The plan and elevation of a body
The images in a vertical parallel projection are called normal images - domyhomework . The plan and elevation of a body are special normal images. Usually a special position of the body is chosen in which as many boundary surfaces as possible are parallel to one of the image planes. Since many edges are then perpendicular to an image plane and are therefore depicted as points, the images are often not very descriptive. For example, the elevation and ground plan of a cube are each a square.
If none of the bounding surfaces of a body is parallel to an image plane, the body is said to be in a general position. In this case, all edges are depicted as a line and the image is thus more vivid. With a perpendicular parallel projection, in contrast to the oblique parallel projection - https://domyhomework.club/math-problem-solver/ , it cannot happen that the images of distances become longer than in the original.
If a body is in a general position, however, all edges are usually shown shortened. The shortening ratios are not independent of each other - https://domyhomework.club/geometry-homework/ . Therefore, an exact construction is difficult. For a cube in general position, a normal image can easily be drawn on box paper in the following steps.
A corner point is defined arbitrarily. A coordinate system is thought of whose origin lies in the corner point.
The three neighbouring corner points are drawn in with the following coordinates:
Variant I: (-4; 1), (0; 4) and (2; 2).
Variant II: (-2; 2), (0; 4) and (4; 1)
The remaining corner points result from suitable parallel shifts of the three edges.