are that the projections on the H surface are gathered into a straight line, and the projections on the V and W surfaces are similar shapes with reduced areas.

2. Normal vertical plane: perpendicular to the V plane and inclined to the H and W planes. Its projection characteristics are that the projections on the V surface accumulate into a straight line, and the projections on the H and W surfaces are similar shapes with reduced areas.

3. Side vertical plane: perpendicular to W plane, inclined to V plane and H plane. Its projection characteristics are that the projections on the W surface accumulate into a straight line, and the projections on the V and H surfaces are similar shapes with reduced areas.