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Edit:
/usr/include/boost/graph/topology.hpp
(20389B)
// 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/config/no_tr1/cmath.hpp> #include <cmath> #include <boost/random/uniform_01.hpp> #include <boost/random/linear_congruential.hpp> #include <boost/math/constants/constants.hpp> // For root_two #include <boost/algorithm/minmax.hpp> #include <boost/config.hpp> // For BOOST_STATIC_CONSTANT #include <boost/math/special_functions/hypot.hpp> // 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
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