Library for working with geographic coordinates?

Question

Qt

I am looking for a library for solving standard geographical problems.
The library should contain some classes:

• Point: latitude + longitude or latitude + longitude + altitude.
  
• Line: a line connecting two points along the shortest route (great circle).
  
• Polygon.
  
• A circle.
  

You must also be able to count:

• Distance between points, point and line, polygonal...
  
• The area of ​​a polygon, a circle...
  
• Checking whether one object belongs to another.
  
• Intersection/union/difference of objects.
  
• Direct/inverse geodetic problems.
  

Can anyone suggest a library that solves all these problems or most of them? It's okay if the library uses Qt.

Answer 1

GEOS of course, what is there to think about.
If you don't believe me, trust the PostGIS team :)

GEOS for many geometry processing algorithms
Proj.4 for coordinate re-projection functions
GDAL for raster processing and format support

Answer 2

https://developers.arcgis.com/qt/ ?