In recent years the measurement of a surface area became one of most the frequent applications required to serve a handheld GPS. Although it is not intended for such a work, especially at the level of precision required, a common handheld GPS can help clarify various issues and the whole process will certainly help the user to reach the base of the concepts related to measurement of surfaces, so to better transact with his engineer, when the time comes for accurate measurement.
The usual question is for the most accurate value for the surface area, but is often requested a table with the coordinates of the plot’s corners (calledvertices of the polygon) and the length of its sides (from where it will arise the circumference). If arisen from downloading data by a handheld GPS, these data can be used as a guide for an overview, a negotiation or an approximate estimate (e.g. earthworks or cost of a fence). However,  they can not be used as reliable values and been included in a document of legal or financial claim.

Determinina surface in Greece on maps or topographic diagrams is presumed to be done on the Greek Geodetic Reference System (EGSA87) and in meters. Any other way does not have the general use and the versatility of EGSA87.

Let’s have a look at some preliminary concepts.Determining a surface in Greece on maps or topographic diagrams is presumed to be done on the Greek Geodetic Reference System (EGSA87) and in meters. Any other way does not have the general use and the versatility of EGSA87.

The surface area calculation is given from known formulas, where the coordinates of its corners are been introduced. These formulas are solved much more easily when given in the form of an algorithm, of an executable routine or an application, where one introduces in a simple way the coordinates of the corners.

The coordinates could be obtained either from the 1:5000 charts build in the plder HATT Reference System (at the cost of small precision, and they should be converted from HATT to EGSA87 using the application CoordGR), or through the services of a surveyor engineer (at the price cost of his fee). A solution of intermediate accuracy, low cost and high flexibility is to use an amateur GPS (presumably handheld, or any other GPS that records points to protocol GPX) to capture the corners of the plot, then transfer the GPX file to TopoNavigator5 and get the plot’s geometric picture.

 

Surface area measurement in TopoNavigator5 HOME.

First step. IN THE FIELD  Get the corners of the plot  With the GPS turned on, we stand AT LEAST 10 MINUTES on each corner and then capture a Waypoint. Since the GPS has such a function, we use the possibility of making the average of a large number of spots (Averaging). If not, we get for each corner 4 spots at intervals of 2 minutes. If possible, we take the points with the correct topological order.

Second step. TOPONAVIGATOR5   Download the points on TopoNavigator5  If we have used the Averaging, we proceed directly to Step 3. If instead we have got 4 points at each corner, we will create the centroid of the virtual polygon defined by the 4 points at each corner. The first picture shows a completed polygon resulted from 4 points taken at the corners of the plot. The ‘Properties’ form is opened and the centroid has been created.

 

The second picture shows more clearly the polygon with the registered and selected centroid. Both the polygon and the 4 points that created it can be deleted, only the centroid is usefull.

 

For greater accuracy, the procedure described in steps 3 and 4 can be used in order to construct a small polygon from the cloud of points for each peak and to turn the centroid of each polygon into a Waypoint. Then the original cloud of Waypoints has to be deleted and remain the centroid.
STEP 3. GOOD TOPOLOGY   Organize items in a serial sequence  In this step we will confirm that the number of points gives a convex polygon (ie a polygon where neither side intersects any other), which will give the correct geometrical shape of land, and therefore the correct surface measurement.

Select all the points from the table (either by clicking the first and last dwell Shift or without anyone been selected press the button “Invert Selection”, so its selects them all) or the screen (by including them all in a selection box). Next, right-click on the table (on the “blue” area of the selection), enter the menu “Convert” and click “Convert selected points to Route”. A Route is readily formed that includes all selected points, in the order that is listed in the table of points. Finilize the route without changing its parameters.

Check the schema that describes the Route: if it is geometrically identical to the shape of the plot, then move to the next step. If not, the sequence of the points has to be changed, so as to arrive at the correct shape. To alter the sequence of points, double-click the entry in the list of routes. Go to the last tab, named “Vertices”. On the screen, locate the point that is not in the correct order and click it  on the list of route points (each selected point flashes on the screen). With the Change Order arrow keys, move the point higher or lower in the table to get it to the correct order. Once complete, press OK.
Step 4. Polygon. Composition of plot’s geometry  Right-click the entry of the route just checked, choose Conversion/Conversion Route to Polygon, which copies the points and builds a closed polygonal line. On the polygon’s properties form, press OK to register. The data table immediately turns to the polygon list, that shows (if there was no file open polygons) an entry to polygon just registered. By double-clicking the entry, opens theAnalysis tab, showing information for the surface (in square meters) and the perimeter. In the section Points the coordinates of the vertices of the polygon are given.
Step 5. FILE / PRINT  If the coordinates of the plot’s corner are needed, they can be printed from the Print menu / Print TVP File. A text file format (TXT) of them can be acquired as follows: save the polygon by right-clicking on New polygon file that has been added to ‘File Manager’ and click ‘Save’, and a file with the suffix TVP will be created. Make a copy of this file (Copy & Paste the file TVP) and change the suffix (of the copy file) to TXT. Open it in Notepad. Below the header, each vertex of the plot corresponds to one row, where the serial number of each point  is followed by the x and y values.

 

Surface area measurement in TopoNavigator5 PRO.

Here an Internet connection is required. After following the above mentioned steps 1–4, save the file with the polygon, and (if being in a GGRS87 environment, close the program and reopen it in WGS84), press F2 on the polygon’s record and by double clicking define the option “Only contour” as the symbol of the polygon. From Legend/Map type call the Satellite map. The aerial photograph is shown under the polygon. Select the polygon either from the table or the screen. The contour linear symbol acquires a bright background, while the vertices of the polygon are indicated by white ovals. Gripping with the mouse one to one the peak points, move them to the most correct positions according to aerial photography. It is better to make a copy of the polygon (by selecting it, clicking Edit/Copy then Edit/Paste) and make it invisible in order not to overlap the editable polygon, instead of using the Undo option (Ctrl-Z). By double clicking on the editable polygon’s entry, the new sizes of area and perimeter.