Points, Lines, and Polygons on Spheres with C/C++ [closed]

Answer 1

I'd suggest you to take a look at this:

http://www.codeguru.com/Cpp/Cpp/algorithms/general/article.php/c5115/

The question 1E solves your problem of intersection between two grand circles. From this you can define the basic operation of your shapes on the sphere without a big dependency like CGAL or GEOS.

Answer 2

Finding the intersection of two objects typically requires setting the equations defining the objects equal to each other.

Here is one way, which perhaps just another phrasing of Vitor's answer.

Start by defining each line(arc) as a parametric equation. For better or worse I see these arcs as the path normalized vectors take when rotated. So that's how i would define them (I bet there is a better way).

So I would take the start and end points, treat them as vectors, take there cross product to get the axis of rotation, and that the dot product to get the angle.

so my equation for a arc would look like

arc(t) = startPoint * (axisAngleToRotationMatrix (axis, t * angle))

You would then set the two arcs equation equal to each other and solve the system of equations that results, for the "t"'s in each equation.

Answer 3

If you want to do general polygon set operation like union/intersection etc., then you can look into General polygon clipper library from http://www.cs.man.ac.uk/~toby/alan/software/