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polygon.hxx
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35 
36 #ifndef VIGRA_POLYGON_HXX
37 #define VIGRA_POLYGON_HXX
38 
39 #include <cmath>
40 #include <cstdlib>
41 #include <iterator>
42 #include <algorithm>
43 #include "config.hxx"
44 #include "error.hxx"
45 #include "array_vector.hxx"
46 
47 namespace vigra {
48 
49 /** \addtogroup MathFunctions
50 */
51 //@{
52 
53 namespace detail {
54 
55 template < class Point >
56 bool sortPoints(Point const & p1, Point const & p2)
57 {
58  return (p1[0]<p2[0]) || (p1[0] == p2[0] && p1[1] < p2[1]);
59 }
60 
61 template < class Point >
62 bool orderedClockwise(const Point &O, const Point &A, const Point &B)
63 {
64  return (A[0] - O[0]) * (B[1] - O[1]) - (A[1] - O[1]) * (B[0] - O[0]) <= 0;
65 }
66 
67 } // namespace detail
68 
69 
70 /** \brief Compute convex hull of a 2D polygon.
71 
72  The input array \a points contains a (not necessarily ordered) set of 2D points
73  whose convex hull is to be computed. The array's <tt>value_type</tt> (i.e. the point type)
74  must be compatible with std::vector (in particular, it must support indexing,
75  copying, and have <tt>size() == 2</tt>). The points of the convex hull will be appended
76  to the output array \a convex_hull (which must support <tt>std::back_inserter(convex_hull)</tt>).
77  Since the convex hull is a closed polygon, the first and last point of the output will
78  be the same (i.e. the first point will simply be inserted at the end again). The points
79  of the convex hull will be ordered counter-clockwise, starting with the leftmost point
80  of the input. The function implements Andrew's Monotone Chain algorithm.
81 */
82 template<class PointArray1, class PointArray2>
83 void convexHull(const PointArray1 &points, PointArray2 & convex_hull)
84 {
85  vigra_precondition(points.size() >= 2,
86  "convexHull(): at least two input points are needed.");
87  vigra_precondition(points[0].size() == 2,
88  "convexHull(): 2-dimensional points required.");
89 
90  typedef typename PointArray1::value_type Point;
91 
92  ArrayVector<Point> ordered(points.begin(), points.end());
93  std::sort(ordered.begin(), ordered.end(), detail::sortPoints<Point>);
94 
96 
97  int n = points.size(), k=0;
98 
99  // Build lower hull
100  for (int i = 0; i < n; i++)
101  {
102  while (k >= 2 && detail::orderedClockwise(H[k-2], H[k-1], ordered[i]))
103  {
104  H.pop_back();
105  --k;
106  }
107  H.push_back(ordered[i]);
108  ++k;
109  }
110 
111  // Build upper hull
112  for (int i = n-2, t = k+1; i >= 0; i--)
113  {
114  while (k >= t && detail::orderedClockwise(H[k-2], H[k-1], ordered[i]))
115  {
116  H.pop_back();
117  --k;
118  }
119  H.push_back(ordered[i]);
120  ++k;
121  }
122 
123  std::copy(H.begin(), H.begin()+k, std::back_inserter(convex_hull));
124 }
125 
126 //@}
127 
128 } // namespace vigra
129 
130 #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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