projection method
Projection method comes from the physical phenomenon that light irradiates a spatial shape to get a shadow on the plane. Taking the S point of the light source as the projection center, S point and descriptive geometry
The connecting line SA of a point on the object is the projection line (i.e. light), and the P plane showing the shadow is the projection plane. The intersection of the projection line SA and the p plane ι is the projection of point A on the projection plane. According to this method, the projection of the rest points and lines on the body can be obtained (figure 1a). This projection method is called central projection, because all the projection lines pass through the S point of the projection center. If the S point moves to infinity, that is, when all projection lines are parallel to each other, it is called parallel projection method. Parallel projection method is divided into oblique projection method (Figure 1b) and orthogonal projection method (Figure 1c) according to whether the projection line is perpendicular to the projection plane. The perspective view can be obtained by central projection and the axonometric view can be obtained by parallel projection, both of which have good stereoscopic effect. In order to display the three-dimensional image of human body, perspective view is often used in building engineering and axonometric view is often used in mechanical engineering. Projection method is to project space objects (usually terrain or surface) onto a horizontally placed projection plane, and add the height values of corresponding points and lines to the projection plane next to them. This map is called elevation projection map. It is used in topographic survey, civil engineering, water conservancy, geology and mining. The above three kinds of graphs are all single-sided projection graphs. A figure that represents the shape and position of a space object by several orthogonal projections is called polyhedral orthogonal projection. This kind of drawing is widely used in various projects.
Polyhedral orthographic map
A space shape has three dimensions: length, width and height, but its projection can only reflect two dimensions. For accurate and complete descriptive geometry
In order to express the spatial shape on a plane, it is necessary to adopt multi-plane orthographic projection. Taking two mutually perpendicular projection planes (vertical projection plane and horizontal projection plane), the spatial shape (triangular pyramid in Figure 2) is projected on the front and horizontal projection planes (black graphic part in Figure 2) by orthogonal projection method. Then the horizontal projection plane is rotated 90 degrees downward around the intersection line OX of the two projection planes, so that it is on the same plane as the vertical projection plane, and then the double-sided orthogonal projection diagram of the space body is obtained. On the basis of the two projection planes, a lateral projection plane perpendicular to both the vertical projection plane and the horizontal projection plane is added, and then the shape (the color graphic part in Figure 2) is projected laterally, and then the lateral projection plane is rotated 90 degrees to the right around its intersection line OZ with the vertical projection plane, so that it is also on the same plane with the vertical projection plane, and the three-sided orthogonal projection diagram of the spatial shape can be obtained. Polyhedral orthographic map can accurately express the shape and position of space objects. Especially when the straight line and plane on the object are in special positions parallel or perpendicular to the projection plane, the actual shape of the plane figure and the real size of the included angle between the straight line, plane or two sides can be reflected in its projection. For lines and faces that are not in special positions, they do not have the above characteristics and need projection transformation to solve them.
Edit this projection transformation
Projection transformation is a new projection method by changing the spatial shape and the relative position of the projection plane. Projection transformation mainly includes surface changing method and rotation method. Descriptive geometry
① Face-changing method: without moving the space shape, replace the original projection surface with a new projection surface that meets the problem-solving requirements to get a new projection of the space shape. For example, in Figure 3, the triangular plate is inclined to the vertical projection plane and perpendicular to the horizontal projection plane before the surface changing method is adopted, and its vertical and horizontal projections cannot reflect the true shape of the triangular plate. Replace the original vertical projection plane with a new projection plane perpendicular to the horizontal projection plane and parallel to the triangular plate, and the true shape of the triangular plate will be reflected in the orthographic drawings of the new projection plane and the horizontal projection plane. The transformation rule of surface transformation method is that the distance from the new projection of a point to the new projection axis is equal to the distance from the replacement projection of a point to the replacement axis. (2) Rotation method: keep the projection plane unchanged, and let the space shape rotate around an axis to the required position to get a new projection. For example, in Figure 3, if the triangle is rotated around its right angle perpendicular to the horizontal projection plane to a position parallel to the vertical projection plane, the new vertical projection can reflect the true shape of the triangle. Intersection line and intersection line The intersection line between the plane and the surface of the space body is called intersection line, and the intersection line between the surfaces of two space bodies is called intersection line. In many cases, although the polyhedron orthographic drawing of a spatial shape can be made according to the relative position between the spatial shape and the projection plane, the intersection line and intersecting line between them cannot be drawn directly, and it needs to be drawn by using auxiliary surface method or other drawing methods. A figure obtained by flattening the surface of a spatial shape on a plane. For parts made of sheet metal, in addition to polyhedral orthographic drawing to represent the shape of the part, the sheet metal shape before the part is made is often represented by expanded drawing. According to the polyhedral orthographic projection of a space object, the development diagram of the space object is drawn in order to obtain the real shape of its surface, which can be obtained by graphic method or calculation method.