...one of the most highly
regarded and expertly designed C++ library projects in the
world.

— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards

// Non-named parameter versiontemplate<typename VertexListAndIncidenceGraph, typename Topology, typename PositionMap, typename VertexIndexMap, typename EdgeWeightMap> void gursoy_atun_layout(const VertexListAndIncidenceGraph& g, const Topology& space, PositionMap position, int nsteps = num_vertices(g), double diameter_initial = sqrt((double)num_vertices(g)), double diameter_final = 1, double learning_constant_initial = 0.8, double learning_constant_final = 0.2, VertexIndexMap vertex_index_map = get(vertex_index, g), EdgeWeightMap weight = dummy_property_map());// Named parameter versiontemplate<typename VertexListAndIncidenceGraph, typename Topology, typename PositionMap, typename P, typename T, typename R> void gursoy_atun_layout(const VertexListAndIncidenceGraph& g, const Topology& space, PositionMap position, const bgl_named_params<P,T,R>& params =all defaults);// Topologiestemplate<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;

This algorithm [60]
performs layout of directed graphs, either weighted or unweighted. This
algorithm is very different from the Kamada-Kawai and Fruchterman-Reingold algorithms,
because it does not explicitly strive to layout graphs in a visually
pleasing manner. Instead, it attempts to distribute the vertices
uniformly within a *topology* (e.g., rectangle, sphere, heart shape),
keeping vertices close to their neighbors. The algorithm itself is
based on Self-Organizing
Maps.

Various topologies are provided that
produce different, interesting results. The square toplogy 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.

The graph object on which the algorithm will be applied. The typeIN:Graphmust be a model of Vertex List Graph and Incidence Graph.

The topology on which the graph will be layed out. The type must model the Topology concept.OUT:

The property map that stores the position of each vertex. The typeIN:PositionMapmust be a model of Lvalue Property Map such that the vertex descriptor type ofGraphis convertible to its key type. Its value type must be the type of a point in the topology.

The number of iterations to perform.IN:

Default:num_vertices(g)

When a vertex is selected to be updated, all vertices that are reachable from that vertex within a certain diameter (in graph terms) will also be updated. This diameter begins atIN:diameter_initialin the first iteration and ends atdiameter_finalin the last iteration, progressing exponentially. Generally the diameter decreases, in a manner similar to the cooling schedule in Fruchterman-Reingold. The diameter should typically decrease in later iterations, so this value should not be less thandiameter_final.

Default:sqrt((double)num_vertices(g))

The final value of the diameter.IN:

Default: 1.0

The learning rate affects how far vertices can moved to rearrange themselves in a given iteration. The learning rate progresses linearly from the initial value to the final value, both of which should be between 0 and 1. The learning rate should typically decrease, so the initial value should not exceed the final value.IN:

Default: 0.8

The final learning rate constant.IN:

Default: 0.2

This maps each vertex to an integer in the rangeIN:[0, num_vertices(g)). The typeVertexIndexMapmust be a model of Readable Property Map. The value type of the map must be an integer type. The vertex descriptor type of the graph needs to be usable as the key type of the map.

Default:get(vertex_index, g)

This maps each edge to an weight. num_vertices(g)). This is only necessary when no displacement map is provided. The typeEdgeWeightMapmust be a model of Readable Property Map. The value type of the map must be an floating-point type compatible withdouble. The edge descriptor type of the graph needs to be usable as the key type of the map. When this map is adummy_property_map, the algorithm assumes the graph is unweighted.

Default:dummy_property_map()

Executes the algorithm forIN:niterations.

Default:num_vertices(g)

Range specifying the parameters (IN:diameter_initial,diameter_final).

Default:std::make_pair(sqrt((double)num_vertices(g)), 1.0)

Range specifying the parameters (IN:learning_constant_initial,learning_constant_final).

Default:std::make_pair(0.8, 0.2)

Equivalent to the non-namedIN:weightparameter.

Default:dummy_property_map()

Equivalent to the non-namedvertex_index_mapparameter.

Default:get(vertex_index, g)

Expression | Type | Description |
---|---|---|

Topology::point_type |
type | The type of points in the space. |

space.random_point() |
point_type | Returns a random point (usually uniformly distributed) within the space. |

space.distance(p1, p2) |
double | Get a quantity representing the distance between p1
and p2 using a path going completely inside the space.
This only needs to have the same < relation as actual
distances, and does not need to satisfy the other properties of a
norm in a Banach space. |

space.move_position_toward(p1, fraction, p2) |
point_type | Returns a point that is a fraction of the way from p1
to p2, moving along a "line" in the space according to
the distance measure. fraction is a double
between 0 and 1, inclusive. |

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 two-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 two-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: typedefunspecifiedpoint_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; };

Copyright © 2004 |
Jeremiah Willcock, Indiana University () Doug Gregor, Indiana University () Andrew Lumsdaine, Indiana University () |