599 lines
18 KiB
C++
599 lines
18 KiB
C++
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// Copyright 2009 The Trustees of Indiana University.
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// Distributed under the Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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// Authors: Jeremiah Willcock
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// Douglas Gregor
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// Andrew Lumsdaine
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#ifndef BOOST_GRAPH_TOPOLOGY_HPP
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#define BOOST_GRAPH_TOPOLOGY_HPP
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#include <boost/config/no_tr1/cmath.hpp>
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#include <cmath>
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#include <boost/random/uniform_01.hpp>
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#include <boost/random/linear_congruential.hpp>
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#include <boost/math/constants/constants.hpp> // For root_two
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#include <boost/algorithm/minmax.hpp>
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#include <boost/config.hpp> // For BOOST_STATIC_CONSTANT
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#include <boost/math/special_functions/hypot.hpp>
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// Classes and concepts to represent points in a space, with distance and move
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// operations (used for Gurson-Atun layout), plus other things like bounding
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// boxes used for other layout algorithms.
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namespace boost {
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/***********************************************************
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* Topologies *
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***********************************************************/
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template<std::size_t Dims>
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class convex_topology
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{
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public: // For VisualAge C++
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struct point
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{
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BOOST_STATIC_CONSTANT(std::size_t, dimensions = Dims);
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point() { }
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double& operator[](std::size_t i) {return values[i];}
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const double& operator[](std::size_t i) const {return values[i];}
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private:
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double values[Dims];
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};
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public: // For VisualAge C++
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struct point_difference
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{
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BOOST_STATIC_CONSTANT(std::size_t, dimensions = Dims);
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point_difference() {
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for (std::size_t i = 0; i < Dims; ++i) values[i] = 0.;
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}
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double& operator[](std::size_t i) {return values[i];}
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const double& operator[](std::size_t i) const {return values[i];}
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friend point_difference operator+(const point_difference& a, const point_difference& b) {
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point_difference result;
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for (std::size_t i = 0; i < Dims; ++i)
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result[i] = a[i] + b[i];
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return result;
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}
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friend point_difference& operator+=(point_difference& a, const point_difference& b) {
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for (std::size_t i = 0; i < Dims; ++i)
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a[i] += b[i];
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return a;
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}
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friend point_difference operator-(const point_difference& a) {
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point_difference result;
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for (std::size_t i = 0; i < Dims; ++i)
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result[i] = -a[i];
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return result;
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}
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friend point_difference operator-(const point_difference& a, const point_difference& b) {
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point_difference result;
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for (std::size_t i = 0; i < Dims; ++i)
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result[i] = a[i] - b[i];
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return result;
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}
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friend point_difference& operator-=(point_difference& a, const point_difference& b) {
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for (std::size_t i = 0; i < Dims; ++i)
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a[i] -= b[i];
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return a;
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}
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friend point_difference operator*(const point_difference& a, const point_difference& b) {
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point_difference result;
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for (std::size_t i = 0; i < Dims; ++i)
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result[i] = a[i] * b[i];
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return result;
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}
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friend point_difference operator*(const point_difference& a, double b) {
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point_difference result;
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for (std::size_t i = 0; i < Dims; ++i)
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result[i] = a[i] * b;
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return result;
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}
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friend point_difference operator*(double a, const point_difference& b) {
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point_difference result;
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for (std::size_t i = 0; i < Dims; ++i)
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result[i] = a * b[i];
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return result;
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}
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friend point_difference operator/(const point_difference& a, const point_difference& b) {
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point_difference result;
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for (std::size_t i = 0; i < Dims; ++i)
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result[i] = (b[i] == 0.) ? 0. : a[i] / b[i];
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return result;
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}
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friend double dot(const point_difference& a, const point_difference& b) {
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double result = 0;
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for (std::size_t i = 0; i < Dims; ++i)
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result += a[i] * b[i];
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return result;
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}
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private:
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double values[Dims];
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};
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public:
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typedef point point_type;
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typedef point_difference point_difference_type;
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double distance(point a, point b) const
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{
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double dist = 0.;
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for (std::size_t i = 0; i < Dims; ++i) {
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double diff = b[i] - a[i];
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dist = boost::math::hypot(dist, diff);
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}
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// Exact properties of the distance are not important, as long as
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// < on what this returns matches real distances; l_2 is used because
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// Fruchterman-Reingold also uses this code and it relies on l_2.
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return dist;
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}
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point move_position_toward(point a, double fraction, point b) const
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{
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point result;
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for (std::size_t i = 0; i < Dims; ++i)
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result[i] = a[i] + (b[i] - a[i]) * fraction;
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return result;
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}
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point_difference difference(point a, point b) const {
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point_difference result;
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for (std::size_t i = 0; i < Dims; ++i)
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result[i] = a[i] - b[i];
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return result;
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}
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point adjust(point a, point_difference delta) const {
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point result;
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for (std::size_t i = 0; i < Dims; ++i)
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result[i] = a[i] + delta[i];
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return result;
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}
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point pointwise_min(point a, point b) const {
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BOOST_USING_STD_MIN();
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point result;
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for (std::size_t i = 0; i < Dims; ++i)
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result[i] = min BOOST_PREVENT_MACRO_SUBSTITUTION (a[i], b[i]);
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return result;
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}
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point pointwise_max(point a, point b) const {
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BOOST_USING_STD_MAX();
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point result;
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for (std::size_t i = 0; i < Dims; ++i)
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result[i] = max BOOST_PREVENT_MACRO_SUBSTITUTION (a[i], b[i]);
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return result;
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}
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double norm(point_difference delta) const {
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double n = 0.;
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for (std::size_t i = 0; i < Dims; ++i)
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n = boost::math::hypot(n, delta[i]);
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return n;
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}
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double volume(point_difference delta) const {
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double n = 1.;
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for (std::size_t i = 0; i < Dims; ++i)
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n *= delta[i];
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return n;
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}
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};
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template<std::size_t Dims,
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typename RandomNumberGenerator = minstd_rand>
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class hypercube_topology : public convex_topology<Dims>
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{
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typedef uniform_01<RandomNumberGenerator, double> rand_t;
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public:
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typedef typename convex_topology<Dims>::point_type point_type;
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typedef typename convex_topology<Dims>::point_difference_type point_difference_type;
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explicit hypercube_topology(double scaling = 1.0)
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: gen_ptr(new RandomNumberGenerator), rand(new rand_t(*gen_ptr)),
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scaling(scaling)
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{ }
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hypercube_topology(RandomNumberGenerator& gen, double scaling = 1.0)
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: gen_ptr(), rand(new rand_t(gen)), scaling(scaling) { }
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point_type random_point() const
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{
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point_type p;
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for (std::size_t i = 0; i < Dims; ++i)
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p[i] = (*rand)() * scaling;
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return p;
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}
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point_type bound(point_type a) const
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{
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BOOST_USING_STD_MIN();
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BOOST_USING_STD_MAX();
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point_type p;
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for (std::size_t i = 0; i < Dims; ++i)
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p[i] = min BOOST_PREVENT_MACRO_SUBSTITUTION (scaling, max BOOST_PREVENT_MACRO_SUBSTITUTION (-scaling, a[i]));
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return p;
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}
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double distance_from_boundary(point_type a) const
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{
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BOOST_USING_STD_MIN();
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BOOST_USING_STD_MAX();
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#ifndef BOOST_NO_STDC_NAMESPACE
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using std::abs;
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#endif
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BOOST_STATIC_ASSERT (Dims >= 1);
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double dist = abs(scaling - a[0]);
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for (std::size_t i = 1; i < Dims; ++i)
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dist = min BOOST_PREVENT_MACRO_SUBSTITUTION (dist, abs(scaling - a[i]));
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return dist;
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}
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point_type center() const {
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point_type result;
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for (std::size_t i = 0; i < Dims; ++i)
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result[i] = scaling * .5;
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return result;
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}
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point_type origin() const {
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point_type result;
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for (std::size_t i = 0; i < Dims; ++i)
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result[i] = 0;
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return result;
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}
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point_difference_type extent() const {
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point_difference_type result;
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for (std::size_t i = 0; i < Dims; ++i)
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result[i] = scaling;
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return result;
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}
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private:
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shared_ptr<RandomNumberGenerator> gen_ptr;
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shared_ptr<rand_t> rand;
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double scaling;
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};
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template<typename RandomNumberGenerator = minstd_rand>
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class square_topology : public hypercube_topology<2, RandomNumberGenerator>
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{
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typedef hypercube_topology<2, RandomNumberGenerator> inherited;
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public:
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explicit square_topology(double scaling = 1.0) : inherited(scaling) { }
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square_topology(RandomNumberGenerator& gen, double scaling = 1.0)
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: inherited(gen, scaling) { }
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};
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template<typename RandomNumberGenerator = minstd_rand>
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class rectangle_topology : public convex_topology<2>
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{
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typedef uniform_01<RandomNumberGenerator, double> rand_t;
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public:
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rectangle_topology(double left, double top, double right, double bottom)
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: gen_ptr(new RandomNumberGenerator), rand(new rand_t(*gen_ptr)),
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left(std::min BOOST_PREVENT_MACRO_SUBSTITUTION (left, right)),
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top(std::min BOOST_PREVENT_MACRO_SUBSTITUTION (top, bottom)),
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right(std::max BOOST_PREVENT_MACRO_SUBSTITUTION (left, right)),
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bottom(std::max BOOST_PREVENT_MACRO_SUBSTITUTION (top, bottom)) { }
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rectangle_topology(RandomNumberGenerator& gen, double left, double top, double right, double bottom)
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: gen_ptr(), rand(new rand_t(gen)),
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left(std::min BOOST_PREVENT_MACRO_SUBSTITUTION (left, right)),
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top(std::min BOOST_PREVENT_MACRO_SUBSTITUTION (top, bottom)),
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right(std::max BOOST_PREVENT_MACRO_SUBSTITUTION (left, right)),
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bottom(std::max BOOST_PREVENT_MACRO_SUBSTITUTION (top, bottom)) { }
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typedef typename convex_topology<2>::point_type point_type;
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typedef typename convex_topology<2>::point_difference_type point_difference_type;
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point_type random_point() const
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{
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point_type p;
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p[0] = (*rand)() * (right - left) + left;
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p[1] = (*rand)() * (bottom - top) + top;
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return p;
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}
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point_type bound(point_type a) const
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{
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BOOST_USING_STD_MIN();
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BOOST_USING_STD_MAX();
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point_type p;
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p[0] = min BOOST_PREVENT_MACRO_SUBSTITUTION (right, max BOOST_PREVENT_MACRO_SUBSTITUTION (left, a[0]));
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p[1] = min BOOST_PREVENT_MACRO_SUBSTITUTION (bottom, max BOOST_PREVENT_MACRO_SUBSTITUTION (top, a[1]));
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return p;
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}
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double distance_from_boundary(point_type a) const
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{
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BOOST_USING_STD_MIN();
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BOOST_USING_STD_MAX();
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#ifndef BOOST_NO_STDC_NAMESPACE
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using std::abs;
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#endif
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double dist = abs(left - a[0]);
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dist = min BOOST_PREVENT_MACRO_SUBSTITUTION (dist, abs(right - a[0]));
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dist = min BOOST_PREVENT_MACRO_SUBSTITUTION (dist, abs(top - a[1]));
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dist = min BOOST_PREVENT_MACRO_SUBSTITUTION (dist, abs(bottom - a[1]));
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return dist;
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}
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point_type center() const {
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point_type result;
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result[0] = (left + right) / 2.;
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result[1] = (top + bottom) / 2.;
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return result;
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}
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point_type origin() const {
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point_type result;
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result[0] = left;
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result[1] = top;
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return result;
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}
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point_difference_type extent() const {
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point_difference_type result;
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result[0] = right - left;
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result[1] = bottom - top;
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return result;
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}
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private:
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shared_ptr<RandomNumberGenerator> gen_ptr;
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shared_ptr<rand_t> rand;
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double left, top, right, bottom;
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};
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|
|
||
|
|
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
|