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vigra/polygon.hxx VIGRA

00001 /************************************************************************/
00002 /*                                                                      */
00003 /*               Copyright 1998-2010 by Ullrich Koethe                  */
00004 /*                                                                      */
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00011 /*                                                                      */
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00035 
00036 #ifndef VIGRA_POLYGON_HXX
00037 #define VIGRA_POLYGON_HXX
00038 
00039 #include <cmath>
00040 #include <cstdlib>
00041 #include <iterator>
00042 #include <algorithm>
00043 #include "config.hxx"
00044 #include "error.hxx"
00045 #include "array_vector.hxx"
00046 
00047 namespace vigra {
00048 
00049 /** \addtogroup MathFunctions
00050 */
00051 //@{
00052 
00053 namespace detail {
00054 
00055 template < class Point >    
00056 bool sortPoints(Point const & p1, Point const & p2) 
00057 {
00058     return (p1[0]<p2[0]) || (p1[0] == p2[0] && p1[1] < p2[1]);
00059 }
00060 
00061 template < class Point >    
00062 bool orderedClockwise(const Point &O, const Point &A, const Point &B)
00063 {
00064     return (A[0] - O[0]) * (B[1] - O[1]) - (A[1] - O[1]) * (B[0] - O[0]) <= 0;
00065 }
00066 
00067 } // namespace detail
00068 
00069 
00070 /** \brief Compute convex hull of a 2D polygon.
00071 
00072     The input array \a points contains a (not necessarily ordered) set of 2D points
00073     whose convex hull is to be computed. The array's <tt>value_type</tt> (i.e. the point type)
00074     must be compatible with std::vector (in particular, it must support indexing, 
00075     copying, and have <tt>size() == 2</tt>). The points of the convex hull will be appended
00076     to the output array \a convex_hull (which must support <tt>std::back_inserter(convex_hull)</tt>). 
00077     Since the convex hull is a closed polygon, the first and last point of the output will 
00078     be the same (i.e. the first point will simply be inserted at the end again). The points
00079     of the convex hull will be ordered counter-clockwise, starting with the leftmost point
00080     of the input. The function implements Andrew's Monotone Chain algorithm.
00081 */
00082 template<class PointArray1, class PointArray2>
00083 void convexHull(const PointArray1 &points, PointArray2 & convex_hull)
00084 {
00085     vigra_precondition(points.size() >= 2,
00086                        "convexHull(): at least two input points are needed.");
00087     vigra_precondition(points[0].size() == 2,
00088                        "convexHull(): 2-dimensional points required.");
00089     
00090     typedef typename PointArray1::value_type Point;
00091     
00092     ArrayVector<Point> ordered(points.begin(), points.end());
00093     std::sort(ordered.begin(), ordered.end(), detail::sortPoints<Point>);
00094     
00095     ArrayVector<Point> H;
00096     
00097     int n = points.size(), k=0;
00098     
00099     // Build lower hull
00100     for (int i = 0; i < n; i++) 
00101     {
00102         while (k >= 2 && detail::orderedClockwise(H[k-2], H[k-1], ordered[i])) 
00103         {
00104             H.pop_back();
00105             --k;
00106         }
00107         H.push_back(ordered[i]);
00108         ++k;
00109     }
00110     
00111     // Build upper hull
00112     for (int i = n-2, t = k+1; i >= 0; i--) 
00113     {
00114         while (k >= t && detail::orderedClockwise(H[k-2], H[k-1], ordered[i])) 
00115         {
00116             H.pop_back();
00117             --k;
00118         }
00119         H.push_back(ordered[i]);
00120         ++k;
00121     }
00122     
00123     std::copy(H.begin(), H.begin()+k, std::back_inserter(convex_hull));
00124 }
00125 
00126 //@}
00127 
00128 } // namespace vigra
00129 
00130 #endif /* VIGRA_POLYGON_HXX */

© Ullrich Köthe (ullrich.koethe@iwr.uni-heidelberg.de)
Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany

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