The purpose of the programme is to enable precise mapping with relatively cheap tools. At first sight GPS seems to be the best tool possible. GPS receivers are dirt-cheap. They come in most mobile devices like smartphones and tablets for free. However, GPS has its downsides: it does not work well near tall buildings, distances can be measured at quite high precission but not absolute positions. However, with six decimal digits (~10cm) short distances (<10m) can’t be measured precisely. On the other hand EDMs available in DIY stores enable very precise (±1.5 mm) measurements in quite wide range of distances (0.05-70 m).
Establishing positions by measuring distances requires some calculations. Fortunately the method, known as trilateration[fn:4] is easy to implement.
Walk around the place you want to survey, count the vertices of the objects you want to map as well as supplementary ones you need to build a well-conditioned network. For anything more complicated than a rectangle sketching a structure of the network will help establishing proper orientation of triangles. Put numbers next to all vertices of your drawing.
| A | B | C | a | b |
|---|---|---|---|---|
Each row holds data for one triangle. The first three colums hold symbols (numbers) of vertices of a particular triangle. The latter two hold lengths of sides opposite to A and B vertices. The length of ‘c’ side is the distance between points A and B which location are known.
NOTE: The order of the verices is crucial. The formulae[fn:1] assume vertices are enumerated counter-clockwise and the location of the last one (C) is unknown.
As of now the programme can’t determine the proper order of calculations and it requires input date to be ordered to allow
In the following example the first two points are A and B. A is assumend to be at (0, 0) and B at (0, c) where c is the distance between them, which is 5 in this case. C is the first unkown point. As soon as it’s position is calculated and lengths of BD and CD are know the location of D can be established.
| A | B | C | a | b |
|---|---|---|---|---|
| A | B | C | 3 | 4 |
| C | B | D | 4 (BD) | 5 (CD) |
.PS
scale=2.54
AB: line right 5
BC: line up 2.4 left 1.8 at AB.end
AC: line up 2.4 right 3.2 at AB.start
BD: line up 2.4 right 3.2 at AB.end
CD: line right 5 at AC.end
"A" at AB.start - (0,0.2)
"B" at AB.end - (0,0.2)
"C" at AC.end + (0,0.15)
"D" at BD.end + (0,0.15)
"a" at BC.center - (0.2,0)
"b" at AC.center + (0.3,0)
"c" at AB.center + (0,0.2)
.PE
The following CSV holds data for this example.
Type,c1,c2,c3,c4,c5 P,A,0,0 P,B,5,0 T,A,B,C,3,4 T,C,B,D,4,5
The output of the programme is a three-column table. The first column is an identifier of a point, the next two are its coordinates. The last is the point’s “distance” from a point with known coordinates. It may be useful to estimate error.
| Point | X | Y | oder |
|---|---|---|---|
| A | 0 | 0 | 0 |
| B | 5 | 0 | 0 |
| C | 3.2 | 2.4 | 1 |
| D | 8.2 | 2.4 | 2 |
Different known values are required depending on requirements regarding output. To get relative location of points in a local coordinate system there is no need to know absolute location of any points in a global reference system (WGS84, UTM etc.). To place points in a global reference system location of two points in that system is required. With three points in a global reference frame availabel the location of the surveyed object can be established as well as possible errors can be estimated.
Either way, the programm requires location of two points in the input. If no global location is needed assume any one point acts as the beginning of the coordinate system (0, 0) and another with a known distance d form the former is placed at (0, d).
The the programme is meant as a tool for surveying flat surfaces which in theory[fn:2] means areas smaller than 30km in diamater and in practice everything an amature mapper with a cheap EDM[fn:3] would like to map.
[fn:1] https://pl.wikipedia.org/wiki/Wci%C4%99cie_liniowe_w_prz%C3%B3d
[fn:2] http://www.wydawnictwopw.pl/index.php?s=karta&id=211
[fn:3] http://www.conrad.com/ce/en/product/826512
[fn:4] https://www.e-education.psu.edu/natureofgeoinfo/c5_p12.html