Topologies for Graph Drawing

Synopsis

template<std::size_t Dims> class convex_topology;
template<std::size_t Dims, typename RandomNumberGenerator = minstd_rand> class hypercube_topology;
template<typename RandomNumberGenerator = minstd_rand> class square_topology;
template<typename RandomNumberGenerator = minstd_rand> class cube_topology;
template<std::size_t Dims, typename RandomNumberGenerator = minstd_rand> class ball_topology;
template<typename RandomNumberGenerator = minstd_rand> class circle_topology;
template<typename RandomNumberGenerator = minstd_rand> class sphere_topology;
template<typename RandomNumberGenerator = minstd_rand> class heart_topology;

Summary

Various topologies are provided that produce different, interesting results for graph layout algorithms. The square topology can be used for normal display of graphs or distributing vertices for parallel computation on a process array, for instance. Other topologies, such as the sphere topology (or N-dimensional ball topology) make sense for different problems, whereas the heart topology is just plain fun. One can also define a topology to suit other particular needs.

Topologies

Class template convex_topology implements the basic distance and point movement functions for any convex topology in Dims dimensions. It is not itself a topology, but is intended as a base class that any convex topology can derive from. The derived topology need only provide a suitable random_point function that returns a random point within the space.

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;
  point move_position_toward(point a, double fraction, point b) const;
};

Class template hypercube_topology implements a Dims-dimensional hypercube. It is a convex topology whose points are drawn from a random number generator of type RandomNumberGenerator. The hypercube_topology can be constructed with a given random number generator; if omitted, a new, default-constructed random number generator will be used. The resulting layout will be contained within the hypercube, whose sides measure 2*scaling long (points will fall in the range [-scaling, scaling] in each dimension).

template<std::size_t Dims, typename RandomNumberGenerator = minstd_rand>
class hypercube_topology : public convex_topology<Dims>
{
public:
  explicit hypercube_topology(double scaling = 1.0);
  hypercube_topology(RandomNumberGenerator& gen, double scaling = 1.0);
  point_type random_point() const;
};

Class template square_topology is a two-dimensional hypercube topology.

template<typename RandomNumberGenerator = minstd_rand>
class square_topology : public hypercube_topology<2, RandomNumberGenerator>
{
 public:
  explicit square_topology(double scaling = 1.0);
  square_topology(RandomNumberGenerator& gen, double scaling = 1.0);
};

Class template cube_topology is a three-dimensional hypercube topology.

template<typename RandomNumberGenerator = minstd_rand>
class cube_topology : public hypercube_topology<3, RandomNumberGenerator>
{
 public:
  explicit cube_topology(double scaling = 1.0);
  cube_topology(RandomNumberGenerator& gen, double scaling = 1.0);
};

Class template ball_topology implements a Dims-dimensional ball. It is a convex topology whose points are drawn from a random number generator of type RandomNumberGenerator but reside inside the ball. The ball_topology can be constructed with a given random number generator; if omitted, a new, default-constructed random number generator will be used. The resulting layout will be contained within the ball with the given radius.

template<std::size_t Dims, typename RandomNumberGenerator = minstd_rand>
class ball_topology : public convex_topology<Dims>
{
public:
  explicit ball_topology(double radius = 1.0);
  ball_topology(RandomNumberGenerator& gen, double radius = 1.0);
  point_type random_point() const;
};

Class template circle_topology is a two-dimensional ball topology.

template<typename RandomNumberGenerator = minstd_rand>
class circle_topology : public ball_topology<2, RandomNumberGenerator>
{
 public:
  explicit circle_topology(double radius = 1.0);
  circle_topology(RandomNumberGenerator& gen, double radius = 1.0);
};

Class template sphere_topology is a three-dimensional ball topology.

template<typename RandomNumberGenerator = minstd_rand>
class sphere_topology : public ball_topology<3, RandomNumberGenerator>
{
 public:
  explicit sphere_topology(double radius = 1.0);
  sphere_topology(RandomNumberGenerator& gen, double radius = 1.0);
};

Class template heart_topology is topology in the shape of a heart. It serves as an example of a non-convex, nontrivial topology for layout.

template<typename RandomNumberGenerator = minstd_rand>
class heart_topology
{
 public:
  typedef unspecified point_type;

  heart_topology();
  heart_topology(RandomNumberGenerator& gen);
  point_type random_point() const;
  double distance(point_type a, point_type b) const;
  point_type move_position_toward(point_type a, double fraction, point_type b) const;
};