Polygon course (geodesy)

A polygon course (ABCDE) for measuring a stretch of road. The eccentric point Exz is required for the rear corners of the house.

A polygon is the trace of a path made up of a finite number of straight lines . In geodesy and construction, polygons are the most important measuring lines for terrestrial detailed measurements . There, polygonal lines are used primarily to determine the coordinates of several new points in one operation. The measurement of polygons is called polygonization .

Word origin

The word polygon comes from the ancient Greek πολυγώνιον ( polygṓnion 'polygon') and comes from πολύς ( polýs , 'much') and γωνία ( gōnía , angle ').

Principle of polygon measurement

A polygon has the following elements: the polygon points PP , the polygon sides and the angles of refraction . The angles of refraction are measured with an angle measuring instrument (e.g. a theodolite ), the horizontal distances with a length measuring device . Instruments that can measure both are called total stations . The coordinates of the individual polygon points are calculated from the angles of refraction and the distances through continued polar appending. ${\displaystyle {s_{i}}}$ ${\displaystyle {\beta _{i}}}$

The individual sections are usually about 50 to 200 meters long , depending on the terrain , buildings or the required accuracy. The polygon points are marketed in the ground by stakes or metal pins so that they can also be used for later measurements or for checks on a case-by-case basis. Tripods with the total station or the target signs (prism reflectors) are set up above the points on the ground and precisely centered so that the exact angles of refraction and distances can be measured. Total station and prisms are interchangeable without changing the tripod (forced centering). The accuracy is in the mm range.

In the past, measuring tables or theodolite and measuring tape were used; since the widespread introduction of electronic total stations, this has become obsolete.

Traverse types

In geodesy there are several types of polygonal lines:

Open polygons

open traverse (3); 1 = known points, 2 = points to be newly determined, 3 = angle of refraction, 4 = polygon sides

polygon (4) connected on both sides; 1 = known points, 2 = points to be newly determined, 3 = angle of refraction, 4 = polygon sides

1. Train with one-sided coordinate and direction connection (i.e. the starting point of the traverse is defined from another measurement, as is the direction to the second point), without coordinate and direction connection (no defined end point, e.g. from another measurement, no defined direction from penultimate to last traverse point)
2. Train with one-sided coordinate and two-sided directional connection
3. Train with one-sided coordinate connection, without directional termination (no long-term destination for the end point)
4. Train with direction and coordinate connection on both sides (fully connected train)

Closed traverse

Ring polygon; 1 = known points, 2 = points to be newly determined, 3 = angle of refraction, 4 = polygon sides

• Ring polygon (start and end point are identical)

Polygon networks

Mesh

Polygon networks are created by knotting several polygons.

application areas

Polygon courses are important measurement lines in geodesy . The polygon points serve as measuring points with which the network of official fixed points is further condensed by calculating the intermediate points between their known coordinates . They are also used for surveying of buildings, large machinery and mines used (see Mine Surveying ). Polygonal lines are used to determine recording points for object measurement (e.g. orthogonal angle recording , polar recording , boundary points ), as well as for topographical surveying (e.g. polar recording for terrain points) and staking out tasks . ${\displaystyle t_{i}}$

conditions

From the new points (polygon points) as much as possible of the area to be recorded should be covered, the sides of the polygon should be as stretched as possible and of the same length. The new points are expediently marketed for re-measurements .

See also

• Network adjustment , surveying network
• Error propagation
• Direction control with long-range target , solar azimuth or surveying gyro (gyro azimuth )
• Traverse (mathematics)

literature

• Eberhard Baumann: surveying. Vol. 2, Dümmler, Bonn 1995, ISBN 978-3-42-779056-3 .
• Paul Knufinke : General. Surveying and marrowing knowledge. Bochum 1990, ISBN 978-3-89-653530-6 .
• Asbeck, Drüppel, Gärtner (Ed.), Skindelies, Stein: Surveying and Geoinformation. 12th edition. Düsseldorf 2012, ISBN 978-3-00-038273-4 , p. 161.

Web links

• Polygonization. (PDF; 177 kB) Accessed November 21, 2013 . 
• Traverse. (PDF; 245 kB) Bochum University of Applied Sciences, accessed on November 21, 2013 (script on surveying). 
• Traverse. Retrieved November 21, 2013 . 

Individual evidence

1. ^ Wilhelm Gemoll : Greek-German school and hand dictionary . G. Freytag Verlag / Hölder-Pichler-Tempsky, Munich / Vienna 1965.