260 lines
8.1 KiB
C++
260 lines
8.1 KiB
C++
/* ----------------------------------------------------------------------------
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* GTSAM Copyright 2010, Georgia Tech Research Corporation,
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* Atlanta, Georgia 30332-0415
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* All Rights Reserved
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* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
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* See LICENSE for the license information
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* -------------------------------------------------------------------------- */
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/**
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* @file Similarity3.cpp
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* @brief Implementation of Similarity3 transform
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* @author Paul Drews
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*/
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#include <gtsam_unstable/geometry/Similarity3.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() :
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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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}
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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::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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bool Similarity3::equals(const Similarity3& sim, double tol) const {
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return R_.equals(sim.R_, tol) && t_.equals(sim.t_, tol) && s_ < (sim.s_ + tol)
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&& s_ > (sim.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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void Similarity3::print(const std::string& s) const {
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std::cout << std::endl;
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std::cout << s;
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rotation().print("R:\n");
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translation().print("t: ");
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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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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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*H1 << DR, R, R * 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 R_ * (s_ * p) + t_;
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// TODO: Effect of scale change is this, right?
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// sR t * (1+v)I 0 * p = s(1+v)R t * p = s(1+v)Rp + t = sRp + vRp + t
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// 0001 000 1 1 000 1 1
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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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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, // 3*7
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Z_3x3, R, Matrix31::Zero(), // 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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Matrix33 Similarity3::GetV(Vector3 w, double lambda){
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Matrix33 wx = skewSymmetric(w[0], w[1], w[2]);
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double lambdasquared = lambda * lambda;
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double thetasquared = w.transpose() * w;
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double theta = sqrt(thetasquared);
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double X, Y, Z, W, alpha, beta, gama, mu, upsilon, A, B, C;
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if (thetasquared > 1e-9 && lambdasquared > 1e-9) {
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X = sin(theta) / theta;
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Y = (1 - cos(theta)) / thetasquared;
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Z = (1 - X) / thetasquared;
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W = (0.5 - Y) / thetasquared;
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alpha = lambdasquared / (lambdasquared + thetasquared);
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beta = (exp(-lambda) - 1 + lambda) / lambdasquared;
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gama = Y - (lambda * Z);
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mu = (1 - lambda + (0.5 * lambdasquared) - exp(-lambda))
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/ (lambdasquared * lambda);
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upsilon = Z - (lambda * W);
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A = (1 - exp(-lambda)) / lambda;
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B = alpha * (beta - gama) + gama;
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C = alpha * (mu - upsilon) + upsilon;
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}
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else if(thetasquared <= 1e-9 && lambdasquared > 1e-9) {
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//Taylor series expansions
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X = 1;
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Y = 0.5-thetasquared/24.0;
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Z = 1.0/6.0 - thetasquared/120.0;
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W = 1.0/24.0 - thetasquared/720.0;
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alpha = lambdasquared / (lambdasquared + thetasquared);
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beta = (exp(-lambda) - 1 + lambda) / lambdasquared;
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gama = Y - (lambda * Z);
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mu = (1 - lambda + (0.5 * lambdasquared) - exp(-lambda))
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/ (lambdasquared * lambda);
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upsilon = Z - (lambda * W);
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A = (1 - exp(-lambda)) / lambda;
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B = alpha * (beta - gama) + gama;
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C = alpha * (mu - upsilon) + upsilon;
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}
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else if(thetasquared > 1e-9 && lambdasquared <= 1e-9) {
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X = sin(theta) / theta;
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Y = (1 - cos(theta)) / thetasquared;
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Z = (1 - X) / thetasquared;
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W = (0.5 - Y) / thetasquared;
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alpha = lambdasquared / (lambdasquared + thetasquared);
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beta = 0.5 - lambda / 6.0 + lambdasquared / 24.0
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- (lambda * lambdasquared) / 120;
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gama = Y - (lambda * Z);
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mu = 1.0 / 6.0 - lambda / 24 + lambdasquared / 120
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- (lambda * lambdasquared) / 720;
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upsilon = Z - (lambda * W);
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if (lambda < 1e-9) {
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A = 1 - lambda / 2.0 + lambdasquared / 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 - gama) + gama;
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C = alpha * (mu - upsilon) + upsilon;
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}
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else {
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X = 1;
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Y = 0.5-thetasquared/24.0;
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Z = 1.0 / 6.0 - thetasquared / 120.0;
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W = 1.0 / 24.0 - thetasquared / 720.0;
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alpha = lambdasquared / (lambdasquared + thetasquared);
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beta = 0.5 - lambda / 6.0 + lambdasquared / 24.0
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- (lambda * lambdasquared) / 120;
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gama = Y - (lambda * Z);
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mu = 1.0 / 6.0 - lambda / 24 + lambdasquared / 120
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- (lambda * lambdasquared) / 720;
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upsilon = Z - (lambda * W);
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if (lambda < 1e-9) {
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A = 1 - lambda / 2.0 + lambdasquared / 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 = gama;
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C = upsilon;
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}
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return A * Matrix33::Identity() + B * wx + C * wx * wx;
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}
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Vector7 Similarity3::Logmap(const Similarity3& s, OptionalJacobian<7, 7> Hm) {
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// To get the logmap, calculate w and lambda, then solve for u as show at ethaneade.org
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// www.ethaneade.org/latex2html/lie/node29.html
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Vector3 w = Rot3::Logmap(s.R_);
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double lambda = log(s.s_);
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Matrix33 V = GetV(w, lambda);
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Vector3 u = V.inverse() * s.t_.vector();
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Vector7 result;
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result << w, u, lambda;
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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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Matrix31 w(v.head<3>());
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double lambda = v[6];
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Matrix31 u(v.segment<3>(3));
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Matrix33 V = GetV(w, lambda);
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// Matrix33 wx = skewSymmetric(w[0], w[1], w[2]);
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// double lambdasquared = lambda * lambda;
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// double thetasquared = w.transpose() * w;
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// double theta = sqrt(thetasquared);
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// double X = sin(theta)/theta;
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// double Y = (1-cos(theta))/thetasquared;
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// double Z = (1-X)/thetasquared;
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// double W = (0.5-Y)/thetasquared;
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// double alpha = lambdasquared / (lambdasquared + thetasquared);
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// double beta = (exp(-lambda)-1+lambda)/lambdasquared;
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// double gama = Y - (lambda * Z);
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// double mu = (1-lambda+(0.5*lambdasquared)-exp(-lambda))/(lambdasquared*lambda);
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// double upsilon = Z-(lambda*W);
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// double A = (1-exp(-lambda))/lambda;
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// double B = alpha*(beta-gama)+gama;
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// double C = alpha*(mu-upsilon)+upsilon;
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// Matrix33 V = A*Matrix33::Identity() + B*wx + C*wx*wx;
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return Similarity3(Rot3::Expmap(w), Point3(V*u), 1.0/exp(-lambda));
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}
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Similarity3 Similarity3::ChartAtOrigin::Retract(const Vector7& v,
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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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// Rot3 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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// Point3(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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// Use the Expmap
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return Similarity3::Expmap(v);
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}
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Vector7 Similarity3::ChartAtOrigin::Local(const Similarity3& other,
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ChartJacobian H) {
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// Rot3 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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// Use the Logmap
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return Similarity3::Logmap(other);
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}
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const Matrix4 Similarity3::matrix() const {
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Matrix4 T;
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T.topRows<3>() << s_ * R_.matrix(), t_.vector();
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T.bottomRows<1>() << 0, 0, 0, 1;
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return T;
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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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