gursoy_atun_layout.hpp

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                        const Topology& space,
                        PositionMap position)
{
  gursoy_atun_layout(graph, space, position, num_vertices(graph));
}

template<typename VertexListAndIncidenceGraph, typename Topology,
         typename PositionMap, typename P, typename T, typename R>
void 
gursoy_atun_layout(const VertexListAndIncidenceGraph& graph,  
                   const Topology& space,
                   PositionMap position,
                   const bgl_named_params<P,T,R>& params)
{
#ifndef BOOST_NO_STDC_NAMESPACE
  using std::sqrt;
#endif

  std::pair<double, double> diam(sqrt(double(num_vertices(graph))), 1.0);
  std::pair<double, double> learn(0.8, 0.2);
  gursoy_atun_layout(graph, space, position,
                     choose_param(get_param(params, iterations_t()),
                                  num_vertices(graph)),
                     choose_param(get_param(params, diameter_range_t()), 
                                  diam).first,
                     choose_param(get_param(params, diameter_range_t()), 
                                  diam).second,
                     choose_param(get_param(params, learning_constant_range_t()), 
                                  learn).first,
                     choose_param(get_param(params, learning_constant_range_t()), 
                                  learn).second,
                     choose_const_pmap(get_param(params, vertex_index), graph,
                                       vertex_index),
                     choose_param(get_param(params, edge_weight), 
                                  dummy_property_map()));
}

/***********************************************************
 * Topologies                                              *
 ***********************************************************/
template<std::size_t Dims>
class convex_topology 
{
  struct point 
  {
    point() { }
    double& operator[](std::size_t i) {return values[i];}
    const double& operator[](std::size_t i) const {return values[i];}

  private:
    double values[Dims];
  };

 public:
  typedef point point_type;

  double distance(point a, point b) const 
  {
    double dist = 0;
    for (std::size_t i = 0; i < Dims; ++i) {
      double diff = b[i] - a[i];
      dist += diff * diff;
    }
    // Exact properties of the distance are not important, as long as
    // < on what this returns matches real distances
    return dist;
  }

  point move_position_toward(point a, double fraction, point b) const 
  {
    point result;
    for (std::size_t i = 0; i < Dims; ++i)
      result[i] = a[i] + (b[i] - a[i]) * fraction;
    return result;
  }
};

template<std::size_t Dims,
         typename RandomNumberGenerator = minstd_rand>
class hypercube_topology : public convex_topology<Dims>
{
  typedef uniform_01<RandomNumberGenerator, double> rand_t;

 public:
  typedef typename convex_topology<Dims>::point_type point_type;

  explicit hypercube_topology(double scaling = 1.0) 
    : gen_ptr(new RandomNumberGenerator), rand(new rand_t(*gen_ptr)), 
      scaling(scaling) 
  { }

  hypercube_topology(RandomNumberGenerator& gen, double scaling = 1.0) 
    : gen_ptr(), rand(new rand_t(gen)), scaling(scaling) { }
                     
  point_type random_point() const 
  {
    point_type p;
    for (std::size_t i = 0; i < Dims; ++i)
      p[i] = (*rand)() * scaling;
    return p;
  }

 private:
  shared_ptr<RandomNumberGenerator> gen_ptr;
  shared_ptr<rand_t> rand;
  double scaling;
};

template<typename RandomNumberGenerator = minstd_rand>
class square_topology : public hypercube_topology<2, RandomNumberGenerator>
{
  typedef hypercube_topology<2, RandomNumberGenerator> inherited;

 public:
  explicit square_topology(double scaling = 1.0) : inherited(scaling) { }
  
  square_topology(RandomNumberGenerator& gen, double scaling = 1.0) 
    : inherited(gen, scaling) { }
};

template<typename RandomNumberGenerator = minstd_rand>
class cube_topology : public hypercube_topology<3, RandomNumberGenerator>
{
  typedef hypercube_topology<3, RandomNumberGenerator> inherited;

 public:
  explicit cube_topology(double scaling = 1.0) : inherited(scaling) { }
  
  cube_topology(RandomNumberGenerator& gen, double scaling = 1.0) 
    : inherited(gen, scaling) { }
};

template<std::size_t Dims,
         typename RandomNumberGenerator = minstd_rand>
class ball_topology : public convex_topology<Dims>
{
  typedef uniform_01<RandomNumberGenerator, double> rand_t;

 public:
  typedef typename convex_topology<Dims>::point_type point_type;

  explicit ball_topology(double radius = 1.0) 
    : gen_ptr(new RandomNumberGenerator), rand(new rand_t(*gen_ptr)), 
      radius(radius) 
  { }

  ball_topology(RandomNumberGenerator& gen, double radius = 1.0) 
    : gen_ptr(), rand(new rand_t(gen)), radius(radius) { }
                     
  point_type random_point() const 
  {
    point_type p;
    double dist_sum;
    do {
      dist_sum = 0.0;
      for (std::size_t i = 0; i < Dims; ++i) {
        double x = (*rand)() * 2*radius - radius;
        p[i] = x;
        dist_sum += x * x;
      }
    } while (dist_sum > radius*radius);
    return p;
  }

 private:
  shared_ptr<RandomNumberGenerator> gen_ptr;
  shared_ptr<rand_t> rand;
  double radius;
};

template<typename RandomNumberGenerator = minstd_rand>
class circle_topology : public ball_topology<2, RandomNumberGenerator>
{
  typedef ball_topology<2, RandomNumberGenerator> inherited;

 public:
  explicit circle_topology(double radius = 1.0) : inherited(radius) { }
  
  circle_topology(RandomNumberGenerator& gen, double radius = 1.0) 
    : inherited(gen, radius) { }
};

template<typename RandomNumberGenerator = minstd_rand>
class sphere_topology : public ball_topology<3, RandomNumberGenerator>
{
  typedef ball_topology<3, RandomNumberGenerator> inherited;

 public:
  explicit sphere_topology(double radius = 1.0) : inherited(radius) { }
  
  sphere_topology(RandomNumberGenerator& gen, double radius = 1.0) 
    : inherited(gen, radius) { }
};

template<typename RandomNumberGenerator = minstd_rand>
class heart_topology 
{
  // Heart is defined as the union of three shapes:
  // Square w/ corners (+-1000, -1000), (0, 0), (0, -2000)
  // Circle centered at (-500, -500) radius 500*sqrt(2)
  // Circle centered at (500, -500) radius 500*sqrt(2)
  // Bounding box (-1000, -2000) - (1000, 500*(sqrt(2) - 1))

  struct point 
  {
    point() { values[0] = 0.0; values[1] = 0.0; }
    point(double x, double y) { values[0] = x; values[1] = y; }

    double& operator[](std::size_t i)       { return values[i]; }
    double  operator[](std::size_t i) const { return values[i]; }

  private:
    double values[2];
  };

  bool in_heart(point p) const 
  {
#ifndef BOOST_NO_STDC_NAMESPACE
    using std::abs;
    using std::pow;
#endif

    if (p[1] < abs(p[0]) - 2000) return false; // Bottom
    if (p[1] <= -1000) return true; // Diagonal of square
    if (pow(p[0] - -500, 2) + pow(p[1] - -500, 2) <= 500000)
      return true; // Left circle
    if (pow(p[0] - 500, 2) + pow(p[1] - -500, 2) <= 500000)
      return true; // Right circle
    return false;
  }

  bool segment_within_heart(point p1, point p2) const 
  {
    // Assumes that p1 and p2 are within the heart
    if ((p1[0] < 0) == (p2[0] < 0)) return true; // Same side of symmetry line
    if (p1[0] == p2[0]) return true; // Vertical
    double slope = (p2[1] - p1[1]) / (p2[0] - p1[0]);
    double intercept = p1[1] - p1[0] * slope;
    if (intercept > 0) return false; // Crosses between circles
    return true;
  }

  typedef uniform_01<RandomNumberGenerator, double> rand_t;

 public:
  typedef point point_type;

  heart_topology() 
    : gen_ptr(new RandomNumberGenerator), rand(new rand_t(*gen_ptr)) { }

  heart_topology(RandomNumberGenerator& gen) 
    : gen_ptr(), rand(new rand_t(gen)) { }

  point random_point() const 
  {
#ifndef BOOST_NO_STDC_NAMESPACE
    using std::sqrt;
#endif

    point result;
    double sqrt2 = sqrt(2.);
    do {
      result[0] = (*rand)() * (1000 + 1000 * sqrt2) - (500 + 500 * sqrt2);
      result[1] = (*rand)() * (2000 + 500 * (sqrt2 - 1)) - 2000;
    } while (!in_heart(result));
    return result;
  }

  double distance(point a, point b) const 
  {
#ifndef BOOST_NO_STDC_NAMESPACE
    using std::sqrt;
#endif
    if (segment_within_heart(a, b)) {
      // Straight line
      return sqrt((b[0] - a[0]) * (b[0] - a[0]) + (b[1] - a[1]) * (b[1] - a[1]));
    } else {
      // Straight line bending around (0, 0)
      return sqrt(a[0] * a[0] + a[1] * a[1]) + sqrt(b[0] * b[0] + b[1] * b[1]);
    }
  }

  point move_position_toward(point a, double fraction, point b) const 
  {
#ifndef BOOST_NO_STDC_NAMESPACE
    using std::sqrt;
#endif

    if (segment_within_heart(a, b)) {
      // Straight line
      return point(a[0] + (b[0] - a[0]) * fraction,
                   a[1] + (b[1] - a[1]) * fraction);
    } else {
      double distance_to_point_a = sqrt(a[0] * a[0] + a[1] * a[1]);
      double distance_to_point_b = sqrt(b[0] * b[0] + b[1] * b[1]);
      double location_of_point = distance_to_point_a / 
                                   (distance_to_point_a + distance_to_point_b);
      if (fraction < location_of_point)
        return point(a[0] * (1 - fraction / location_of_point), 
                     a[1] * (1 - fraction / location_of_point));
      else
        return point(
          b[0] * ((fraction - location_of_point) / (1 - location_of_point)),
          b[1] * ((fraction - location_of_point) / (1 - location_of_point)));
    }
  }

 private:
  shared_ptr<RandomNumberGenerator> gen_ptr;
  shared_ptr<rand_t> rand;
};

} // namespace boost

#endif // BOOST_GRAPH_GURSOY_ATUN_LAYOUT_HPP