Marble: Add Polygon Area feature
completed by: Ilya Kowalewski
mentors: Dennis Nienhüser, shentey, Sanjiban Bairagya, Torsten Rahn
The settings dialog for the Measure Tool contains an entry for Polygon "Area" measurement already.
Please enhance the Measure tool so that
- The setting for the Polygon Area is reenabled
In case the checkmark for the Area is set:
- the polyline ("lineString") that holds the measure points should be used ("casted" ?) as a linear ring and it should be filled in the same way as the circle area ruler.
- In the center of the area inside the polygon the text should be displayed in the same way as for the circle measure tool
- the value for the polygon area is calculated like this:
In a previous task the bearing change for each node was calculated. We need the bearing change for every single node in the polygon - so we need to calculate the bearing change for the first and last node in addition.
then we need to sum up all bearing changes for all n nodes:
theta1 = bearingChange1 + bearingChange2 + .... + bearingchangen
In addition we need to calculate:
theta2 = n * 2 * pi - theta1
Now we pick the smaller one to make a good guess for the inner angle set:
theta = (theta1 < theta2) ? theta1 : theta2
and we use theta to calculate the area:
Please verify the result value by roughly drawing along a border of a country (e.g. poland, ukraine, france, germany or romania, etc.) and compare the resulting value with the one displayed when clicking the country label.