Straight track
In analytical and representational geometry (see two-panel projection ), a straight line is called the intersection between a plane in space and a basic plane of the spatial coordinate system . A plane generally has three straight tracks, s xy with the plan plane (xy plane), s yz with the elevation plane (yz plane) and s xz with the side elevation plane (xz plane).
At the same time, the plane intersects the coordinate axes in the track points S x , S y and S z .
In the case of special positions on the plane, the number of track points can be reduced to two or one and the number of straight track lines to two. Such planes are parallel to one or two coordinate axes:
If the plane is parallel to one of the axes, it has no point of intersection with this axis and therefore only two track points. Two of the straight track lines are then parallel to one another and to this axis. If the plane is parallel to one of the basic planes, it has only one track point and only two straight track lines.
If the plane passes through the origin of the coordinates, the track points coincide here, and at the same time all three straight lines intersect here. Otherwise, only two of the straight track lines intersect, precisely at the track points.
See also
literature
- Fucke, Kirch, Nickel: Descriptive Geometry. Fachbuch-Verlag, Leipzig 1998, ISBN 3-446-00778-4 , p. 113.
- C. Leopold: Geometric Basics of Architectural Representation. Verlag W. Kohlhammer, Stuttgart 2005, ISBN 3-17-018489-X , p. 86.