    // Copyright (C) 2008  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.

    #include <dlib/geometry.h>
    #include <sstream>
    #include <string>
    #include <cstdlib>
    #include <ctime>
    #include <dlib/string.h>
    #include <dlib/matrix.h>
    #include <dlib/rand.h>
    #include <dlib/array2d.h>
    #include <dlib/image_transforms.h>

    #include "tester.h"

    namespace
    {

        using namespace test;
        using namespace dlib;
        using namespace std;

        logger dlog("test.geometry");

        void geometry_test (
        )
        /*!
            ensures
                - runs tests on the geometry stuff compliance with the specs
        !*/
        {
            print_spinner();

            point p1;
            point p2(2,3);

            DLIB_TEST(p1.x() == 0);
            DLIB_TEST(p1.y() == 0);
            DLIB_TEST(p2.x() == 2);
            DLIB_TEST(p2.y() == 3);

            DLIB_TEST((-p2).x() == -2);
            DLIB_TEST((-p2).y() == -3);

            p2 += p2;
            DLIB_TEST(p2.x() == 4);
            DLIB_TEST(p2.y() == 6);

            dlib::vector<double> v1 = point(1,0);
            dlib::vector<double> v2(0,0,1);

            p1 = v2.cross(v1);
            DLIB_TEST(p1 == point(0,1));
            DLIB_TEST(p1 != point(1,1));
            DLIB_TEST(p1 != point(1,0));

            p1 = point(2,3);
            rectangle rect1 = p1;
            DLIB_TEST(rect1.width() == 1);
            DLIB_TEST(rect1.height() == 1);
            p2 = point(1,1);

            rect1 += p2;
            DLIB_TEST(rect1.left() == 1);
            DLIB_TEST(rect1.top() == 1);
            DLIB_TEST(rect1.right() == 2);
            DLIB_TEST(rect1.bottom() == 3);

            DLIB_TEST(rect1.width() == 2);
            DLIB_TEST(rect1.height() == 3);

            // test the iostream << and >> operators (via string_cast and cast_to_string)
            DLIB_TEST(string_cast<point>(" (1, 2 )") == point(1,2));
            DLIB_TEST(string_cast<point>(" ( -1, 2 )") == point(-1,2));
            DLIB_TEST(string_cast<rectangle>(" [(1, 2 )(3,4)]") == rectangle(1,2,3,4));
            DLIB_TEST(string_cast<dlib::vector<double> >(" (1, 2 , 3.5)") == dlib::vector<double>(1,2,3.5));

            DLIB_TEST(string_cast<rectangle>(cast_to_string(rect1)) == rect1);
            DLIB_TEST(string_cast<point>(cast_to_string(p1)) == p1);
            DLIB_TEST(string_cast<dlib::vector<double> >(cast_to_string(v1)) == v1);

            rectangle rect2;

            // test the serialization code
            ostringstream sout;
            serialize(rect1,sout);
            serialize(p1,sout);
            serialize(v1,sout);
            serialize(rect1,sout);
            serialize(p1,sout);
            serialize(v1,sout);

            istringstream sin(sout.str());

            deserialize(rect2,sin);
            deserialize(p2,sin);
            deserialize(v2,sin);
            DLIB_TEST(rect2 == rect1);
            DLIB_TEST(p2 == p1);
            DLIB_TEST(v2 == v1);
            deserialize(rect2,sin);
            deserialize(p2,sin);
            deserialize(v2,sin);
            DLIB_TEST(rect2 == rect1);
            DLIB_TEST(p2 == p1);
            DLIB_TEST(v2 == v1);
            DLIB_TEST(sin.good());
            DLIB_TEST(sin.get() == EOF);

            v1.x() = 1;
            v1.y() = 2;
            v1.z() = 3;

            matrix<double> mv = v1;
            DLIB_TEST(mv.nr() == 3);
            DLIB_TEST(mv.nc() == 1);
            DLIB_TEST(mv(0) == 1);
            DLIB_TEST(mv(1) == 2);
            DLIB_TEST(mv(2) == 3);

            set_all_elements(mv,0);
            DLIB_TEST(mv(0) == 0);
            DLIB_TEST(mv(1) == 0);
            DLIB_TEST(mv(2) == 0);

            mv(0) = 5;
            mv(1) = 6;
            mv(2) = 7;

            v1 = mv;
            DLIB_TEST(v1.x() == 5);
            DLIB_TEST(v1.y() == 6);
            DLIB_TEST(v1.z() == 7);

            {
                dlib::vector<double,2> vd2;
                dlib::vector<double,3> vd3;
                dlib::vector<long,2> vl2;
                dlib::vector<long,3> vl3;

                vd2.x() = 2.3;
                vd2.y() = 4.7;

                vd3.z() = 9;

                vd3 = vd2;

                vl2 = vd3;
                vl3 = vd3;

                DLIB_TEST(vd2.z() == 0);
                DLIB_TEST(vd3.z() == 0);
                DLIB_TEST(vl2.z() == 0);
                DLIB_TEST(vl3.z() == 0);

                DLIB_TEST(vl2.x() == 2);
                DLIB_TEST(vl3.x() == 2);
                DLIB_TEST(vl2.y() == 5);
                DLIB_TEST(vl3.y() == 5);

                DLIB_TEST(abs(vd2.cross(vd3).dot(vd2)) < 1e-7);
                DLIB_TEST(abs(vd3.cross(vd2).dot(vd2)) < 1e-7);
                DLIB_TEST(abs(vd2.cross(vd3).dot(vd3)) < 1e-7);
                DLIB_TEST(abs(vd3.cross(vd2).dot(vd3)) < 1e-7);

                DLIB_TEST(abs(vl2.cross(vl3).dot(vl2)) == 0);
                DLIB_TEST(abs(vl3.cross(vl2).dot(vl2)) == 0);
                DLIB_TEST(abs(vl2.cross(vl3).dot(vl3)) == 0);
                DLIB_TEST(abs(vl3.cross(vl2).dot(vl3)) == 0);

                DLIB_TEST((vd2-vd3).length() < 1e-7);

                DLIB_TEST(vl2 == vl3);

                vl2.x() = 0;
                vl2.y() = 0;
                vl3 = vl2;

                vl2.x() = 4;
                vl3.y() = 3;

                DLIB_TEST(vl2.cross(vl3).length() == 12);
                DLIB_TEST(vl3.cross(vl2).length() == 12);

                matrix<double> m(3,3);
                m = 1,2,3,
                    4,5,6,
                    7,8,9;

                vd3.x() = 2;
                vd3.y() = 3;
                vd3.z() = 4;

                vd3 = m*vd3;

                DLIB_TEST_MSG(vd3.x() == 1*2 + 2*3 + 3*4,vd3.x() << " == " << (1*2 + 2*3 + 3*4));
                DLIB_TEST(vd3.y() == 4*2 + 5*3 + 6*4);
                DLIB_TEST(vd3.z() == 7*2 + 8*3 + 9*4);

                (vd3*2).dot(vd3);
                (vd2*2).dot(vd3);
                (vd3*2).dot(vd2);
                (vd2*2).dot(vd2);
                (2*vd3*2).dot(vd3);
                (2*vd2*2).dot(vd3);
                (2*vd3*2).dot(vd2);
                (2*vd2*2).dot(vd2);

                (vd2 + vd3).dot(vd2);
                (vd2 - vd3).dot(vd2);
                (vd2/2).dot(vd2);
                (vd3/2).dot(vd2);
            }

            {
                dlib::vector<double,2> vd2;
                dlib::vector<long,3> vl3;

                vl3.x() = 1;
                vl3.y() = 2;
                vl3.z() = 3;

                vd2.x() = 6.5;
                vd2.y() = 7.5;

                DLIB_TEST((vl3 + vd2).x() == 1+6.5);
                DLIB_TEST((vl3 + vd2).y() == 2+7.5);
                DLIB_TEST((vl3 + vd2).z() == 3+0);

                DLIB_TEST((vl3 - vd2).x() == 1-6.5);
                DLIB_TEST((vl3 - vd2).y() == 2-7.5);
                DLIB_TEST((vl3 - vd2).z() == 3-0);

            }

            {
                dlib::vector<double> v(3,4,5);
                DLIB_TEST((-v).x() == -3.0);
                DLIB_TEST((-v).y() == -4.0);
                DLIB_TEST((-v).z() == -5.0);
            }

            {
                rectangle rect;

                point tl(2,3);
                point tr(8,3);
                point bl(2,9);
                point br(8,9);

                rect += tl;
                rect += tr;
                rect += bl;
                rect += br;

                DLIB_TEST(rect.tl_corner() == tl);
                DLIB_TEST(rect.tr_corner() == tr);
                DLIB_TEST(rect.bl_corner() == bl);
                DLIB_TEST(rect.br_corner() == br);

            }

            {
                point p1, center;

                center = point(3,4);
                p1 = point(10,4);

                DLIB_TEST(rotate_point(center, p1, pi/2) == point(3,7+4));

                center = point(3,3);
                p1 = point(10,3);

                DLIB_TEST(rotate_point(center, p1, pi/4) == point(8,8));
                DLIB_TEST(rotate_point(center, p1, -pi/4) == point(8,-2));

                DLIB_TEST(rotate_point(center, p1, pi/4 + 10*pi) == point(8,8));
                DLIB_TEST(rotate_point(center, p1, -pi/4 + 10*pi) == point(8,-2));
                DLIB_TEST(rotate_point(center, p1, pi/4 - 10*pi) == point(8,8));
                DLIB_TEST(rotate_point(center, p1, -pi/4 - 10*pi) == point(8,-2));

                point_rotator rot(pi/2);
                DLIB_TEST(rot(point(1,0)) == point(0,1));
                DLIB_TEST(rot(point(0,1)) == point(-1,0));
                DLIB_TEST(point(rot.get_m()*(dlib::vector<double,2>(1,0))) == point(0,1));
                DLIB_TEST(point(rot.get_m()*(dlib::vector<double,2>(0,1))) == point(-1,0));
            }

            {
                rectangle rect;

                rect = grow_rect(rect,1);
                DLIB_TEST(rect.width() == 2);
                DLIB_TEST(rect.height() == 2);
                DLIB_TEST(rect.left() == -1);
                DLIB_TEST(rect.top() == -1);
                DLIB_TEST(rect.right() == 0);
                DLIB_TEST(rect.bottom() == 0);
            }
            {
                rectangle rect;

                rect = grow_rect(rect,2);
                DLIB_TEST(rect.width() == 4);
                DLIB_TEST(rect.height() == 4);
                DLIB_TEST(rect.left() == -2);
                DLIB_TEST(rect.top() == -2);
                DLIB_TEST(rect.right() == 1);
                DLIB_TEST(rect.bottom() == 1);

                rect = shrink_rect(rect,1);
                DLIB_TEST(rect.width() == 2);
                DLIB_TEST(rect.height() == 2);
                DLIB_TEST(rect.left() == -1);
                DLIB_TEST(rect.top() == -1);
                DLIB_TEST(rect.right() == 0);
                DLIB_TEST(rect.bottom() == 0);
            }
            {
                std::vector< dlib::vector<double> > a;

                dlib::vector<double> v;
                dlib::rand rnd;

                for (int i = 0; i < 10; ++i)
                {
                    v.x() = rnd.get_random_double();
                    v.y() = rnd.get_random_double();
                    v.z() = rnd.get_random_double();
                    a.push_back(v);

                }

                // This test is just to make sure the covariance function can compile when used
                // on a dlib::vector.  The actual test doesn't matter.
                DLIB_TEST(sum(covariance(mat(a))) < 10);

            }

            DLIB_TEST(rectangle() + point(5,4) + point(10,10) == rectangle(5,4,10,10));

            // make sure the center of a centered rectangle is always right
            for (long x = -10; x <= 10; ++x)
            {
                for (long y = -10; y <= 10; ++y)
                {
                    for (long w = 0; w < 10; ++w)
                    {
                        for (long h = 0; h < 10; ++h)
                        {
                            DLIB_TEST(center(centered_rect(x,y,w,h)) == point(x,y));
                        }
                    }
                }
            }

        }

    // ----------------------------------------------------------------------------------------

        void test_border_enumerator()
        {

            border_enumerator be;
            DLIB_TEST(be.at_start() == true);
            DLIB_TEST(be.size() == 0);
            DLIB_TEST(be.current_element_valid() == false);
            DLIB_TEST(be.move_next() == false);
            DLIB_TEST(be.at_start() == false);
            DLIB_TEST(be.current_element_valid() == false);
            DLIB_TEST(be.move_next() == false);
            DLIB_TEST(be.at_start() == false);
            DLIB_TEST(be.current_element_valid() == false);
            DLIB_TEST(be.size() == 0);

            be = border_enumerator(rectangle(4,4,4,4),1);
            DLIB_TEST(be.at_start() == true);
            DLIB_TEST(be.size() == 1);
            be = border_enumerator(rectangle(4,4,4,4),3);
            DLIB_TEST(be.at_start() == true);
            DLIB_TEST(be.size() == 1);
            be = border_enumerator(rectangle(4,4,4,4),0);
            DLIB_TEST(be.at_start() == true);
            DLIB_TEST(be.size() == 0);
            be = border_enumerator(rectangle(4,4,5,5),0);
            DLIB_TEST(be.at_start() == true);
            DLIB_TEST(be.size() == 0);
            be = border_enumerator(rectangle(4,4,5,5),1);
            DLIB_TEST(be.at_start() == true);
            DLIB_TEST(be.size() == 4);
            be = border_enumerator(rectangle(4,4,5,5),2);
            DLIB_TEST(be.size() == 4);
            be = border_enumerator(rectangle(4,4,6,6),1);
            DLIB_TEST(be.size() == 8);
            be = border_enumerator(rectangle(4,4,6,6),2);
            DLIB_TEST(be.size() == 9);
            be = border_enumerator(rectangle(4,4,6,6),3);
            DLIB_TEST(be.size() == 9);
            DLIB_TEST(be.at_start() == true);

            array2d<unsigned char> img, img2;
            for (int size = 1; size < 10; ++size)
            {
                for (int bs = 0; bs < 4; ++bs)
                {
                    img.set_size(size,size);
                    img2.set_size(size,size);

                    assign_all_pixels(img, 1);
                    assign_all_pixels(img2, 1);

                    zero_border_pixels(img2, bs,bs);

                    be = border_enumerator(get_rect(img),bs);
                    DLIB_TEST(be.at_start() == true);
                    DLIB_TEST(be.current_element_valid() == false);
                    while (be.move_next())
                    {
                        DLIB_TEST(be.at_start() == false);
                        DLIB_TEST(be.current_element_valid() == true);
                        DLIB_TEST_MSG(get_rect(img).contains(be.element()) == true,
                                     get_rect(img) << "   " << be.element()
                        );
                        const point p = be.element();
                        img[p.y()][p.x()] = 0;
                    }
                    DLIB_TEST(be.at_start() == false);
                    DLIB_TEST(be.current_element_valid() == false);
                    DLIB_TEST(be.move_next() == false);
                    DLIB_TEST(be.current_element_valid() == false);
                    DLIB_TEST(be.move_next() == false);
                    DLIB_TEST(be.current_element_valid() == false);
                    DLIB_TEST(be.at_start() == false);

                    DLIB_TEST(mat(img) == mat(img2));

                }
            }

            for (int size = 1; size < 10; ++size)
            {
                for (int bs = 0; bs < 4; ++bs)
                {
                    img.set_size(size,size+5);
                    img2.set_size(size,size+5);

                    assign_all_pixels(img, 1);
                    assign_all_pixels(img2, 1);

                    zero_border_pixels(img2, bs,bs);

                    const point shift(4,5);

                    be = border_enumerator(translate_rect(get_rect(img),shift),bs);
                    DLIB_TEST(be.at_start() == true);
                    DLIB_TEST(be.current_element_valid() == false);
                    while (be.move_next())
                    {
                        DLIB_TEST(be.current_element_valid() == true);
                        DLIB_TEST(be.at_start() == false);
                        DLIB_TEST_MSG(get_rect(img).contains(be.element()-shift) == true,
                                     get_rect(img) << "   " << be.element()
                        );
                        const point p = be.element()-shift;
                        img[p.y()][p.x()] = 0;
                    }
                    DLIB_TEST(be.current_element_valid() == false);
                    DLIB_TEST(be.move_next() == false);
                    DLIB_TEST(be.current_element_valid() == false);
                    DLIB_TEST(be.move_next() == false);
                    DLIB_TEST(be.current_element_valid() == false);
                    DLIB_TEST(be.at_start() == false);

                    DLIB_TEST(mat(img) == mat(img2));

                }
            }

            for (int size = 1; size < 10; ++size)
            {
                for (int bs = 0; bs < 4; ++bs)
                {
                    img.set_size(size+2,size);
                    img2.set_size(size+2,size);

                    assign_all_pixels(img, 1);
                    assign_all_pixels(img2, 1);

                    zero_border_pixels(img2, bs,bs);

                    const point shift(-4,5);

                    be = border_enumerator(translate_rect(get_rect(img),shift),bs);
                    DLIB_TEST(be.current_element_valid() == false);
                    while (be.move_next())
                    {
                        DLIB_TEST(be.current_element_valid() == true);
                        DLIB_TEST_MSG(get_rect(img).contains(be.element()-shift) == true,
                                     get_rect(img) << "   " << be.element()
                        );
                        const point p = be.element()-shift;
                        img[p.y()][p.x()] = 0;
                    }
                    DLIB_TEST(be.current_element_valid() == false);
                    DLIB_TEST(be.move_next() == false);
                    DLIB_TEST(be.current_element_valid() == false);
                    DLIB_TEST(be.move_next() == false);
                    DLIB_TEST(be.current_element_valid() == false);

                    DLIB_TEST(mat(img) == mat(img2));

                }
            }

            {
                matrix<bool,4,5> hits, truth;
                const rectangle rect = rectangle(1,1,4,3);

                border_enumerator be(rect, rectangle(2,2, 3, 3));
                DLIB_TEST(be.size() == 8);
                hits = false;
                while (be.move_next())
                {
                    DLIB_TEST(rect.contains(be.element()));
                    hits(be.element().y(), be.element().x()) = true;
                }
                DLIB_TEST(be.current_element_valid() == false);
                DLIB_TEST(be.size() == 8);
                truth = false;
                truth(1,1) = truth(1,2) = truth(1,3) = truth(1,4) = truth(2,1) =
                    truth(3,1) = truth(2,4) = truth(3,4) = true;
                DLIB_TEST_MSG(truth == hits, truth << endl << hits);

                be = border_enumerator(rect, rectangle(0,0, 9, 9));
                DLIB_TEST(be.size() == 0);
                hits = false;
                while (be.move_next())
                {
                    DLIB_TEST(rect.contains(be.element()));
                    hits(be.element().y(), be.element().x()) = true;
                }
                DLIB_TEST(be.current_element_valid() == false);
                DLIB_TEST(be.size() == 0);
                truth = false;
                DLIB_TEST(truth == hits);

                be = border_enumerator(rect, rectangle(0,0, 3, 9));
                DLIB_TEST(be.size() == 3);
                hits = false;
                while (be.move_next())
                {
                    DLIB_TEST(rect.contains(be.element()));
                    hits(be.element().y(), be.element().x()) = true;
                }
                DLIB_TEST(be.current_element_valid() == false);
                DLIB_TEST(be.size() == 3);
                truth = false;
                truth(1,4) = truth(2,4) = truth(3,4) = true;
                DLIB_TEST(truth == hits);

                be = border_enumerator(rect, rectangle(2,1, 4, 3));
                DLIB_TEST(be.size() == 3);
                hits = false;
                while (be.move_next())
                {
                    DLIB_TEST(rect.contains(be.element()));
                    hits(be.element().y(), be.element().x()) = true;
                }
                DLIB_TEST(be.current_element_valid() == false);
                DLIB_TEST(be.size() == 3);
                truth = false;
                truth(1,1) = truth(2,1) = truth(3,1) = true;
                DLIB_TEST(truth == hits);

                be = border_enumerator(rect, rectangle(1,1, 5, 2));
                DLIB_TEST(be.size() == 4);
                hits = false;
                while (be.move_next())
                {
                    DLIB_TEST(rect.contains(be.element()));
                    hits(be.element().y(), be.element().x()) = true;
                }
                DLIB_TEST(be.current_element_valid() == false);
                DLIB_TEST(be.size() == 4);
                truth = false;
                truth(3,1) = truth(3,2) = truth(3,3) = truth(3,4) = true;
                DLIB_TEST(truth == hits);

            }

        }

    // ----------------------------------------------------------------------------------------

        void test_find_affine_transform()
        {
            //typedef dlib::vector<double,2> vect;
            typedef point vect;
            std::vector<vect> from, to;

            from.push_back(vect(0,0));
            to.push_back(vect(0,1));

            from.push_back(vect(0,1));
            to.push_back(vect(1,1));

            from.push_back(vect(1,1));
            to.push_back(vect(1,0));

            from.push_back(vect(1,0));
            to.push_back(vect(0,0));

            point_transform_affine t = find_affine_transform(from,to);
            point_transform_affine tinv = inv(t);

            for (unsigned long i = 0; i < from.size(); ++i)
            {
                dlog << LINFO << "affine transformation error: "<< length(t(from[i])-to[i]);
                DLIB_TEST(length(t(from[i])-to[i]) < 1e-14);
                DLIB_TEST(length(tinv(t(from[i]))-from[i]) < 1e-14);
                DLIB_TEST(length(t(tinv(from[i]))-from[i]) < 1e-14);

                point_transform_affine temp = t*inv(t);
                DLIB_TEST(length(temp.get_b()) < 1e-14);
                DLIB_TEST(max(abs(temp.get_m() - identity_matrix<double>(2))) < 1e-14);
            }

            ostringstream sout;
            serialize(t, sout);
            istringstream sin(sout.str());
            point_transform_affine t2;
            DLIB_TEST(length(t2(point(2,3)) - point(2,3)) < 1e-14);
            deserialize(t2, sin);
            DLIB_TEST(max(abs(t2.get_m()-t.get_m())) < 1e-14);
            DLIB_TEST(max(abs(t2.get_b()-t.get_b())) < 1e-14);
        }

    // ----------------------------------------------------------------------------------------

        double projective_transform_pass_rate(const double error_rate)
        {
            print_spinner();
            dlog << LINFO << "projective_transform_pass_rate, error_rate: "<< error_rate;
            dlib::rand rnd;
            running_stats<double> pass_rate;
            for (int rounds = 0; rounds < 1000; ++rounds)
            {
                running_stats<double> rs, rs_true;
                matrix<double> H = 2*(randm(3,3,rnd)-0.5);

                H(0,2) = rnd.get_random_gaussian()*10;
                H(1,2) = rnd.get_random_gaussian()*10;

                H(2,0) = rnd.get_random_double()*2.1;
                H(2,1) = rnd.get_random_double()*2.1;
                H(2,2) = 1 + rnd.get_random_gaussian()*3.1;

                point_transform_projective tran(H);
                point_transform_projective traninv = inv(tran);

                const int num = rnd.get_random_32bit_number()%8 + 4;

                std::vector<dlib::vector<double,2> > from_points, to_points;
                for (int i = 0; i < num; ++i)
                {
                    dlib::vector<double,2> p = randm(2,1,rnd)*1000;
                    from_points.push_back(p);
                    to_points.push_back(tran(p) + (randm(2,1,rnd)-0.5)*error_rate);
                    DLIB_TEST(length(traninv(tran(p))-p) <= 1e-5);
                    DLIB_TEST(length(tran(traninv(p))-p) <= 1e-5);

                    point_transform_projective temp = tran*traninv;
                    DLIB_TEST_MSG(max(abs(temp.get_m() - identity_matrix<double>(3))) < 1e-10, temp.get_m());
                    temp = traninv*tran;
                    DLIB_TEST_MSG(max(abs(temp.get_m() - identity_matrix<double>(3))) < 1e-10, temp.get_m());
                }

                point_transform_projective tran2 = find_projective_transform(from_points, to_points);

                for (unsigned long i = 0; i < from_points.size(); ++i)
                {
                    const double err = length_squared(tran2(from_points[i]) - to_points[i]);
                    rs.add(err);
                    const double err_true = length_squared(tran(from_points[i]) - to_points[i]);
                    rs_true.add(err_true);
                }

                if ( rs.mean() < 0.01)
                {
                    pass_rate.add(1);
                }
                else
                {
                    dlog << LINFO << " errors: mean/max: " << rs.mean() << "  " << rs.max();
                    pass_rate.add(0);
                }

                ostringstream sout;
                serialize(tran, sout);
                istringstream sin(sout.str());
                point_transform_projective tran3;
                DLIB_TEST(length(tran3(point(2,3)) - point(2,3)) < 1e-14);
                deserialize(tran3, sin);
                DLIB_TEST(max(abs(tran3.get_m()-tran.get_m())) < 1e-14);
            }

            dlog << LINFO << " pass_rate.mean(): "<< pass_rate.mean();
            return pass_rate.mean();
        }

    // ----------------------------------------------------------------------------------------

        template <typename T>
        void test_find_similarity_transform()
        {
            print_spinner();
            std::vector<dlib::vector<T,2> > from_points, to_points;

            from_points.push_back(dlib::vector<T,2>(0,0));
            from_points.push_back(dlib::vector<T,2>(0,1));
            from_points.push_back(dlib::vector<T,2>(1,0));

            to_points.push_back(dlib::vector<T,2>(8,0));
            to_points.push_back(dlib::vector<T,2>(6,0));
            to_points.push_back(dlib::vector<T,2>(8,2));

            point_transform_affine tform = find_similarity_transform(from_points, to_points);

            for (unsigned long i = 0; i < from_points.size(); ++i)
            {
                DLIB_TEST(length(tform(from_points[i]) - to_points[i]) < 1e-14);
            }
        }

        template <typename T>
        void test_find_similarity_transform2()
        {
            print_spinner();
            std::vector<dlib::vector<T,2> > from_points, to_points;

            from_points.push_back(dlib::vector<T,2>(0,0));
            from_points.push_back(dlib::vector<T,2>(0,1));

            to_points.push_back(dlib::vector<T,2>(8,0));
            to_points.push_back(dlib::vector<T,2>(6,0));

            point_transform_affine tform = find_similarity_transform(from_points, to_points);

            for (unsigned long i = 0; i < from_points.size(); ++i)
            {
                DLIB_TEST(length(tform(from_points[i]) - to_points[i]) < 1e-14);
            }
        }

    // ----------------------------------------------------------------------------------------

        void test_rect_to_drect()
        {
            print_spinner();
            dlib::rand rnd;
            for (int i = 0; i < 5000; ++i)
            {
                rectangle rect = centered_rect(rnd.get_random_32bit_number()%100,
                    rnd.get_random_32bit_number()%100,
                    rnd.get_random_32bit_number()%100,
                    rnd.get_random_32bit_number()%100);

                drectangle drect = rect;
                rectangle rect2 = drect;
                DLIB_TEST(rect2 == rect);
                DLIB_TEST(rect.width() == drect.width());
                DLIB_TEST(rect.height() == drect.height());
                DLIB_TEST(dcenter(rect) == dcenter(drect));
                DLIB_TEST(rect.is_empty() == drect.is_empty());
            }
        }

    // ----------------------------------------------------------------------------------------

        void test_affine3d()
        {
            const dlib::vector<double> x(1,0,0);
            const dlib::vector<double> y(0,1,0);
            const dlib::vector<double> z(0,0,1);
            const dlib::vector<double> e(1,1,1);
            const dlib::vector<double> ex(-1,1,1);
            const dlib::vector<double> ey(1,-1,1);
            const dlib::vector<double> ez(1,1,-1);

            dlib::vector<double> w;

            w = rotate_around_z(pi/2)(x);
            DLIB_TEST(length(w-y) < 1e-12);
            w = rotate_around_z(pi/2)(e);
            DLIB_TEST(length(w-ex) < 1e-12);

            w = rotate_around_y(-pi/2)(x);
            DLIB_TEST(length(w-z) < 1e-12);
            w = rotate_around_y(pi/2)(e);
            DLIB_TEST(length(w-ez) < 1e-12);

            w = rotate_around_x(pi/2)(y);
            DLIB_TEST(length(w-z) < 1e-12);
            w = rotate_around_x(pi/2)(e);
            DLIB_TEST(length(w-ey) < 1e-12);

            w = translate_point(x)(y);
            DLIB_TEST(length(w-x-y) < 1e-12);

            point_transform_affine3d tform;
            tform = rotate_around_x(pi/2)*rotate_around_z(pi/2)*translate_point(x);
            DLIB_TEST(length(tform(dlib::vector<double>())-z) < 1e-12);
            DLIB_TEST(length(inv(tform)(z)) < 1e-12);

            point_transform_affine tform2;
            tform = tform*tform2;// the default tform is the identity mapping so this shouldn't do anything different
            DLIB_TEST(length(tform(dlib::vector<double>())-z) < 1e-12);
            DLIB_TEST(length(inv(tform)(z)) < 1e-12);
        }

    // ----------------------------------------------------------------------------------------

        class geometry_tester : public tester
        {
        public:
            geometry_tester (
            ) :
                tester ("test_geometry",
                        "Runs tests on the geometry stuff.")
            {}

            void perform_test (
            )
            {
                test_affine3d();
                test_rect_to_drect();
                geometry_test();
                test_border_enumerator();
                test_find_affine_transform();
                DLIB_TEST(projective_transform_pass_rate(0.1) > 0.99);
                DLIB_TEST(projective_transform_pass_rate(0.0) == 1);

                test_find_similarity_transform<double>();
                test_find_similarity_transform2<double>();
                test_find_similarity_transform<float>();
                test_find_similarity_transform2<float>();
            }
        } a;

    }