dlib C++ Library - geometry.cpp

// 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));
 }
 }
 }
 }
 {
 const rectangle input(1,1,6,4); 
 const rectangle output = set_rect_area(input,4*input.area());
 DLIB_TEST(output.area() == 4*input.area());
 DLIB_TEST(output.width() == 2*input.width());
 DLIB_TEST(output.height() == 2*input.height());
 const auto input_center = center(input);
 const auto output_center = center(output);
 DLIB_TEST(std::abs(input_center.x() - output_center.x()) <= 1);
 DLIB_TEST(std::abs(input_center.y() - output_center.y()) <= 1);
 }
 }
// ----------------------------------------------------------------------------------------
 void test_find_convex_hull()
 {
 print_spinner();
 std::vector<dpoint> points{
 { 0.0, 0.0 },
 { 1.0, 1.0 },
 { 2.0, 2.0 },
 { 3.0, 1.0 },
 { 4.0, 0.0 },
 { 2.0, 4.0 },
 { 1.0, 3.0 },
 };
 const auto hull = find_convex_hull(points);
 DLIB_TEST(hull.size() == 4);
 DLIB_TEST(hull[0] == dpoint(0, 0));
 DLIB_TEST(hull[1] == dpoint(1, 3));
 DLIB_TEST(hull[2] == dpoint(2, 4));
 DLIB_TEST(hull[3] == dpoint(4, 0));
 }
// ----------------------------------------------------------------------------------------
 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);
 }
// ----------------------------------------------------------------------------------------
 
 void test_line()
 {
 print_spinner();
 line l1(point(0,1),point(1,0));
 line l2(point(0,0),point(1,1));
 DLIB_TEST(length(intersect(l1,l2) - dpoint(0.5,0.5)) < 1e-12);
 DLIB_TEST(std::abs(distance_to_line(l1, l1.p1())) < 1e-12);
 DLIB_TEST(std::abs(distance_to_line(l1, dpoint(0,0)) - sqrt(0.5)) < 1e-12);
 DLIB_TEST(std::abs(distance_to_line(l1, dpoint(1,1)) - sqrt(0.5)) < 1e-12);
 DLIB_TEST(std::abs(signed_distance_to_line(l1, dpoint(0,0)) + sqrt(0.5)) < 1e-12);
 DLIB_TEST(std::abs(signed_distance_to_line(l1, dpoint(1,1)) - sqrt(0.5)) < 1e-12);
 DLIB_TEST(std::abs(signed_distance_to_line(reverse(l1), dpoint(1,1)) + sqrt(0.5)) < 1e-12);
 dpoint reference_point(0.7,0.5);
 std::vector<dpoint> pts = {dpoint(0.01,0), dpoint(1,0.5), dpoint(0.9, 0.3), dpoint(0.4, 2), dpoint(1.3, 0.9)};
 DLIB_TEST(count_points_between_lines(l1,l2,reference_point,pts) == 3);
 DLIB_TEST(count_points_on_side_of_line(l1,reference_point,pts) == 4);
 reference_point = dpoint(0,0.5);
 DLIB_TEST(count_points_between_lines(l1,l2,reference_point,pts) == 0);
 DLIB_TEST(count_points_on_side_of_line(l1,reference_point,pts) == 1);
 }
// ----------------------------------------------------------------------------------------
 void test_polygon()
 {
 print_spinner();
 /* Let's define this triangle
 * 0 . . . . . . . . . . .
 * 1 . . . . . . . . .
 * 2 . . . . . . .
 * 3 . . . . .
 * 4 . . .
 * 5 .
 * 0 1 2 3 4 5 6 7 8 9 10
 */
 const polygon triangle({{0, 0}, {5, 5}, {10, 0}});
 DLIB_TEST(triangle.area() == 25);
 const rectangle rect = triangle.get_rect();
 std::vector<double> left_boundary;
 std::vector<double> right_boundary;
 triangle.get_left_and_right_bounds(rect.top(), rect.bottom(), left_boundary, right_boundary);
 DLIB_TEST(left_boundary.size() == right_boundary.size());
 const long top = rect.top();
 const long bottom = rect.bottom();
 for (long y = top, i = 0; y <= bottom; ++y, ++i)
 DLIB_TEST(left_boundary[y - top] == i);
 for (long y = top, i = 10; y <= bottom; ++y, --i)
 DLIB_TEST(right_boundary[y - top] == i);
 }
// ----------------------------------------------------------------------------------------
 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>(); 
 test_line();
 test_polygon();
 test_find_convex_hull();
 }
 } a;
}