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boost/graph/topology.hpp

// Copyright 2009 The Trustees of Indiana University.

// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)

//  Authors: Jeremiah Willcock
//           Douglas Gregor
//           Andrew Lumsdaine
#ifndef BOOST_GRAPH_TOPOLOGY_HPP
#define BOOST_GRAPH_TOPOLOGY_HPP

#include <boost/algorithm/minmax.hpp>
#include <boost/config.hpp> // For BOOST_STATIC_CONSTANT
#include <boost/config/no_tr1/cmath.hpp>
#include <boost/math/constants/constants.hpp> // For root_two
#include <boost/math/special_functions/hypot.hpp>
#include <boost/random/uniform_01.hpp>
#include <boost/random/linear_congruential.hpp>
#include <boost/shared_ptr.hpp>

#include <cmath>

// Classes and concepts to represent points in a space, with distance and move
// operations (used for Gurson-Atun layout), plus other things like bounding
// boxes used for other layout algorithms.

namespace boost
{

/***********************************************************
 * Topologies                                              *
 ***********************************************************/
template < std::size_t Dims > class convex_topology
{
public: // For VisualAge C++
    struct point
    {
        BOOST_STATIC_CONSTANT(std::size_t, dimensions = Dims);
        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: // For VisualAge C++
    struct point_difference
    {
        BOOST_STATIC_CONSTANT(std::size_t, dimensions = Dims);
        point_difference()
        {
            for (std::size_t i = 0; i < Dims; ++i)
                values[i] = 0.;
        }
        double& operator[](std::size_t i) { return values[i]; }
        const double& operator[](std::size_t i) const { return values[i]; }

        friend point_difference operator+(
            const point_difference& a, const point_difference& b)
        {
            point_difference result;
            for (std::size_t i = 0; i < Dims; ++i)
                result[i] = a[i] + b[i];
            return result;
        }

        friend point_difference& operator+=(
            point_difference& a, const point_difference& b)
        {
            for (std::size_t i = 0; i < Dims; ++i)
                a[i] += b[i];
            return a;
        }

        friend point_difference operator-(const point_difference& a)
        {
            point_difference result;
            for (std::size_t i = 0; i < Dims; ++i)
                result[i] = -a[i];
            return result;
        }

        friend point_difference operator-(
            const point_difference& a, const point_difference& b)
        {
            point_difference result;
            for (std::size_t i = 0; i < Dims; ++i)
                result[i] = a[i] - b[i];
            return result;
        }

        friend point_difference& operator-=(
            point_difference& a, const point_difference& b)
        {
            for (std::size_t i = 0; i < Dims; ++i)
                a[i] -= b[i];
            return a;
        }

        friend point_difference operator*(
            const point_difference& a, const point_difference& b)
        {
            point_difference result;
            for (std::size_t i = 0; i < Dims; ++i)
                result[i] = a[i] * b[i];
            return result;
        }

        friend point_difference operator*(const point_difference& a, double b)
        {
            point_difference result;
            for (std::size_t i = 0; i < Dims; ++i)
                result[i] = a[i] * b;
            return result;
        }

        friend point_difference operator*(double a, const point_difference& b)
        {
            point_difference result;
            for (std::size_t i = 0; i < Dims; ++i)
                result[i] = a * b[i];
            return result;
        }

        friend point_difference operator/(
            const point_difference& a, const point_difference& b)
        {
            point_difference result;
            for (std::size_t i = 0; i < Dims; ++i)
                result[i] = (b[i] == 0.) ? 0. : a[i] / b[i];
            return result;
        }

        friend double dot(const point_difference& a, const point_difference& b)
        {
            double result = 0;
            for (std::size_t i = 0; i < Dims; ++i)
                result += a[i] * b[i];
            return result;
        }

    private:
        double values[Dims];
    };

public:
    typedef point point_type;
    typedef point_difference point_difference_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 = boost::math::hypot(dist, diff);
        }
        // Exact properties of the distance are not important, as long as
        // < on what this returns matches real distances; l_2 is used because
        // Fruchterman-Reingold also uses this code and it relies on l_2.
        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;
    }

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

    point adjust(point a, point_difference delta) const
    {
        point result;
        for (std::size_t i = 0; i < Dims; ++i)
            result[i] = a[i] + delta[i];
        return result;
    }

    point pointwise_min(point a, point b) const
    {
        BOOST_USING_STD_MIN();
        point result;
        for (std::size_t i = 0; i < Dims; ++i)
            result[i] = min BOOST_PREVENT_MACRO_SUBSTITUTION(a[i], b[i]);
        return result;
    }

    point pointwise_max(point a, point b) const
    {
        BOOST_USING_STD_MAX();
        point result;
        for (std::size_t i = 0; i < Dims; ++i)
            result[i] = max BOOST_PREVENT_MACRO_SUBSTITUTION(a[i], b[i]);
        return result;
    }

    double norm(point_difference delta) const
    {
        double n = 0.;
        for (std::size_t i = 0; i < Dims; ++i)
            n = boost::math::hypot(n, delta[i]);
        return n;
    }

    double volume(point_difference delta) const
    {
        double n = 1.;
        for (std::size_t i = 0; i < Dims; ++i)
            n *= delta[i];
        return n;
    }
};

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;
    typedef typename convex_topology< Dims >::point_difference_type
        point_difference_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;
    }

    point_type bound(point_type a) const
    {
        BOOST_USING_STD_MIN();
        BOOST_USING_STD_MAX();
        point_type p;
        for (std::size_t i = 0; i < Dims; ++i)
            p[i] = min BOOST_PREVENT_MACRO_SUBSTITUTION(
                scaling, max BOOST_PREVENT_MACRO_SUBSTITUTION(-scaling, a[i]));
        return p;
    }

    double distance_from_boundary(point_type a) const
    {
        BOOST_USING_STD_MIN();
        BOOST_USING_STD_MAX();
#ifndef BOOST_NO_STDC_NAMESPACE
        using std::abs;
#endif
        BOOST_STATIC_ASSERT(Dims >= 1);
        double dist = abs(scaling - a[0]);
        for (std::size_t i = 1; i < Dims; ++i)
            dist = min BOOST_PREVENT_MACRO_SUBSTITUTION(
                dist, abs(scaling - a[i]));
        return dist;
    }

    point_type center() const
    {
        point_type result;
        for (std::size_t i = 0; i < Dims; ++i)
            result[i] = scaling * .5;
        return result;
    }

    point_type origin() const
    {
        point_type result;
        for (std::size_t i = 0; i < Dims; ++i)
            result[i] = 0;
        return result;
    }

    point_difference_type extent() const
    {
        point_difference_type result;
        for (std::size_t i = 0; i < Dims; ++i)
            result[i] = scaling;
        return result;
    }

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 rectangle_topology : public convex_topology< 2 >
{
    typedef uniform_01< RandomNumberGenerator, double > rand_t;

public:
    rectangle_topology(double left, double top, double right, double bottom)
    : gen_ptr(new RandomNumberGenerator)
    , rand(new rand_t(*gen_ptr))
    , left(std::min BOOST_PREVENT_MACRO_SUBSTITUTION(left, right))
    , top(std::min BOOST_PREVENT_MACRO_SUBSTITUTION(top, bottom))
    , right(std::max BOOST_PREVENT_MACRO_SUBSTITUTION(left, right))
    , bottom(std::max BOOST_PREVENT_MACRO_SUBSTITUTION(top, bottom))
    {
    }

    rectangle_topology(RandomNumberGenerator& gen, double left, double top,
        double right, double bottom)
    : gen_ptr()
    , rand(new rand_t(gen))
    , left(std::min BOOST_PREVENT_MACRO_SUBSTITUTION(left, right))
    , top(std::min BOOST_PREVENT_MACRO_SUBSTITUTION(top, bottom))
    , right(std::max BOOST_PREVENT_MACRO_SUBSTITUTION(left, right))
    , bottom(std::max BOOST_PREVENT_MACRO_SUBSTITUTION(top, bottom))
    {
    }

    typedef typename convex_topology< 2 >::point_type point_type;
    typedef typename convex_topology< 2 >::point_difference_type
        point_difference_type;

    point_type random_point() const
    {
        point_type p;
        p[0] = (*rand)() * (right - left) + left;
        p[1] = (*rand)() * (bottom - top) + top;
        return p;
    }

    point_type bound(point_type a) const
    {
        BOOST_USING_STD_MIN();
        BOOST_USING_STD_MAX();
        point_type p;
        p[0] = min BOOST_PREVENT_MACRO_SUBSTITUTION(
            right, max BOOST_PREVENT_MACRO_SUBSTITUTION(left, a[0]));
        p[1] = min BOOST_PREVENT_MACRO_SUBSTITUTION(
            bottom, max BOOST_PREVENT_MACRO_SUBSTITUTION(top, a[1]));
        return p;
    }

    double distance_from_boundary(point_type a) const
    {
        BOOST_USING_STD_MIN();
        BOOST_USING_STD_MAX();
#ifndef BOOST_NO_STDC_NAMESPACE
        using std::abs;
#endif
        double dist = abs(left - a[0]);
        dist = min BOOST_PREVENT_MACRO_SUBSTITUTION(dist, abs(right - a[0]));
        dist = min BOOST_PREVENT_MACRO_SUBSTITUTION(dist, abs(top - a[1]));
        dist = min BOOST_PREVENT_MACRO_SUBSTITUTION(dist, abs(bottom - a[1]));
        return dist;
    }

    point_type center() const
    {
        point_type result;
        result[0] = (left + right) / 2.;
        result[1] = (top + bottom) / 2.;
        return result;
    }

    point_type origin() const
    {
        point_type result;
        result[0] = left;
        result[1] = top;
        return result;
    }

    point_difference_type extent() const
    {
        point_difference_type result;
        result[0] = right - left;
        result[1] = bottom - top;
        return result;
    }

private:
    shared_ptr< RandomNumberGenerator > gen_ptr;
    shared_ptr< rand_t > rand;
    double left, top, right, bottom;
};

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;
    typedef typename convex_topology< Dims >::point_difference_type
        point_difference_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;
    }

    point_type bound(point_type a) const
    {
        BOOST_USING_STD_MIN();
        BOOST_USING_STD_MAX();
        double r = 0.;
        for (std::size_t i = 0; i < Dims; ++i)
            r = boost::math::hypot(r, a[i]);
        if (r <= radius)
            return a;
        double scaling_factor = radius / r;
        point_type p;
        for (std::size_t i = 0; i < Dims; ++i)
            p[i] = a[i] * scaling_factor;
        return p;
    }

    double distance_from_boundary(point_type a) const
    {
        double r = 0.;
        for (std::size_t i = 0; i < Dims; ++i)
            r = boost::math::hypot(r, a[i]);
        return radius - r;
    }

    point_type center() const
    {
        point_type result;
        for (std::size_t i = 0; i < Dims; ++i)
            result[i] = 0;
        return result;
    }

    point_type origin() const
    {
        point_type result;
        for (std::size_t i = 0; i < Dims; ++i)
            result[i] = -radius;
        return result;
    }

    point_difference_type extent() const
    {
        point_difference_type result;
        for (std::size_t i = 0; i < Dims; ++i)
            result[i] = 2. * radius;
        return result;
    }

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;
#endif

        if (p[1] < abs(p[0]) - 2000)
            return false; // Bottom
        if (p[1] <= -1000)
            return true; // Diagonal of square
        if (boost::math::hypot(p[0] - -500, p[1] - -500)
            <= 500. * boost::math::constants::root_two< double >())
            return true; // Left circle
        if (boost::math::hypot(p[0] - 500, p[1] - -500)
            <= 500. * boost::math::constants::root_two< double >())
            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
    {
        point result;
        do
        {
            result[0] = (*rand)()
                    * (1000
                        + 1000 * boost::math::constants::root_two< double >())
                - (500 + 500 * boost::math::constants::root_two< double >());
            result[1] = (*rand)()
                    * (2000
                        + 500
                            * (boost::math::constants::root_two< double >()
                                - 1))
                - 2000;
        } while (!in_heart(result));
        return result;
    }

    // Not going to provide clipping to bounding region or distance from
    // boundary

    double distance(point a, point b) const
    {
        if (segment_within_heart(a, b))
        {
            // Straight line
            return boost::math::hypot(b[0] - a[0], b[1] - a[1]);
        }
        else
        {
            // Straight line bending around (0, 0)
            return boost::math::hypot(a[0], a[1])
                + boost::math::hypot(b[0], b[1]);
        }
    }

    point move_position_toward(point a, double fraction, point b) const
    {
        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 = boost::math::hypot(a[0], a[1]);
            double distance_to_point_b = boost::math::hypot(b[0], 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_TOPOLOGY_HPP