[ VIGRA Homepage | Function Index | Class Index | Namespaces | File List | Main Page ]

vigra/polygon.hxx |

    00001 /************************************************************************/
    00002 /*                                                                      */
    00003 /*               Copyright 1998-2010 by Ullrich Koethe                  */
    00004 /*                                                                      */
    00005 /*    This file is part of the VIGRA computer vision library.           */
    00006 /*    The VIGRA Website is                                              */
    00007 /*        http://hci.iwr.uni-heidelberg.de/vigra/                       */
    00008 /*    Please direct questions, bug reports, and contributions to        */
    00009 /*        ullrich.koethe@iwr.uni-heidelberg.de    or                    */
    00010 /*        vigra@informatik.uni-hamburg.de                               */
    00011 /*                                                                      */
    00012 /*    Permission is hereby granted, free of charge, to any person       */
    00013 /*    obtaining a copy of this software and associated documentation    */
    00014 /*    files (the "Software"), to deal in the Software without           */
    00015 /*    restriction, including without limitation the rights to use,      */
    00016 /*    copy, modify, merge, publish, distribute, sublicense, and/or      */
    00017 /*    sell copies of the Software, and to permit persons to whom the    */
    00018 /*    Software is furnished to do so, subject to the following          */
    00019 /*    conditions:                                                       */
    00020 /*                                                                      */
    00021 /*    The above copyright notice and this permission notice shall be    */
    00022 /*    included in all copies or substantial portions of the             */
    00023 /*    Software.                                                         */
    00024 /*                                                                      */
    00025 /*    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND    */
    00026 /*    EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES   */
    00027 /*    OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND          */
    00028 /*    NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT       */
    00029 /*    HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,      */
    00030 /*    WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING      */
    00031 /*    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR     */
    00032 /*    OTHER DEALINGS IN THE SOFTWARE.                                   */
    00033 /*                                                                      */
    00034 /************************************************************************/
    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 | html generated using doxygen and Python vigra 1.9.0 (Tue Nov 6 2012)