CGAL users discussion list

[Monique Teillaud <>]

infblnpf wrote:
> Hello,
> My application is to represent shapes on the Earth's (using a sphere is
> sufficient) surface. Those can be points, lines, and polygons. Coordinates
> should be defined by using degrees or radians (just like geographic
> coordinates).  
>
> A (straight) line for example should be defined by two coordinates and use
> the great circle ( http://en.wikipedia.org/wiki/Great_circle
> http://en.wikipedia.org/wiki/Great_circle ) to connect them.
> Polygons should consist of a collection of the lines mentioned.
> Furthermore I would like to perform operations like intersection, union,
> difference, complement on the shapes mentioned. 
> http://en.wikipedia.org/wiki/Set_%28mathematics%29#Basic_operations Set
> (mathematics) - Basic Operations  gives an idea of the operations assuming
> that the circles would be polygons. Of course those operations would differ
> if I for example intersect two lines.
> These operations only need to output collections of coordinates.
>
> What I don't need is extended functionality like Voronoi diagrams,
> Triangulations, and so on. Also I don't need to graphically display the
> results.

> I tried to figure that out using CGAL. More precisely I was looking at the
> "3D Spherical Geometry Kernel" and "2D Boolean Operations on Nef Polygons
> Embedded on the Sphere".  Actually I already had problems with putting a
> line on the sphere without previously defining another sphere or a plane.

Hi,

The 3D spherical kernel allows you to define general circular arcs on 
the sphere, ie arcs that are not necessarily supported by great circles.
So, you are right, you need to give for instance the plane defining the 
circle, to specify that it is a great circle. (We could think of adding 
special constructors for great circles in the future.)

> Additionally CGAL works in the Euclidean Space, which still leaves me with
> the geometric operations necessary, to work with great circles placed on the
> sphere.

I don't really understand what you mean here. Which geometric operations 
are you referring to? The 3D spherical kernel gives functionality like 
intersections of circular arcs.

best,

> I would highly appreciate it, if you could assist me in realizing that with
> CGAL if possible.
>
> Thank you very much!


--
Monique Teillaud
INRIA Sophia Antipolis - Méditerranée
http://www.inria.fr/sophia/members/Monique.Teillaud/