How to find the projection of a straight line on a plane
The projection of a three-dimensional object called its image plane. The ability to build a projection must be representatives of different professions. This is such a common phenomenon that people often do not even think about it, just make plans and maps, images of parts under one or another angle, etc. First of all, you must learn how to build the projection of a straight line.
You will need:
- plane; - Straight, does not belong to this plane; - Gon; - Pencil.
Instruction how to find the projection of a straight line on a plane
Imagine a plane on which to project the line. Mark it, for example, on a sheet of paper. In any case, you get an image on the plane so that it will be quite arbitrary. You have to use a spatial imagination, to imagine how it will look like in three dimensions.
Draw a line which does not lie on this plane. Of course, you can build and projection of any line belonging to this plane, but it will be completely different from the original line. If no additional parameter is not specified, build arbitrary line. However, conditions can be specified and the angle between your objects. It is formed at the point of their intersection.
In order to build the most simple orthogonal (rectangular) projection, lower of any two points belonging to the given straight line, perpendicular to the plane. Connect them to the segment. This will be a rectangular projection of the line onto the plane. If the source is a straight line segment, it is necessary to project the ends. For the starting point of the ray is taken, and any other. To direct an arbitrary length is best to first find a place of its intersection with the plane.
To better understand how to form a rectangular projection, perform the following experiment. Hang on the wall of the small screen. You can also use a white wall. You will need another piece of rope and 2 chairs and a table attached to the rack, as well as any light source. Tie a rope to the posts. Place them so that the cord was stretched and was at an angle to the screen. Measure the cord. Put a table lamp so that its beam is incident on the screen at right angles. At the same time it must cover and a rope. Having paid off the overhead light, you will see that stretched cord casts a shadow on the screen, and the length of the shadow is not the same as the length of the cord. Shadow and a projection - in this case rectangular. Experiment by placing the light source so that the beam is incident on the screen from different angles.