Polygon detection library for C++

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Project Description:
Hi everybody,
I need someone to implement a c++ library for polygon detection from a point.Something like the algorithm in the paper below.
[url removed, login to view]

This library should take a list of line segments and a point as input
and as output
-it should give back a polygon where the point resides in
-island polygons to exclude
-All lose line segments which are not a part of any polygons
Acceptable complexity is around O(n) or some variety of it (e.g O(n) + nlogn etc)
O(n2) and worse is not acceptable

Please have a look at the drawing attached and read the rest

INPUT:
Line Segments List(AB,EF,AG,CD,HI,JK,KL,ML,MN)
Point pt1 (x,y)

OUTPUT
Included Polygon:points H,J,K,L,M,N,2,I (as a list)
Excluded Polygons (island(s)):points 4,5,6,7 (as a list)
and if there are more excluded polygons they should be the part of outputs

Loose Line Segments List (E1,G1,D2,2F,3C,3B)

Additional Project Description:
04/09/2013 at 2:19 IST
I made a mistake when stating the desired complexity
Just ignore that O(n2) comment


04/09/2013 at 5:16 IST
//HERE IS THE HEADER FILE OF THE LIBRARY:
/* you can use std lists for List containers or your home made list, i dont care
I asked for a complexity less than O(n^2) but I think it is not possible , so I will accept O(n^2) as well
One more thing about your intersection calculations , with float numbers it is always a good idea to work with a delta for point comparisions
*/
#define List YourPrefferedListContainer

struct RAPointF
{
RAPointF(float xx,float yy): x(xx),y(yy);
float x,y;
/*add whatever you need to after this point*/

};


struct RALineSegment
{
RALineSegment(RAPointF A,RAPointF B);
RAPointF start;
RAPointF end;
/*add whatever you need to after this point*/

};
struct RAPolygon
{
List<RAPointF> points;
bool island; //here keep it true for the real bordering polygon , set false if it is an island polygon.Only one polygon has this value false , rest (if there are should be true.
/*add whatever you need to after this point*/

}

class RAPolygonDetect
{
void init(List<RALineSegment> lineSegments); //this will be called once and re- called if line segments are changed
List<RAPolygon> getPolygons(RAPointF targetPoint); //i will call this one repeatedly to get different polygons for different points
/*add whatever you need to after this point*/

};

Skills required:
Algorithm, C++ Programming, Mathematics
Additional Files: polygons.png
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