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polygon.hxx |

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3 /* Copyright 1998-2010 by Ullrich Koethe */
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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
95 ArrayVector<Point> H;
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 | html generated using doxygen and Python vigra 1.10.0 (Mon Nov 18 2013)