571 lines
19 KiB
C++
571 lines
19 KiB
C++
/**
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* @file testPose2.cpp
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* @brief Unit tests for Pose2 class
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*/
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#include <cmath>
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#include <iostream>
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#include <boost/foreach.hpp>
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#include <boost/optional.hpp>
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#include <boost/assign/std/vector.hpp> // for operator +=
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using namespace boost::assign;
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#include <gtsam/CppUnitLite/TestHarness.h>
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#include <gtsam/base/numericalDerivative.h>
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#include <gtsam/base/lieProxies.h>
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#include <gtsam/geometry/Pose2.h>
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#include <gtsam/geometry/Point2.h>
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#include <gtsam/geometry/Rot2.h>
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using namespace gtsam;
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using namespace std;
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// #define SLOW_BUT_CORRECT_EXPMAP
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/* ************************************************************************* */
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TEST(Pose2, constructors) {
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//cout << "constructors" << endl;
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Point2 p;
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Pose2 pose(0,p);
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Pose2 origin;
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assert_equal(pose,origin);
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Pose2 t(M_PI_2+0.018, Point2(1.015, 2.01));
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EXPECT(assert_equal(t,Pose2(t.matrix())));
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}
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/* ************************************************************************* */
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TEST(Pose2, manifold) {
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//cout << "manifold" << endl;
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Pose2 t1(M_PI_2, Point2(1, 2));
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Pose2 t2(M_PI_2+0.018, Point2(1.015, 2.01));
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Pose2 origin;
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Vector d12 = t1.logmap(t2);
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EXPECT(assert_equal(t2, t1.expmap(d12)));
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EXPECT(assert_equal(t2, t1*origin.expmap(d12)));
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Vector d21 = t2.logmap(t1);
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EXPECT(assert_equal(t1, t2.expmap(d21)));
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EXPECT(assert_equal(t1, t2*origin.expmap(d21)));
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}
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/* ************************************************************************* */
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TEST(Pose2, expmap) {
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//cout << "expmap" << endl;
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Pose2 pose(M_PI_2, Point2(1, 2));
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#ifdef SLOW_BUT_CORRECT_EXPMAP
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Pose2 expected(1.00811, 2.01528, 2.5608);
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#else
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Pose2 expected(M_PI_2+0.99, Point2(1.015, 2.01));
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#endif
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Pose2 actual = pose.expmap(Vector_(3, 0.01, -0.015, 0.99));
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EXPECT(assert_equal(expected, actual, 1e-5));
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}
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/* ************************************************************************* */
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TEST(Pose2, expmap2) {
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// do an actual series exponential map
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// see e.g. http://www.cis.upenn.edu/~cis610/cis610lie1.ps
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Matrix A = Matrix_(3,3,
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0.0, -0.99, 0.01,
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0.99, 0.0, -0.015,
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0.0, 0.0, 0.0);
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Matrix A2 = A*A/2.0, A3 = A2*A/3.0, A4=A3*A/4.0;
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Matrix expected = eye(3) + A + A2 + A3 + A4;
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Pose2 pose = Pose2::Expmap(Vector_(3, 0.01, -0.015, 0.99));
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Matrix actual = pose.matrix();
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//EXPECT(assert_equal(expected, actual));
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}
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/* ************************************************************************* */
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TEST(Pose2, expmap0) {
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//cout << "expmap0" << endl;
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Pose2 pose(M_PI_2, Point2(1, 2));
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#ifdef SLOW_BUT_CORRECT_EXPMAP
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Pose2 expected(1.01491, 2.01013, 1.5888);
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#else
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Pose2 expected(M_PI_2+0.018, Point2(1.015, 2.01));
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#endif
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Pose2 actual = pose * Pose2::Expmap(Vector_(3, 0.01, -0.015, 0.018));
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EXPECT(assert_equal(expected, actual, 1e-5));
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}
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#ifdef SLOW_BUT_CORRECT_EXPMAP
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/* ************************************************************************* */
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// test case for screw motion in the plane
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namespace screw {
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double w=0.3;
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Vector xi = Vector_(3, 0.0, w, w);
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Rot2 expectedR = Rot2::fromAngle(w);
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Point2 expectedT(-0.0446635, 0.29552);
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Pose2 expected(expectedR, expectedT);
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}
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TEST(Pose3, expmap_c)
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{
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EXPECT(assert_equal(screw::expected, expm<Pose2>(screw::xi),1e-6));
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EXPECT(assert_equal(screw::expected, Pose2::Expmap(screw::xi),1e-6));
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EXPECT(assert_equal(screw::xi, Pose2::Logmap(screw::expected),1e-6));
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}
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#endif
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/* ************************************************************************* */
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TEST(Pose2, logmap) {
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//cout << "logmap" << endl;
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Pose2 pose0(M_PI_2, Point2(1, 2));
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Pose2 pose(M_PI_2+0.018, Point2(1.015, 2.01));
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#ifdef SLOW_BUT_CORRECT_EXPMAP
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Vector expected = Vector_(3, 0.00986473, -0.0150896, 0.018);
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#else
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Vector expected = Vector_(3, 0.01, -0.015, 0.018);
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#endif
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Vector actual = pose0.logmap(pose);
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EXPECT(assert_equal(expected, actual, 1e-5));
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}
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/* ************************************************************************* */
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Point2 transform_to_proxy(const Pose2& pose, const Point2& point) {
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return pose.transform_to(point);
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}
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TEST( Pose2, transform_to )
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{
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Pose2 pose(M_PI_2, Point2(1,2)); // robot at (1,2) looking towards y
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Point2 point(-1,4); // landmark at (-1,4)
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// expected
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Point2 expected(2,2);
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Matrix expectedH1 = Matrix_(2,3, -1.0, 0.0, 2.0, 0.0, -1.0, -2.0);
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Matrix expectedH2 = Matrix_(2,2, 0.0, 1.0, -1.0, 0.0);
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// actual
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Matrix actualH1, actualH2;
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Point2 actual = pose.transform_to(point, actualH1, actualH2);
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EXPECT(assert_equal(expected,actual));
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EXPECT(assert_equal(expectedH1,actualH1));
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Matrix numericalH1 = numericalDerivative21(transform_to_proxy, pose, point, 1e-5);
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EXPECT(assert_equal(numericalH1,actualH1));
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EXPECT(assert_equal(expectedH2,actualH2));
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Matrix numericalH2 = numericalDerivative22(transform_to_proxy, pose, point, 1e-5);
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EXPECT(assert_equal(numericalH2,actualH2));
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}
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/* ************************************************************************* */
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Point2 transform_from_proxy(const Pose2& pose, const Point2& point) {
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return pose.transform_from(point);
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}
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TEST (Pose2, transform_from)
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{
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Pose2 pose(1., 0., M_PI_2);
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Point2 pt(2., 1.);
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Matrix H1, H2;
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Point2 actual = pose.transform_from(pt, H1, H2);
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Point2 expected(0., 2.);
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EXPECT(assert_equal(expected, actual));
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Matrix H1_expected = Matrix_(2, 3, 0., -1., -2., 1., 0., -1.);
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Matrix H2_expected = Matrix_(2, 2, 0., -1., 1., 0.);
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Matrix numericalH1 = numericalDerivative21(transform_from_proxy, pose, pt, 1e-5);
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EXPECT(assert_equal(H1_expected, H1));
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EXPECT(assert_equal(H1_expected, numericalH1));
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Matrix numericalH2 = numericalDerivative22(transform_from_proxy, pose, pt, 1e-5);
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EXPECT(assert_equal(H2_expected, H2));
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EXPECT(assert_equal(H2_expected, numericalH2));
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}
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/* ************************************************************************* */
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TEST(Pose2, compose_a)
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{
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//cout << "compose_a" << endl;
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Pose2 pose1(M_PI/4.0, Point2(sqrt(0.5), sqrt(0.5)));
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Pose2 pose2(M_PI/2.0, Point2(0.0, 2.0));
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Matrix actualDcompose1;
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Matrix actualDcompose2;
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Pose2 actual = pose1.compose(pose2, actualDcompose1, actualDcompose2);
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Pose2 expected(3.0*M_PI/4.0, Point2(-sqrt(0.5), 3.0*sqrt(0.5)));
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EXPECT(assert_equal(expected, actual));
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Matrix expectedH1 = Matrix_(3,3,
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0.0, 1.0, 0.0,
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-1.0, 0.0, 2.0,
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0.0, 0.0, 1.0
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);
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Matrix expectedH2 = eye(3);
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Matrix numericalH1 = numericalDerivative21<Pose2, Pose2, Pose2>(testing::compose, pose1, pose2, 1e-5);
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Matrix numericalH2 = numericalDerivative22<Pose2, Pose2, Pose2>(testing::compose, pose1, pose2, 1e-5);
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EXPECT(assert_equal(expectedH1,actualDcompose1));
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EXPECT(assert_equal(numericalH1,actualDcompose1));
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EXPECT(assert_equal(expectedH2,actualDcompose2));
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EXPECT(assert_equal(numericalH2,actualDcompose2));
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Point2 point(sqrt(0.5), 3.0*sqrt(0.5));
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Point2 expected_point(-1.0, -1.0);
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Point2 actual_point1 = (pose1 * pose2).transform_to(point);
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Point2 actual_point2 = pose2.transform_to(pose1.transform_to(point));
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EXPECT(assert_equal(expected_point, actual_point1));
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EXPECT(assert_equal(expected_point, actual_point2));
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}
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/* ************************************************************************* */
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TEST(Pose2, compose_b)
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{
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//cout << "compose_b" << endl;
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Pose2 pose1(Rot2::fromAngle(M_PI/10.0), Point2(.75, .5));
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Pose2 pose2(Rot2::fromAngle(M_PI/4.0-M_PI/10.0), Point2(0.701289620636, 1.34933052585));
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Pose2 pose_expected(Rot2::fromAngle(M_PI/4.0), Point2(1.0, 2.0));
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Pose2 pose_actual_op = pose1 * pose2;
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Matrix actualDcompose1, actualDcompose2;
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Pose2 pose_actual_fcn = pose1.compose(pose2, actualDcompose1, actualDcompose2);
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Matrix numericalH1 = numericalDerivative21<Pose2, Pose2, Pose2>(testing::compose, pose1, pose2, 1e-5);
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Matrix numericalH2 = numericalDerivative22<Pose2, Pose2, Pose2>(testing::compose, pose1, pose2, 1e-5);
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EXPECT(assert_equal(numericalH1,actualDcompose1,1e-5));
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EXPECT(assert_equal(numericalH2,actualDcompose2));
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EXPECT(assert_equal(pose_expected, pose_actual_op));
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EXPECT(assert_equal(pose_expected, pose_actual_fcn));
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}
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/* ************************************************************************* */
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TEST(Pose2, compose_c)
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{
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//cout << "compose_c" << endl;
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Pose2 pose1(Rot2::fromAngle(M_PI/4.0), Point2(1.0, 1.0));
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Pose2 pose2(Rot2::fromAngle(M_PI/4.0), Point2(sqrt(.5), sqrt(.5)));
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Pose2 pose_expected(Rot2::fromAngle(M_PI/2.0), Point2(1.0, 2.0));
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Pose2 pose_actual_op = pose1 * pose2;
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Matrix actualDcompose1, actualDcompose2;
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Pose2 pose_actual_fcn = pose1.compose(pose2, actualDcompose1, actualDcompose2);
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Matrix numericalH1 = numericalDerivative21<Pose2, Pose2, Pose2>(testing::compose, pose1, pose2, 1e-5);
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Matrix numericalH2 = numericalDerivative22<Pose2, Pose2, Pose2>(testing::compose, pose1, pose2, 1e-5);
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EXPECT(assert_equal(numericalH1,actualDcompose1,1e-5));
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EXPECT(assert_equal(numericalH2,actualDcompose2));
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EXPECT(assert_equal(pose_expected, pose_actual_op));
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EXPECT(assert_equal(pose_expected, pose_actual_fcn));
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}
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/* ************************************************************************* */
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TEST(Pose2, inverse )
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{
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Point2 origin, t(1,2);
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Pose2 gTl(M_PI_2, t); // robot at (1,2) looking towards y
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Pose2 identity, lTg = gTl.inverse();
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EXPECT(assert_equal(identity,lTg.compose(gTl)));
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EXPECT(assert_equal(identity,gTl.compose(lTg)));
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Point2 l(4,5), g(-4,6);
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EXPECT(assert_equal(g,gTl*l));
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EXPECT(assert_equal(l,lTg*g));
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// Check derivative
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Matrix numericalH = numericalDerivative11<Pose2,Pose2>(testing::inverse, lTg, 1e-5);
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Matrix actualDinverse;
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lTg.inverse(actualDinverse);
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EXPECT(assert_equal(numericalH,actualDinverse));
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}
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/* ************************************************************************* */
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Vector homogeneous(const Point2& p) {
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return Vector_(3, p.x(), p.y(), 1.0);
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}
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/* ************************************************************************* */
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Matrix matrix(const Pose2& gTl) {
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Matrix gRl = gTl.r().matrix();
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Point2 gt = gTl.t();
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return Matrix_(3, 3,
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gRl(0, 0), gRl(0, 1), gt.x(),
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gRl(1, 0), gRl(1, 1), gt.y(),
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0.0, 0.0, 1.0);
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}
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/* ************************************************************************* */
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TEST( Pose2, matrix )
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{
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Point2 origin, t(1,2);
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Pose2 gTl(M_PI_2, t); // robot at (1,2) looking towards y
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Matrix gMl = matrix(gTl);
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EXPECT(assert_equal(Matrix_(3,3,
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0.0, -1.0, 1.0,
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1.0, 0.0, 2.0,
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0.0, 0.0, 1.0),
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gMl));
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Rot2 gR1 = gTl.r();
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EXPECT(assert_equal(homogeneous(t),gMl*homogeneous(origin)));
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Point2 x_axis(1,0), y_axis(0,1);
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EXPECT(assert_equal(Matrix_(2,2,
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0.0, -1.0,
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1.0, 0.0),
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gR1.matrix()));
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EXPECT(assert_equal(Point2(0,1),gR1*x_axis));
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EXPECT(assert_equal(Point2(-1,0),gR1*y_axis));
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EXPECT(assert_equal(homogeneous(Point2(1+0,2+1)),gMl*homogeneous(x_axis)));
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EXPECT(assert_equal(homogeneous(Point2(1-1,2+0)),gMl*homogeneous(y_axis)));
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// check inverse pose
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Matrix lMg = matrix(gTl.inverse());
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EXPECT(assert_equal(Matrix_(3,3,
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0.0, 1.0,-2.0,
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-1.0, 0.0, 1.0,
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0.0, 0.0, 1.0),
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lMg));
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}
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/* ************************************************************************* */
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TEST( Pose2, compose_matrix )
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{
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Pose2 gT1(M_PI_2, Point2(1,2)); // robot at (1,2) looking towards y
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Pose2 _1T2(M_PI, Point2(-1,4)); // local robot at (-1,4) loooking at negative x
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Matrix gM1(matrix(gT1)),_1M2(matrix(_1T2));
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EXPECT(assert_equal(gM1*_1M2,matrix(gT1.compose(_1T2)))); // RIGHT DOES NOT
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}
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/* ************************************************************************* */
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TEST( Pose2, between )
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{
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// <
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//
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// ^
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//
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// *--0--*--*
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Pose2 gT1(M_PI_2, Point2(1,2)); // robot at (1,2) looking towards y
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Pose2 gT2(M_PI, Point2(-1,4)); // robot at (-1,4) loooking at negative x
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Matrix actualH1,actualH2;
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Pose2 expected(M_PI_2, Point2(2,2));
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Pose2 actual1 = gT1.between(gT2);
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Pose2 actual2 = gT1.between(gT2,actualH1,actualH2);
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EXPECT(assert_equal(expected,actual1));
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EXPECT(assert_equal(expected,actual2));
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Matrix expectedH1 = Matrix_(3,3,
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0.0,-1.0,-2.0,
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1.0, 0.0,-2.0,
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0.0, 0.0,-1.0
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);
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Matrix numericalH1 = numericalDerivative21<Pose2,Pose2,Pose2>(testing::between, gT1, gT2, 1e-5);
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EXPECT(assert_equal(expectedH1,actualH1));
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EXPECT(assert_equal(numericalH1,actualH1));
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// Assert H1 = -AdjointMap(between(p2,p1)) as in doc/math.lyx
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EXPECT(assert_equal(-gT2.between(gT1).AdjointMap(),actualH1));
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Matrix expectedH2 = Matrix_(3,3,
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1.0, 0.0, 0.0,
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0.0, 1.0, 0.0,
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0.0, 0.0, 1.0
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);
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Matrix numericalH2 = numericalDerivative22<Pose2,Pose2,Pose2>(testing::between, gT1, gT2, 1e-5);
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EXPECT(assert_equal(expectedH2,actualH2));
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EXPECT(assert_equal(numericalH2,actualH2));
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}
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/* ************************************************************************* */
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// reverse situation for extra test
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TEST( Pose2, between2 )
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{
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Pose2 p2(M_PI_2, Point2(1,2)); // robot at (1,2) looking towards y
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Pose2 p1(M_PI, Point2(-1,4)); // robot at (-1,4) loooking at negative x
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Matrix actualH1,actualH2;
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p1.between(p2,actualH1,actualH2);
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Matrix numericalH1 = numericalDerivative21<Pose2,Pose2,Pose2>(testing::between, p1, p2, 1e-5);
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EXPECT(assert_equal(numericalH1,actualH1));
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Matrix numericalH2 = numericalDerivative22<Pose2,Pose2,Pose2>(testing::between, p1, p2, 1e-5);
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EXPECT(assert_equal(numericalH2,actualH2));
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}
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/* ************************************************************************* */
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TEST( Pose2, round_trip )
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{
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Pose2 p1(1.23, 2.30, 0.2);
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Pose2 odo(0.53, 0.39, 0.15);
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Pose2 p2 = p1.compose(odo);
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EXPECT(assert_equal(odo, p1.between(p2)));
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}
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/* ************************************************************************* */
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TEST(Pose2, members)
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{
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Pose2 pose;
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EXPECT(pose.dim() == 3);
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}
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/* ************************************************************************* */
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// some shared test values
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Pose2 x1, x2(1, 1, 0), x3(1, 1, M_PI_4);
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Point2 l1(1, 0), l2(1, 1), l3(2, 2), l4(1, 3);
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/* ************************************************************************* */
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Rot2 bearing_proxy(const Pose2& pose, const Point2& pt) {
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return pose.bearing(pt);
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}
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TEST( Pose2, bearing )
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{
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Matrix expectedH1, actualH1, expectedH2, actualH2;
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// establish bearing is indeed zero
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EXPECT(assert_equal(Rot2(),x1.bearing(l1)));
|
|
|
|
// establish bearing is indeed 45 degrees
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EXPECT(assert_equal(Rot2::fromAngle(M_PI_4),x1.bearing(l2)));
|
|
|
|
// establish bearing is indeed 45 degrees even if shifted
|
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Rot2 actual23 = x2.bearing(l3, actualH1, actualH2);
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EXPECT(assert_equal(Rot2::fromAngle(M_PI_4),actual23));
|
|
|
|
// Check numerical derivatives
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expectedH1 = numericalDerivative21(bearing_proxy, x2, l3, 1e-5);
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EXPECT(assert_equal(expectedH1,actualH1));
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|
expectedH2 = numericalDerivative22(bearing_proxy, x2, l3, 1e-5);
|
|
EXPECT(assert_equal(expectedH1,actualH1));
|
|
|
|
// establish bearing is indeed 45 degrees even if rotated
|
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Rot2 actual34 = x3.bearing(l4, actualH1, actualH2);
|
|
EXPECT(assert_equal(Rot2::fromAngle(M_PI_4),actual34));
|
|
|
|
// Check numerical derivatives
|
|
expectedH1 = numericalDerivative21(bearing_proxy, x3, l4, 1e-5);
|
|
expectedH2 = numericalDerivative22(bearing_proxy, x3, l4, 1e-5);
|
|
EXPECT(assert_equal(expectedH1,actualH1));
|
|
EXPECT(assert_equal(expectedH1,actualH1));
|
|
}
|
|
|
|
/* ************************************************************************* */
|
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LieVector range_proxy(const Pose2& pose, const Point2& point) {
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return LieVector(pose.range(point));
|
|
}
|
|
TEST( Pose2, range )
|
|
{
|
|
Matrix expectedH1, actualH1, expectedH2, actualH2;
|
|
|
|
// establish range is indeed zero
|
|
EXPECT_DOUBLES_EQUAL(1,x1.range(l1),1e-9);
|
|
|
|
// establish range is indeed 45 degrees
|
|
EXPECT_DOUBLES_EQUAL(sqrt(2),x1.range(l2),1e-9);
|
|
|
|
// Another pair
|
|
double actual23 = x2.range(l3, actualH1, actualH2);
|
|
EXPECT_DOUBLES_EQUAL(sqrt(2),actual23,1e-9);
|
|
|
|
// Check numerical derivatives
|
|
expectedH1 = numericalDerivative21(range_proxy, x2, l3, 1e-5);
|
|
expectedH2 = numericalDerivative22(range_proxy, x2, l3, 1e-5);
|
|
EXPECT(assert_equal(expectedH1,actualH1));
|
|
EXPECT(assert_equal(expectedH2,actualH2));
|
|
|
|
// Another test
|
|
double actual34 = x3.range(l4, actualH1, actualH2);
|
|
EXPECT_DOUBLES_EQUAL(2,actual34,1e-9);
|
|
|
|
// Check numerical derivatives
|
|
expectedH1 = numericalDerivative21(range_proxy, x3, l4, 1e-5);
|
|
expectedH2 = numericalDerivative22(range_proxy, x3, l4, 1e-5);
|
|
EXPECT(assert_equal(expectedH1,actualH1));
|
|
EXPECT(assert_equal(expectedH2,actualH2));
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
|
|
TEST(Pose2, align_1) {
|
|
Pose2 expected(Rot2::fromAngle(0), Point2(10,10));
|
|
|
|
vector<Point2Pair> correspondences;
|
|
Point2Pair pq1(make_pair(Point2(0,0), Point2(10,10)));
|
|
Point2Pair pq2(make_pair(Point2(20,10), Point2(30,20)));
|
|
correspondences += pq1, pq2;
|
|
|
|
boost::optional<Pose2> actual = align(correspondences);
|
|
EXPECT(assert_equal(expected, *actual));
|
|
}
|
|
|
|
TEST(Pose2, align_2) {
|
|
Point2 t(20,10);
|
|
Rot2 R = Rot2::fromAngle(M_PI_2);
|
|
Pose2 expected(R, t);
|
|
|
|
vector<Point2Pair> correspondences;
|
|
Point2 p1(0,0), p2(10,0);
|
|
Point2 q1 = expected.transform_from(p1), q2 = expected.transform_from(p2);
|
|
EXPECT(assert_equal(Point2(20,10),q1));
|
|
EXPECT(assert_equal(Point2(20,20),q2));
|
|
Point2Pair pq1(make_pair(p1, q1));
|
|
Point2Pair pq2(make_pair(p2, q2));
|
|
correspondences += pq1, pq2;
|
|
|
|
boost::optional<Pose2> actual = align(correspondences);
|
|
EXPECT(assert_equal(expected, *actual));
|
|
}
|
|
|
|
namespace align_3 {
|
|
Point2 t(10,10);
|
|
Pose2 expected(Rot2::fromAngle(2*M_PI/3), t);
|
|
Point2 p1(0,0), p2(10,0), p3(10,10);
|
|
Point2 q1 = expected.transform_from(p1), q2 = expected.transform_from(p2), q3 = expected.transform_from(p3);
|
|
}
|
|
|
|
TEST(Pose2, align_3) {
|
|
using namespace align_3;
|
|
|
|
vector<Point2Pair> correspondences;
|
|
Point2Pair pq1(make_pair(p1, q1));
|
|
Point2Pair pq2(make_pair(p2, q2));
|
|
Point2Pair pq3(make_pair(p3, q3));
|
|
correspondences += pq1, pq2, pq3;
|
|
|
|
boost::optional<Pose2> actual = align(correspondences);
|
|
EXPECT(assert_equal(expected, *actual));
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
// Prototype code to align two triangles using a rigid transform
|
|
/* ************************************************************************* */
|
|
struct Triangle { size_t i_,j_,k_;};
|
|
|
|
boost::optional<Pose2> align(const vector<Point2>& ps, const vector<Point2>& qs,
|
|
const pair<Triangle, Triangle>& trianglePair) {
|
|
const Triangle& t1 = trianglePair.first, t2 = trianglePair.second;
|
|
vector<Point2Pair> correspondences;
|
|
correspondences += make_pair(ps[t1.i_],qs[t2.i_]), make_pair(ps[t1.j_],qs[t2.j_]), make_pair(ps[t1.k_],qs[t2.k_]);
|
|
return align(correspondences);
|
|
}
|
|
|
|
TEST(Pose2, align_4) {
|
|
using namespace align_3;
|
|
|
|
vector<Point2> ps,qs;
|
|
ps += p1, p2, p3;
|
|
qs += q3, q1, q2; // note in 3,1,2 order !
|
|
|
|
Triangle t1; t1.i_=0; t1.j_=1; t1.k_=2;
|
|
Triangle t2; t2.i_=1; t2.j_=2; t2.k_=0;
|
|
|
|
boost::optional<Pose2> actual = align(ps, qs, make_pair(t1,t2));
|
|
EXPECT(assert_equal(expected, *actual));
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
int main() {
|
|
TestResult tr;
|
|
return TestRegistry::runAllTests(tr);
|
|
}
|
|
/* ************************************************************************* */
|
|
|