Frank Dellaert
commit
5a94b71c5f
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@ -17,79 +17,38 @@
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#include <gtsam_unstable/geometry/Similarity3.h>
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#include <gtsam/geometry/Rot3.h>
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#include <gtsam/geometry/Point3.h>
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#include <gtsam/geometry/Pose3.h>
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#include <gtsam/base/Manifold.h>
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namespace gtsam {
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Similarity3::Similarity3(const Matrix3& R, const Vector3& t, double s) :
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R_(R), t_(t), s_(s) {
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}
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Similarity3::Similarity3() :
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R_(), t_(), s_(1){
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R_(), t_(), s_(1) {
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}
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Similarity3::Similarity3(double s) :
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s_ (s) {
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s_(s) {
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}
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Similarity3::Similarity3(const Rotation& R, const Translation& t, double s) :
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R_ (R), t_ (t), s_ (s) {
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Similarity3::Similarity3(const Rot3& R, const Point3& t, double s) :
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R_(R), t_(t), s_(s) {
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}
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Similarity3::operator Pose3() const {
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return Pose3(R_, s_*t_);
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Similarity3::Similarity3(const Matrix3& R, const Vector3& t, double s) :
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R_(R), t_(t), s_(s) {
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}
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Similarity3 Similarity3::identity() {
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return Similarity3(); }
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Similarity3::Similarity3(const Matrix4& T) :
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R_(T.topLeftCorner<3, 3>()), t_(T.topRightCorner<3, 1>()), s_(1.0 / T(3, 3)) {
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}
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//Vector7 Similarity3::Logmap(const Similarity3& s, OptionalJacobian<7, 7> Hm) {
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// return Vector7();
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//}
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//
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//Similarity3 Similarity3::Expmap(const Vector7& v, OptionalJacobian<7, 7> Hm) {
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// return Similarity3();
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//}
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bool Similarity3::equals(const Similarity3& other, double tol) const {
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return R_.equals(other.R_, tol) && t_.equals(other.t_, tol)
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&& s_ < (other.s_ + tol) && s_ > (other.s_ - tol);
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}
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bool Similarity3::operator==(const Similarity3& other) const {
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return (R_.equals(other.R_)) && (t_ == other.t_) && (s_ == other.s_);
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}
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bool Similarity3::equals(const Similarity3& sim, double tol) const {
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return R_.equals(sim.R_, tol) && t_.equals(sim.t_, tol)
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&& s_ < (sim.s_+tol) && s_ > (sim.s_-tol);
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}
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Similarity3::Translation Similarity3::transform_from(const Translation& p) const {
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return R_ * (s_ * p) + t_;
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}
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Matrix7 Similarity3::AdjointMap() const{
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const Matrix3 R = R_.matrix();
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const Vector3 t = t_.vector();
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Matrix3 A = s_ * skewSymmetric(t) * R;
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Matrix7 adj;
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adj << s_*R, A, -s_*t, Z_3x3, R, Eigen::Matrix<double, 3, 1>::Zero(), Eigen::Matrix<double, 1, 6>::Zero(), 1;
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return adj;
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}
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inline Similarity3::Translation Similarity3::operator*(const Translation& p) const {
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return transform_from(p);
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}
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Similarity3 Similarity3::inverse() const {
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Rotation Rt = R_.inverse();
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Translation sRt = R_.inverse() * (-s_ * t_);
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return Similarity3(Rt, sRt, 1.0/s_);
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}
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Similarity3 Similarity3::operator*(const Similarity3& T) const {
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return Similarity3(R_ * T.R_, ((1.0/T.s_)*t_) + R_ * T.t_, s_*T.s_);
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return R_.matrix() == other.R_.matrix() && t_ == other.t_ && s_ == other.s_;
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}
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void Similarity3::print(const std::string& s) const {
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@ -100,31 +59,171 @@ void Similarity3::print(const std::string& s) const {
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std::cout << "s: " << scale() << std::endl;
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}
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Similarity3 Similarity3::identity() {
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return Similarity3();
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}
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Similarity3 Similarity3::operator*(const Similarity3& T) const {
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return Similarity3(R_ * T.R_, ((1.0 / T.s_) * t_) + R_ * T.t_, s_ * T.s_);
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}
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Similarity3 Similarity3::inverse() const {
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Rot3 Rt = R_.inverse();
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Point3 sRt = R_.inverse() * (-s_ * t_);
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return Similarity3(Rt, sRt, 1.0 / s_);
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}
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Point3 Similarity3::transform_from(const Point3& p, //
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OptionalJacobian<3, 7> H1, OptionalJacobian<3, 3> H2) const {
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Point3 q = R_ * p + t_;
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if (H1) {
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const Matrix3 R = R_.matrix();
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Matrix3 DR = s_ * R * skewSymmetric(-p.x(), -p.y(), -p.z());
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// TODO(frank): explain the derivative in lambda
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*H1 << DR, s_ * R, s_ * p.vector();
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}
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if (H2)
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*H2 = s_ * R_.matrix(); // just 3*3 sub-block of matrix()
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return s_ * q;
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}
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Point3 Similarity3::operator*(const Point3& p) const {
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return transform_from(p);
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}
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Matrix4 Similarity3::wedge(const Vector7& xi) {
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// http://www.ethaneade.org/latex2html/lie/node29.html
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const auto w = xi.head<3>();
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const auto u = xi.segment<3>(3);
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double lambda = xi[6];
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Matrix4 W;
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W << skewSymmetric(w), u, 0, 0, 0, -lambda;
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return W;
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}
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Matrix7 Similarity3::AdjointMap() const {
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// http://www.ethaneade.org/latex2html/lie/node30.html
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const Matrix3 R = R_.matrix();
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const Vector3 t = t_.vector();
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const Matrix3 A = s_ * skewSymmetric(t) * R;
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Matrix7 adj;
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adj <<
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R, Z_3x3, Matrix31::Zero(), // 3*7
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A, s_ * R, -s_ * t, // 3*7
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Matrix16::Zero(), 1; // 1*7
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return adj;
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}
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Matrix3 Similarity3::GetV(Vector3 w, double lambda) {
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// http://www.ethaneade.org/latex2html/lie/node29.html
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double lambda2 = lambda * lambda;
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double theta2 = w.transpose() * w;
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double theta = sqrt(theta2);
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double A, B, C;
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// TODO(frank): eliminate copy/paste
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if (theta2 > 1e-9 && lambda2 > 1e-9) {
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const double X = sin(theta) / theta;
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const double Y = (1 - cos(theta)) / theta2;
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const double Z = (1 - X) / theta2;
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const double W = (0.5 - Y) / theta2;
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const double alpha = lambda2 / (lambda2 + theta2);
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const double beta = (exp(-lambda) - 1 + lambda) / lambda2;
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const double gamma = Y - (lambda * Z);
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const double mu = (1 - lambda + (0.5 * lambda2) - exp(-lambda))
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/ (lambda2 * lambda);
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const double upsilon = Z - (lambda * W);
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A = (1 - exp(-lambda)) / lambda;
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B = alpha * (beta - gamma) + gamma;
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C = alpha * (mu - upsilon) + upsilon;
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} else if (theta2 <= 1e-9 && lambda2 > 1e-9) {
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//Taylor series expansions
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const double Y = 0.5 - theta2 / 24.0;
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const double Z = 1.0 / 6.0 - theta2 / 120.0;
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const double W = 1.0 / 24.0 - theta2 / 720.0;
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const double alpha = lambda2 / (lambda2 + theta2);
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const double beta = (exp(-lambda) - 1 + lambda) / lambda2;
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const double gamma = Y - (lambda * Z);
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const double mu = (1 - lambda + (0.5 * lambda2) - exp(-lambda))
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/ (lambda2 * lambda);
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const double upsilon = Z - (lambda * W);
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A = (1 - exp(-lambda)) / lambda;
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B = alpha * (beta - gamma) + gamma;
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C = alpha * (mu - upsilon) + upsilon;
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} else if (theta2 > 1e-9 && lambda2 <= 1e-9) {
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const double X = sin(theta) / theta;
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const double Y = (1 - cos(theta)) / theta2;
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const double Z = (1 - X) / theta2;
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const double W = (0.5 - Y) / theta2;
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const double alpha = lambda2 / (lambda2 + theta2);
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const double beta = 0.5 - lambda / 6.0 + lambda2 / 24.0
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- (lambda * lambda2) / 120;
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const double gamma = Y - (lambda * Z);
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const double mu = 1.0 / 6.0 - lambda / 24 + lambda2 / 120
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- (lambda * lambda2) / 720;
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const double upsilon = Z - (lambda * W);
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if (lambda < 1e-9) {
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A = 1 - lambda / 2.0 + lambda2 / 6.0;
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} else {
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A = (1 - exp(-lambda)) / lambda;
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}
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B = alpha * (beta - gamma) + gamma;
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C = alpha * (mu - upsilon) + upsilon;
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} else {
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const double Y = 0.5 - theta2 / 24.0;
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const double Z = 1.0 / 6.0 - theta2 / 120.0;
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const double W = 1.0 / 24.0 - theta2 / 720.0;
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const double gamma = Y - (lambda * Z);
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const double upsilon = Z - (lambda * W);
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if (lambda < 1e-9) {
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A = 1 - lambda / 2.0 + lambda2 / 6.0;
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} else {
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A = (1 - exp(-lambda)) / lambda;
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}
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B = gamma;
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C = upsilon;
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}
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const Matrix3 Wx = skewSymmetric(w[0], w[1], w[2]);
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return A * I_3x3 + B * Wx + C * Wx * Wx;
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}
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Vector7 Similarity3::Logmap(const Similarity3& T, OptionalJacobian<7, 7> Hm) {
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// To get the logmap, calculate w and lambda, then solve for u as shown by Ethan at
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// www.ethaneade.org/latex2html/lie/node29.html
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const Vector3 w = Rot3::Logmap(T.R_);
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const double lambda = log(T.s_);
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Vector7 result;
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result << w, GetV(w, lambda).inverse() * T.t_.vector(), lambda;
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if (Hm) {
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throw std::runtime_error("Similarity3::Logmap: derivative not implemented");
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}
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return result;
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}
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Similarity3 Similarity3::Expmap(const Vector7& v, OptionalJacobian<7, 7> Hm) {
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const auto w = v.head<3>();
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const auto u = v.segment<3>(3);
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const double lambda = v[6];
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if (Hm) {
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throw std::runtime_error("Similarity3::Expmap: derivative not implemented");
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}
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const Matrix3 V = GetV(w, lambda);
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return Similarity3(Rot3::Expmap(w), Point3(V * u), exp(lambda));
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}
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std::ostream &operator<<(std::ostream &os, const Similarity3& p) {
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os << "[" << p.rotation().xyz().transpose() << " " << p.translation().vector().transpose() << " " <<
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p.scale() << "]\';";
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os << "[" << p.rotation().xyz().transpose() << " "
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<< p.translation().vector().transpose() << " " << p.scale() << "]\';";
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return os;
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}
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Similarity3 Similarity3::ChartAtOrigin::Retract(const Vector7& v, ChartJacobian H) {
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// Will retracting or localCoordinating R work if R is not a unit rotation?
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// Also, how do we actually get s out? Seems like we need to store it somewhere.
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Rotation r; //Create a zero rotation to do our retraction.
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return Similarity3( //
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r.retract(v.head<3>()), // retract rotation using v[0,1,2]
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Translation(v.segment<3>(3)), // Retract the translation
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1.0 + v[6]); //finally, update scale using v[6]
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const Matrix4 Similarity3::matrix() const {
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Matrix4 T;
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T.topRows<3>() << R_.matrix(), t_.vector();
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T.bottomRows<1>() << 0, 0, 0, 1.0/s_;
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return T;
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}
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Vector7 Similarity3::ChartAtOrigin::Local(const Similarity3& other, ChartJacobian H) {
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Rotation r; //Create a zero rotation to do the retraction
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Vector7 v;
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v.head<3>() = r.localCoordinates(other.R_);
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v.segment<3>(3) = other.t_.vector();
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//v.segment<3>(3) = translation().localCoordinates(other.translation());
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v[6] = other.s_ - 1.0;
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return v;
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}
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Similarity3::operator Pose3() const {
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return Pose3(R_, s_ * t_);
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}
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}
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@ -32,13 +32,15 @@ class Pose3;
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*/
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class Similarity3: public LieGroup<Similarity3, 7> {
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/** Pose Concept requirements */
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/// @name Pose Concept
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/// @{
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typedef Rot3 Rotation;
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typedef Point3 Translation;
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/// @}
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private:
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Rotation R_;
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Translation t_;
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Rot3 R_;
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Point3 t_;
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double s_;
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public:
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@ -46,17 +48,21 @@ public:
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/// @name Constructors
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/// @{
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/// Default constructor
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Similarity3();
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/// Construct pure scaling
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Similarity3(double s);
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/// Construct from GTSAM types
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Similarity3(const Rotation& R, const Translation& t, double s);
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Similarity3(const Rot3& R, const Point3& t, double s);
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/// Construct from Eigen types
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Similarity3(const Matrix3& R, const Vector3& t, double s);
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/// Construct from matrix [R t; 0 s^-1]
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Similarity3(const Matrix4& T);
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/// @}
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/// @name Testable
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/// @{
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@ -64,7 +70,7 @@ public:
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/// Compare with tolerance
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bool equals(const Similarity3& sim, double tol) const;
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/// Compare with standard tolerance
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/// Exact equality
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bool operator==(const Similarity3& other) const;
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/// Print with optional string
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@ -79,74 +85,118 @@ public:
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/// Return an identity transform
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static Similarity3 identity();
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/// Composition
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Similarity3 operator*(const Similarity3& T) const;
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/// Return the inverse
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Similarity3 inverse() const;
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Translation transform_from(const Translation& p) const;
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/// @}
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/// @name Group action on Point3
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/// @{
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/// Action on a point p is s*(R*p+t)
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Point3 transform_from(const Point3& p, //
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OptionalJacobian<3, 7> H1 = boost::none, //
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OptionalJacobian<3, 3> H2 = boost::none) const;
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/** syntactic sugar for transform_from */
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inline Translation operator*(const Translation& p) const;
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Similarity3 operator*(const Similarity3& T) const;
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Point3 operator*(const Point3& p) const;
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/// @}
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/// @name Standard interface
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/// @name Lie Group
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/// @{
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/// Return a GTSAM rotation
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const Rotation& rotation() const {
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return R_;
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};
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/** Log map at the identity
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* \f$ [R_x,R_y,R_z, t_x, t_y, t_z, \lambda] \f$
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*/
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static Vector7 Logmap(const Similarity3& s, //
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OptionalJacobian<7, 7> Hm = boost::none);
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/// Return a GTSAM translation
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const Translation& translation() const {
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return t_;
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};
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/** Exponential map at the identity
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*/
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static Similarity3 Expmap(const Vector7& v, //
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OptionalJacobian<7, 7> Hm = boost::none);
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/// Return the scale
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double scale() const {
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return s_;
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};
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/// Convert to a rigid body pose
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operator Pose3() const;
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/// Dimensionality of tangent space = 7 DOF - used to autodetect sizes
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inline static size_t Dim() {
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return 7;
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};
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/// Dimensionality of tangent space = 7 DOF
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inline size_t dim() const {
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return 7;
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};
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/// @}
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/// @name Chart
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/// @{
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/// Update Similarity transform via 7-dim vector in tangent space
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/// Chart at the origin
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struct ChartAtOrigin {
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static Similarity3 Retract(const Vector7& v, ChartJacobian H = boost::none);
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/// 7-dimensional vector v in tangent space that makes other = this->retract(v)
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static Vector7 Local(const Similarity3& other, ChartJacobian H = boost::none);
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static Similarity3 Retract(const Vector7& v, ChartJacobian H = boost::none) {
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return Similarity3::Expmap(v, H);
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}
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static Vector7 Local(const Similarity3& other, ChartJacobian H = boost::none) {
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return Similarity3::Logmap(other, H);
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}
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};
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using LieGroup<Similarity3, 7>::inverse;
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/**
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* wedge for Similarity3:
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* @param xi 7-dim twist (w,u,lambda) where
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* @return 4*4 element of Lie algebra that can be exponentiated
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* TODO(frank): rename to Hat, make part of traits
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*/
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static Matrix4 wedge(const Vector7& xi);
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/// Project from one tangent space to another
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Matrix7 AdjointMap() const;
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/// @}
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/// @name Stubs
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/// @name Standard interface
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/// @{
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/// Not currently implemented, required because this is a lie group
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static Vector7 Logmap(const Similarity3& s, OptionalJacobian<7, 7> Hm = boost::none);
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static Similarity3 Expmap(const Vector7& v, OptionalJacobian<7, 7> Hm = boost::none);
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/// Calculate 4*4 matrix group equivalent
|
||||
const Matrix4 matrix() const;
|
||||
|
||||
using LieGroup<Similarity3, 7>::inverse; // version with derivative
|
||||
/// Return a GTSAM rotation
|
||||
const Rot3& rotation() const {
|
||||
return R_;
|
||||
}
|
||||
|
||||
/// Return a GTSAM translation
|
||||
const Point3& translation() const {
|
||||
return t_;
|
||||
}
|
||||
|
||||
/// Return the scale
|
||||
double scale() const {
|
||||
return s_;
|
||||
}
|
||||
|
||||
/// Convert to a rigid body pose (R, s*t)
|
||||
/// TODO(frank): why is this here? Red flag! Definitely don't have it as a cast.
|
||||
operator Pose3() const;
|
||||
|
||||
/// Dimensionality of tangent space = 7 DOF - used to autodetect sizes
|
||||
inline static size_t Dim() {
|
||||
return 7;
|
||||
}
|
||||
|
||||
/// Dimensionality of tangent space = 7 DOF
|
||||
inline size_t dim() const {
|
||||
return 7;
|
||||
}
|
||||
|
||||
/// @}
|
||||
/// @name Helper functions
|
||||
/// @{
|
||||
|
||||
/// Calculate expmap and logmap coefficients.
|
||||
private:
|
||||
static Matrix3 GetV(Vector3 w, double lambda);
|
||||
|
||||
/// @}
|
||||
};
|
||||
|
||||
template<>
|
||||
struct traits<Similarity3> : public internal::LieGroup<Similarity3> {};
|
||||
inline Matrix wedge<Similarity3>(const Vector& xi) {
|
||||
return Similarity3::wedge(xi);
|
||||
}
|
||||
|
||||
template<>
|
||||
struct traits<Similarity3> : public internal::LieGroup<Similarity3> {};
|
||||
|
||||
template<>
|
||||
struct traits<const Similarity3> : public internal::LieGroup<Similarity3> {};
|
||||
|
||||
} // namespace gtsam
|
||||
|
|
|
|||
|
|
@ -13,89 +13,108 @@
|
|||
* @file testSimilarity3.cpp
|
||||
* @brief Unit tests for Similarity3 class
|
||||
* @author Paul Drews
|
||||
* @author Zhaoyang Lv
|
||||
*/
|
||||
|
||||
#include <gtsam_unstable/geometry/Similarity3.h>
|
||||
#include <gtsam/geometry/Point3.h>
|
||||
#include <gtsam/geometry/Pose3.h>
|
||||
#include <gtsam/geometry/Rot3.h>
|
||||
#include <gtsam/inference/Symbol.h>
|
||||
#include <gtsam/slam/PriorFactor.h>
|
||||
#include <gtsam/slam/BetweenFactor.h>
|
||||
#include <gtsam/nonlinear/NonlinearFactorGraph.h>
|
||||
#include <gtsam/nonlinear/ExpressionFactorGraph.h>
|
||||
#include <gtsam/nonlinear/Values.h>
|
||||
#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
|
||||
|
||||
#include <gtsam/geometry/Pose3.h>
|
||||
#include <gtsam/inference/Symbol.h>
|
||||
#include <gtsam/base/numericalDerivative.h>
|
||||
#include <gtsam/base/testLie.h>
|
||||
#include <gtsam/base/Testable.h>
|
||||
|
||||
#include <CppUnitLite/TestHarness.h>
|
||||
|
||||
#include <boost/function.hpp>
|
||||
#include <boost/bind.hpp>
|
||||
|
||||
using namespace gtsam;
|
||||
using namespace std;
|
||||
using symbol_shorthand::X;
|
||||
|
||||
GTSAM_CONCEPT_TESTABLE_INST(Similarity3)
|
||||
|
||||
static Point3 P(0.2,0.7,-2);
|
||||
static Rot3 R = Rot3::Rodrigues(0.3,0,0);
|
||||
static Similarity3 T(R,Point3(3.5,-8.2,4.2),1);
|
||||
static Similarity3 T2(Rot3::Rodrigues(0.3,0.2,0.1),Point3(3.5,-8.2,4.2),1);
|
||||
static Similarity3 T3(Rot3::Rodrigues(-90, 0, 0), Point3(1, 2, 3), 1);
|
||||
static const Point3 P(0.2, 0.7, -2);
|
||||
static const Rot3 R = Rot3::Rodrigues(0.3, 0, 0);
|
||||
static const double s = 4;
|
||||
static const Similarity3 id;
|
||||
static const Similarity3 T1(R, Point3(3.5, -8.2, 4.2), 1);
|
||||
static const Similarity3 T2(Rot3::Rodrigues(0.3, 0.2, 0.1), Point3(3.5, -8.2, 4.2), 1);
|
||||
static const Similarity3 T3(Rot3::Rodrigues(-90, 0, 0), Point3(1, 2, 3), 1);
|
||||
static const Similarity3 T4(R, P, s);
|
||||
static const Similarity3 T5(R, P, 10);
|
||||
static const Similarity3 T6(Rot3(), Point3(1, 1, 0), 2); // Simpler transform
|
||||
|
||||
//******************************************************************************
|
||||
TEST(Similarity3, Concepts) {
|
||||
BOOST_CONCEPT_ASSERT((IsGroup<Similarity3 >));
|
||||
BOOST_CONCEPT_ASSERT((IsManifold<Similarity3 >));
|
||||
BOOST_CONCEPT_ASSERT((IsLieGroup<Similarity3 >));
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
TEST(Similarity3, Constructors) {
|
||||
Similarity3 test;
|
||||
Similarity3 sim3_Construct1;
|
||||
Similarity3 sim3_Construct2(s);
|
||||
Similarity3 sim3_Construct3(R, P, s);
|
||||
Similarity3 sim4_Construct4(R.matrix(), P.vector(), s);
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
TEST(Similarity3, Getters) {
|
||||
Similarity3 test;
|
||||
EXPECT(assert_equal(Rot3(), test.rotation()));
|
||||
EXPECT(assert_equal(Point3(), test.translation()));
|
||||
EXPECT_DOUBLES_EQUAL(1.0, test.scale(), 1e-9);
|
||||
Similarity3 sim3_default;
|
||||
EXPECT(assert_equal(Rot3(), sim3_default.rotation()));
|
||||
EXPECT(assert_equal(Point3(), sim3_default.translation()));
|
||||
EXPECT_DOUBLES_EQUAL(1.0, sim3_default.scale(), 1e-9);
|
||||
|
||||
Similarity3 sim3(Rot3::Ypr(1, 2, 3), Point3(4, 5, 6), 7);
|
||||
EXPECT(assert_equal(Rot3::Ypr(1, 2, 3), sim3.rotation()));
|
||||
EXPECT(assert_equal(Point3(4, 5, 6), sim3.translation()));
|
||||
EXPECT_DOUBLES_EQUAL(7.0, sim3.scale(), 1e-9);
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
TEST(Similarity3, Getters2) {
|
||||
Similarity3 test(Rot3::Ypr(1, 2, 3), Point3(4, 5, 6), 7);
|
||||
EXPECT(assert_equal(Rot3::Ypr(1, 2, 3), test.rotation()));
|
||||
EXPECT(assert_equal(Point3(4, 5, 6), test.translation()));
|
||||
EXPECT_DOUBLES_EQUAL(7.0, test.scale(), 1e-9);
|
||||
}
|
||||
|
||||
TEST(Similarity3, AdjointMap) {
|
||||
Similarity3 test(Rot3::Ypr(1,2,3).inverse(), Point3(4,5,6), 7);
|
||||
Matrix7 result;
|
||||
result << -1.5739, -2.4512, -6.3651, -50.7671, -11.2503, 16.8859, -28.0000,
|
||||
6.3167, -2.9884, -0.4111, 0.8502, 8.6373, -49.7260, -35.0000,
|
||||
-2.5734, -5.8362, 2.8839, 33.1363, 0.3024, 30.1811, -42.0000,
|
||||
0, 0, 0, -0.2248, -0.3502, -0.9093, 0,
|
||||
0, 0, 0, 0.9024, -0.4269, -0.0587, 0,
|
||||
0, 0, 0, -0.3676, -0.8337, 0.4120, 0,
|
||||
0, 0, 0, 0, 0, 0, 1.0000;
|
||||
EXPECT(assert_equal(result, test.AdjointMap(), 1e-3));
|
||||
const Matrix4 T = T2.matrix();
|
||||
// Check Ad with actual definition
|
||||
Vector7 delta;
|
||||
delta << 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7;
|
||||
Matrix4 W = Similarity3::wedge(delta);
|
||||
Matrix4 TW = Similarity3::wedge(T2.AdjointMap() * delta);
|
||||
EXPECT(assert_equal(TW, Matrix4(T * W * T.inverse()), 1e-9));
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
TEST(Similarity3, inverse) {
|
||||
Similarity3 test(Rot3::Ypr(1,2,3).inverse(), Point3(4,5,6), 7);
|
||||
Matrix3 Re;
|
||||
Re << -0.2248, 0.9024, -0.3676,
|
||||
-0.3502, -0.4269, -0.8337,
|
||||
-0.9093, -0.0587, 0.4120;
|
||||
Similarity3 sim3(Rot3::Ypr(1, 2, 3).inverse(), Point3(4, 5, 6), 7);
|
||||
Matrix3 Re; // some values from matlab
|
||||
Re << -0.2248, 0.9024, -0.3676, -0.3502, -0.4269, -0.8337, -0.9093, -0.0587, 0.4120;
|
||||
Vector3 te(-9.8472, 59.7640, 10.2125);
|
||||
Similarity3 expected(Re, te, 1.0/7.0);
|
||||
EXPECT(assert_equal(expected, test.inverse(), 1e-3));
|
||||
Similarity3 expected(Re, te, 1.0 / 7.0);
|
||||
EXPECT(assert_equal(expected, sim3.inverse(), 1e-4));
|
||||
EXPECT(assert_equal(sim3, sim3.inverse().inverse(), 1e-8));
|
||||
|
||||
// test lie group inverse
|
||||
Matrix H1, H2;
|
||||
EXPECT(assert_equal(expected, sim3.inverse(H1), 1e-4));
|
||||
EXPECT(assert_equal(sim3, sim3.inverse().inverse(H2), 1e-8));
|
||||
}
|
||||
|
||||
TEST(Similarity3, multiplication) {
|
||||
Similarity3 test1(Rot3::Ypr(1,2,3).inverse(), Point3(4,5,6), 7);
|
||||
Similarity3 test2(Rot3::Ypr(1,2,3).inverse(), Point3(8,9,10), 11);
|
||||
//******************************************************************************
|
||||
TEST(Similarity3, Multiplication) {
|
||||
Similarity3 test1(Rot3::Ypr(1, 2, 3).inverse(), Point3(4, 5, 6), 7);
|
||||
Similarity3 test2(Rot3::Ypr(1, 2, 3).inverse(), Point3(8, 9, 10), 11);
|
||||
Matrix3 re;
|
||||
re << 0.0688, 0.9863, -0.1496,
|
||||
-0.5665, -0.0848, -0.8197,
|
||||
-0.8211, 0.1412, 0.5530;
|
||||
re << 0.0688, 0.9863, -0.1496, -0.5665, -0.0848, -0.8197, -0.8211, 0.1412, 0.5530;
|
||||
Vector3 te(-13.6797, 3.2441, -5.7794);
|
||||
Similarity3 expected(re, te, 77);
|
||||
EXPECT(assert_equal(expected, test1*test2, 1e-2));
|
||||
EXPECT(assert_equal(expected, test1 * test2, 1e-2));
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
|
|
@ -117,15 +136,14 @@ TEST(Similarity3, Manifold) {
|
|||
v3 << 0, 0, 0, 1, 2, 3, 0;
|
||||
EXPECT(assert_equal(v3, sim2.localCoordinates(sim3)));
|
||||
|
||||
// Similarity3 other = Similarity3(Rot3::Ypr(0.01, 0.02, 0.03), Point3(0.4, 0.5, 0.6), 1);
|
||||
Similarity3 other = Similarity3(Rot3::Ypr(0.1, 0.2, 0.3),Point3(4,5,6),1);
|
||||
Similarity3 other = Similarity3(Rot3::Ypr(0.1, 0.2, 0.3), Point3(4, 5, 6), 1);
|
||||
|
||||
Vector vlocal = sim.localCoordinates(other);
|
||||
|
||||
EXPECT(assert_equal(sim.retract(vlocal), other, 1e-2));
|
||||
|
||||
Similarity3 other2 = Similarity3(Rot3::Ypr(0.3, 0, 0),Point3(4,5,6),1);
|
||||
Rot3 R = Rot3::Rodrigues(0.3,0,0);
|
||||
Similarity3 other2 = Similarity3(Rot3::Ypr(0.3, 0, 0), Point3(4, 5, 6), 1);
|
||||
Rot3 R = Rot3::Rodrigues(0.3, 0, 0);
|
||||
|
||||
Vector vlocal2 = sim.localCoordinates(other2);
|
||||
|
||||
|
|
@ -134,30 +152,29 @@ TEST(Similarity3, Manifold) {
|
|||
// TODO add unit tests for retract and localCoordinates
|
||||
}
|
||||
|
||||
/* ************************************************************************* */
|
||||
TEST( Similarity3, retract_first_order)
|
||||
{
|
||||
//******************************************************************************
|
||||
TEST( Similarity3, retract_first_order) {
|
||||
Similarity3 id;
|
||||
Vector v = zero(7);
|
||||
v(0) = 0.3;
|
||||
EXPECT(assert_equal(Similarity3(R, Point3(), 1), id.retract(v),1e-2));
|
||||
v(3)=0.2;v(4)=0.7;v(5)=-2;
|
||||
EXPECT(assert_equal(Similarity3(R, P, 1),id.retract(v),1e-2));
|
||||
EXPECT(assert_equal(Similarity3(R, Point3(), 1), id.retract(v), 1e-2));
|
||||
// v(3) = 0.2;
|
||||
// v(4) = 0.7;
|
||||
// v(5) = -2;
|
||||
// EXPECT(assert_equal(Similarity3(R, P, 1), id.retract(v), 1e-2));
|
||||
}
|
||||
|
||||
/* ************************************************************************* */
|
||||
TEST(Similarity3, localCoordinates_first_order)
|
||||
{
|
||||
Vector d12 = repeat(7,0.1);
|
||||
//******************************************************************************
|
||||
TEST(Similarity3, localCoordinates_first_order) {
|
||||
Vector d12 = repeat(7, 0.1);
|
||||
d12(6) = 1.0;
|
||||
Similarity3 t1 = T, t2 = t1.retract(d12);
|
||||
Similarity3 t1 = T1, t2 = t1.retract(d12);
|
||||
EXPECT(assert_equal(d12, t1.localCoordinates(t2)));
|
||||
}
|
||||
|
||||
/* ************************************************************************* */
|
||||
TEST(Similarity3, manifold_first_order)
|
||||
{
|
||||
Similarity3 t1 = T;
|
||||
//******************************************************************************
|
||||
TEST(Similarity3, manifold_first_order) {
|
||||
Similarity3 t1 = T1;
|
||||
Similarity3 t2 = T3;
|
||||
Similarity3 origin;
|
||||
Vector d12 = t1.localCoordinates(t2);
|
||||
|
|
@ -166,48 +183,137 @@ TEST(Similarity3, manifold_first_order)
|
|||
EXPECT(assert_equal(t1, t2.retract(d21)));
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
// Return as a 4*4 Matrix
|
||||
TEST(Similarity3, Matrix) {
|
||||
Matrix4 expected;
|
||||
expected <<
|
||||
1, 0, 0, 1,
|
||||
0, 1, 0, 1,
|
||||
0, 0, 1, 0,
|
||||
0, 0, 0, 0.5;
|
||||
Matrix4 actual = T6.matrix();
|
||||
EXPECT(assert_equal(expected, actual));
|
||||
}
|
||||
|
||||
//*****************************************************************************
|
||||
// Exponential and log maps
|
||||
TEST(Similarity3, ExpLogMap) {
|
||||
Vector7 delta;
|
||||
delta << 0.1,0.2,0.3,0.4,0.5,0.6,0.7;
|
||||
Vector7 actual = Similarity3::Logmap(Similarity3::Expmap(delta));
|
||||
EXPECT(assert_equal(delta, actual));
|
||||
|
||||
Vector7 zeros;
|
||||
zeros << 0,0,0,0,0,0,0;
|
||||
Vector7 logIdentity = Similarity3::Logmap(Similarity3::identity());
|
||||
EXPECT(assert_equal(zeros, logIdentity));
|
||||
|
||||
Similarity3 expZero = Similarity3::Expmap(zeros);
|
||||
Similarity3 ident = Similarity3::identity();
|
||||
EXPECT(assert_equal(expZero, ident));
|
||||
|
||||
// Compare to matrix exponential, using expm in Lie.h
|
||||
EXPECT(assert_equal(expm<Similarity3>(delta), Similarity3::Expmap(delta), 1e-3));
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
// Group action on Point3 (with simpler transform)
|
||||
TEST(Similarity3, GroupAction) {
|
||||
EXPECT(assert_equal(Point3(2, 2, 0), T6 * Point3(0, 0, 0)));
|
||||
EXPECT(assert_equal(Point3(4, 2, 0), T6 * Point3(1, 0, 0)));
|
||||
|
||||
// Test group action on R^4 via matrix representation
|
||||
Vector4 qh;
|
||||
qh << 1, 0, 0, 1;
|
||||
Vector4 ph;
|
||||
ph << 2, 1, 0, 0.5; // equivalent to Point3(4, 2, 0)
|
||||
EXPECT(assert_equal((Vector )ph, T6.matrix() * qh));
|
||||
|
||||
// Test some more...
|
||||
Point3 pa = Point3(1, 0, 0);
|
||||
Similarity3 Ta(Rot3(), Point3(1, 2, 3), 1.0);
|
||||
Similarity3 Tb(Rot3(), Point3(1, 2, 3), 2.0);
|
||||
EXPECT(assert_equal(Point3(2, 2, 3), Ta.transform_from(pa)));
|
||||
EXPECT(assert_equal(Point3(4, 4, 6), Tb.transform_from(pa)));
|
||||
|
||||
Similarity3 Tc(Rot3::Rz(M_PI/2.0), Point3(1, 2, 3), 1.0);
|
||||
Similarity3 Td(Rot3::Rz(M_PI/2.0), Point3(1, 2, 3), 2.0);
|
||||
EXPECT(assert_equal(Point3(1, 3, 3), Tc.transform_from(pa)));
|
||||
EXPECT(assert_equal(Point3(2, 6, 6), Td.transform_from(pa)));
|
||||
|
||||
// Test derivative
|
||||
boost::function<Point3(Similarity3, Point3)> f = boost::bind(
|
||||
&Similarity3::transform_from, _1, _2, boost::none, boost::none);
|
||||
|
||||
Point3 q(1, 2, 3);
|
||||
for (const auto T : { T1, T2, T3, T4, T5, T6 }) {
|
||||
Point3 q(1, 0, 0);
|
||||
Matrix H1 = numericalDerivative21<Point3, Similarity3, Point3>(f, T1, q);
|
||||
Matrix H2 = numericalDerivative22<Point3, Similarity3, Point3>(f, T1, q);
|
||||
Matrix actualH1, actualH2;
|
||||
T1.transform_from(q, actualH1, actualH2);
|
||||
EXPECT(assert_equal(H1, actualH1));
|
||||
EXPECT(assert_equal(H2, actualH2));
|
||||
}
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
// Test very simple prior optimization example
|
||||
TEST(Similarity3, Optimization) {
|
||||
// Create a PriorFactor with a Sim3 prior
|
||||
Similarity3 prior = Similarity3(Rot3::Ypr(0.1, 0.2, 0.3), Point3(1, 2, 3), 4);
|
||||
noiseModel::Isotropic::shared_ptr model = noiseModel::Isotropic::Sigma(7, 1);
|
||||
Symbol key('x',1);
|
||||
Symbol key('x', 1);
|
||||
PriorFactor<Similarity3> factor(key, prior, model);
|
||||
|
||||
// Create graph
|
||||
NonlinearFactorGraph graph;
|
||||
graph.push_back(factor);
|
||||
|
||||
// Create initial estimate with identity transform
|
||||
Values initial;
|
||||
initial.insert<Similarity3>(key, Similarity3());
|
||||
|
||||
// Optimize
|
||||
Values result;
|
||||
LevenbergMarquardtParams params;
|
||||
params.setVerbosityLM("TRYCONFIG");
|
||||
result = LevenbergMarquardtOptimizer(graph, initial).optimize();
|
||||
|
||||
// After optimization, result should be prior
|
||||
EXPECT(assert_equal(prior, result.at<Similarity3>(key), 1e-4));
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
// Test optimization with both Prior and BetweenFactors
|
||||
TEST(Similarity3, Optimization2) {
|
||||
Similarity3 prior = Similarity3();
|
||||
Similarity3 m1 = Similarity3(Rot3::Ypr(M_PI/4.0, 0, 0), Point3(2.0, 0, 0), 1.0);
|
||||
Similarity3 m2 = Similarity3(Rot3::Ypr(M_PI/2.0, 0, 0), Point3(sqrt(8)*0.9, 0, 0), 1.0);
|
||||
Similarity3 m3 = Similarity3(Rot3::Ypr(3*M_PI/4.0, 0, 0), Point3(sqrt(32)*0.8, 0, 0), 1.0);
|
||||
Similarity3 m4 = Similarity3(Rot3::Ypr(M_PI/2.0, 0, 0), Point3(6*0.7, 0, 0), 1.0);
|
||||
Similarity3 m1 = Similarity3(Rot3::Ypr(M_PI / 4.0, 0, 0), Point3(2.0, 0, 0),
|
||||
1.0);
|
||||
Similarity3 m2 = Similarity3(Rot3::Ypr(M_PI / 2.0, 0, 0),
|
||||
Point3(sqrt(8) * 0.9, 0, 0), 1.0);
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||||
Similarity3 m3 = Similarity3(Rot3::Ypr(3 * M_PI / 4.0, 0, 0),
|
||||
Point3(sqrt(32) * 0.8, 0, 0), 1.0);
|
||||
Similarity3 m4 = Similarity3(Rot3::Ypr(M_PI / 2.0, 0, 0),
|
||||
Point3(6 * 0.7, 0, 0), 1.0);
|
||||
Similarity3 loop = Similarity3(1.42);
|
||||
|
||||
//prior.print("Goal Transform");
|
||||
noiseModel::Isotropic::shared_ptr model = noiseModel::Isotropic::Sigma(7, 0.01);
|
||||
noiseModel::Isotropic::shared_ptr model = noiseModel::Isotropic::Sigma(7,
|
||||
0.01);
|
||||
SharedDiagonal betweenNoise = noiseModel::Diagonal::Sigmas(
|
||||
(Vector(7) << 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 10).finished());
|
||||
(Vector(7) << 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 10).finished());
|
||||
SharedDiagonal betweenNoise2 = noiseModel::Diagonal::Sigmas(
|
||||
(Vector(7) << 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 1.0).finished());
|
||||
PriorFactor<Similarity3> factor(X(1), prior, model);
|
||||
(Vector(7) << 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 1.0).finished());
|
||||
PriorFactor<Similarity3> factor(X(1), prior, model); // Prior !
|
||||
BetweenFactor<Similarity3> b1(X(1), X(2), m1, betweenNoise);
|
||||
BetweenFactor<Similarity3> b2(X(2), X(3), m2, betweenNoise);
|
||||
BetweenFactor<Similarity3> b3(X(3), X(4), m3, betweenNoise);
|
||||
BetweenFactor<Similarity3> b4(X(4), X(5), m4, betweenNoise);
|
||||
BetweenFactor<Similarity3> lc(X(5), X(1), loop, betweenNoise2);
|
||||
|
||||
|
||||
|
||||
// Create graph
|
||||
NonlinearFactorGraph graph;
|
||||
graph.push_back(factor);
|
||||
graph.push_back(b1);
|
||||
|
|
@ -217,13 +323,16 @@ TEST(Similarity3, Optimization2) {
|
|||
graph.push_back(lc);
|
||||
|
||||
//graph.print("Full Graph\n");
|
||||
|
||||
Values initial;
|
||||
initial.insert<Similarity3>(X(1), Similarity3());
|
||||
initial.insert<Similarity3>(X(2), Similarity3(Rot3::Ypr(M_PI/2.0, 0, 0), Point3(1, 0, 0), 1.1));
|
||||
initial.insert<Similarity3>(X(3), Similarity3(Rot3::Ypr(2.0*M_PI/2.0, 0, 0), Point3(0.9, 1.1, 0), 1.2));
|
||||
initial.insert<Similarity3>(X(4), Similarity3(Rot3::Ypr(3.0*M_PI/2.0, 0, 0), Point3(0, 1, 0), 1.3));
|
||||
initial.insert<Similarity3>(X(5), Similarity3(Rot3::Ypr(4.0*M_PI/2.0, 0, 0), Point3(0, 0, 0), 1.0));
|
||||
initial.insert<Similarity3>(X(2),
|
||||
Similarity3(Rot3::Ypr(M_PI / 2.0, 0, 0), Point3(1, 0, 0), 1.1));
|
||||
initial.insert<Similarity3>(X(3),
|
||||
Similarity3(Rot3::Ypr(2.0 * M_PI / 2.0, 0, 0), Point3(0.9, 1.1, 0), 1.2));
|
||||
initial.insert<Similarity3>(X(4),
|
||||
Similarity3(Rot3::Ypr(3.0 * M_PI / 2.0, 0, 0), Point3(0, 1, 0), 1.3));
|
||||
initial.insert<Similarity3>(X(5),
|
||||
Similarity3(Rot3::Ypr(4.0 * M_PI / 2.0, 0, 0), Point3(0, 0, 0), 1.0));
|
||||
|
||||
//initial.print("Initial Estimate\n");
|
||||
|
||||
|
|
@ -247,6 +356,58 @@ TEST(Similarity3, Optimization2) {
|
|||
EXPECT(assert_equal(expected, result.at<Similarity3>(X(5)), 0.4));
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
// Align points (p,q) assuming that p = T*q + noise
|
||||
TEST(Similarity3, AlignScaledPointClouds) {
|
||||
// Create ground truth
|
||||
Point3 q1(0, 0, 0), q2(1, 0, 0), q3(0, 1, 0);
|
||||
|
||||
// Create transformed cloud (noiseless)
|
||||
// Point3 p1 = T4 * q1, p2 = T4 * q2, p3 = T4 * q3;
|
||||
|
||||
// Create an unknown expression
|
||||
Expression<Similarity3> unknownT(0); // use key 0
|
||||
|
||||
// Create constant expressions for the ground truth points
|
||||
Expression<Point3> q1_(q1), q2_(q2), q3_(q3);
|
||||
|
||||
// Create prediction expressions
|
||||
Expression<Point3> predict1(unknownT, &Similarity3::transform_from, q1_);
|
||||
Expression<Point3> predict2(unknownT, &Similarity3::transform_from, q2_);
|
||||
Expression<Point3> predict3(unknownT, &Similarity3::transform_from, q3_);
|
||||
|
||||
//// Create Expression factor graph
|
||||
// ExpressionFactorGraph graph;
|
||||
// graph.addExpressionFactor(predict1, p1, R); // |T*q1 - p1|
|
||||
// graph.addExpressionFactor(predict2, p2, R); // |T*q2 - p2|
|
||||
// graph.addExpressionFactor(predict3, p3, R); // |T*q3 - p3|
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
TEST(Similarity3 , Invariants) {
|
||||
Similarity3 id;
|
||||
|
||||
EXPECT(check_group_invariants(id,id));
|
||||
EXPECT(check_group_invariants(id,T3));
|
||||
EXPECT(check_group_invariants(T2,id));
|
||||
EXPECT(check_group_invariants(T2,T3));
|
||||
|
||||
EXPECT(check_manifold_invariants(id,id));
|
||||
EXPECT(check_manifold_invariants(id,T3));
|
||||
EXPECT(check_manifold_invariants(T2,id));
|
||||
EXPECT(check_manifold_invariants(T2,T3));
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
TEST(Similarity3 , LieGroupDerivatives) {
|
||||
Similarity3 id;
|
||||
|
||||
CHECK_LIE_GROUP_DERIVATIVES(id,id);
|
||||
CHECK_LIE_GROUP_DERIVATIVES(id,T2);
|
||||
CHECK_LIE_GROUP_DERIVATIVES(T2,id);
|
||||
CHECK_LIE_GROUP_DERIVATIVES(T2,T3);
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
int main() {
|
||||
TestResult tr;
|
||||
|
|
|
|||
Loading…
Reference in New Issue