250 lines
8.4 KiB
C++
250 lines
8.4 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 Pose3.cpp
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* @brief 3D Pose
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*/
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#include <gtsam/geometry/Pose3.h>
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#include <gtsam/geometry/Pose2.h>
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#include <gtsam/geometry/concepts.h>
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#include <gtsam/base/Lie-inl.h>
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#include <iostream>
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#include <cmath>
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using namespace std;
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namespace gtsam {
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/** Explicit instantiation of base class to export members */
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INSTANTIATE_LIE(Pose3);
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/** instantiate concept checks */
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GTSAM_CONCEPT_POSE_INST(Pose3);
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static const Matrix I3 = eye(3), Z3 = zeros(3, 3), _I3=-I3, I6 = eye(6);
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/* ************************************************************************* */
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Pose3::Pose3(const Pose2& pose2) :
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R_(Rot3::rodriguez(0, 0, pose2.theta())),
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t_(Point3(pose2.x(), pose2.y(), 0)) {
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}
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/* ************************************************************************* */
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// Calculate Adjoint map
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// Ad_pose is 6*6 matrix that when applied to twist xi, returns Ad_pose(xi)
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// Experimental - unit tests of derivatives based on it do not check out yet
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Matrix Pose3::adjointMap() const {
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const Matrix R = R_.matrix();
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const Vector t = t_.vector();
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Matrix A = skewSymmetric(t)*R;
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Matrix DR = collect(2, &R, &Z3);
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Matrix Dt = collect(2, &A, &R);
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return gtsam::stack(2, &DR, &Dt);
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}
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/* ************************************************************************* */
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void Pose3::print(const string& s) const {
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R_.print(s + ".R");
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t_.print(s + ".t");
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}
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/* ************************************************************************* */
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bool Pose3::equals(const Pose3& pose, double tol) const {
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return R_.equals(pose.R_,tol) && t_.equals(pose.t_,tol);
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}
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/* ************************************************************************* */
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/** Modified from Murray94book version (which assumes w and v normalized?) */
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Pose3 Pose3::Expmap(const Vector& xi) {
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// get angular velocity omega and translational velocity v from twist xi
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Point3 w(xi(0),xi(1),xi(2)), v(xi(3),xi(4),xi(5));
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double theta = w.norm();
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if (theta < 1e-10) {
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static const Rot3 I;
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return Pose3(I, v);
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}
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else {
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Point3 n(w/theta); // axis unit vector
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Rot3 R = Rot3::rodriguez(n.vector(),theta);
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double vn = n.dot(v); // translation parallel to n
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Point3 n_cross_v = n.cross(v); // points towards axis
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Point3 t = (n_cross_v - R*n_cross_v)/theta + vn*n;
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return Pose3(R, t);
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}
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}
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/* ************************************************************************* */
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Vector Pose3::Logmap(const Pose3& p) {
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Vector w = Rot3::Logmap(p.rotation()), T = p.translation().vector();
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double t = w.norm();
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if (t < 1e-10)
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return concatVectors(2, &w, &T);
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else {
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Matrix W = skewSymmetric(w/t);
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// Formula from Agrawal06iros, equation (14)
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// simplified with Mathematica, and multiplying in T to avoid matrix math
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double Tan = tan(0.5*t);
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Vector WT = W*T;
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Vector u = T - (0.5*t)*WT + (1 - t/(2.*Tan)) * (W * WT);
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return concatVectors(2, &w, &u);
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}
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}
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/* ************************************************************************* */
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Pose3 Pose3::retractFirstOrder(const Vector& xi) const {
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Vector omega(sub(xi, 0, 3));
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Point3 v(sub(xi, 3, 6));
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Rot3 R = R_.retract(omega); // R is done exactly
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Point3 t = t_ + R_ * v; // First order t approximation
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return Pose3(R, t);
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}
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/* ************************************************************************* */
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// Different versions of retract
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Pose3 Pose3::retract(const Vector& xi, Pose3::CoordinatesMode mode) const {
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if(mode == Pose3::EXPMAP) {
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// Lie group exponential map, traces out geodesic
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return compose(Expmap(xi));
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} else if(mode == Pose3::FIRST_ORDER) {
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// First order
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return retractFirstOrder(xi);
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} else {
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// Point3 t = t_.retract(v.vector()); // Incorrect version retracts t independently
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// Point3 t = t_ + R_ * (v+Point3(omega).cross(v)/2); // Second order t approximation
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assert(false);
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exit(1);
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}
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}
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/* ************************************************************************* */
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// different versions of localCoordinates
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Vector Pose3::localCoordinates(const Pose3& T, Pose3::CoordinatesMode mode) const {
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if(mode == Pose3::EXPMAP) {
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// Lie group logarithm map, exact inverse of exponential map
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return Logmap(between(T));
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} else if(mode == Pose3::FIRST_ORDER) {
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// R is always done exactly in all three retract versions below
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Vector omega = R_.localCoordinates(T.rotation());
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// Incorrect version
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// Independently computes the logmap of the translation and rotation
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// Vector v = t_.localCoordinates(T.translation());
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// Correct first order t inverse
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Point3 d = R_.unrotate(T.translation() - t_);
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// TODO: correct second order t inverse
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return Vector_(6,omega(0),omega(1),omega(2),d.x(),d.y(),d.z());
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} else {
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assert(false);
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exit(1);
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}
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}
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/* ************************************************************************* */
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Matrix Pose3::matrix() const {
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const Matrix R = R_.matrix(), T = Matrix_(3,1, t_.vector());
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const Matrix A34 = collect(2, &R, &T);
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const Matrix A14 = Matrix_(1,4, 0.0, 0.0, 0.0, 1.0);
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return gtsam::stack(2, &A34, &A14);
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}
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/* ************************************************************************* */
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Pose3 Pose3::transform_to(const Pose3& pose) const {
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Rot3 cRv = R_ * Rot3(pose.R_.inverse());
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Point3 t = pose.transform_to(t_);
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return Pose3(cRv, t);
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}
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/* ************************************************************************* */
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Point3 Pose3::transform_from(const Point3& p,
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boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
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if (H1) {
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const Matrix R = R_.matrix();
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Matrix DR = R*skewSymmetric(-p.x(), -p.y(), -p.z());
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*H1 = collect(2,&DR,&R);
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}
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if (H2) *H2 = R_.matrix();
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return R_ * p + t_;
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}
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/* ************************************************************************* */
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Point3 Pose3::transform_to(const Point3& p,
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boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
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const Point3 result = R_.unrotate(p - t_);
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if (H1) {
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const Point3& q = result;
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Matrix DR = skewSymmetric(q.x(), q.y(), q.z());
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*H1 = collect(2, &DR, &_I3);
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}
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if (H2) *H2 = R_.transpose();
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return result;
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}
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/* ************************************************************************* */
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Pose3 Pose3::compose(const Pose3& p2,
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boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
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if (H1) *H1 = p2.inverse().adjointMap();
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if (H2) *H2 = I6;
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return (*this) * p2;
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}
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/* ************************************************************************* */
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Pose3 Pose3::inverse(boost::optional<Matrix&> H1) const {
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if (H1) *H1 = -adjointMap();
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Rot3 Rt = R_.inverse();
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return Pose3(Rt, Rt*(-t_));
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}
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/* ************************************************************************* */
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// between = compose(p2,inverse(p1));
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Pose3 Pose3::between(const Pose3& p2, boost::optional<Matrix&> H1,
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boost::optional<Matrix&> H2) const {
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Matrix invH;
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Pose3 invp1 = inverse(invH);
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Matrix composeH1;
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Pose3 result = invp1.compose(p2, composeH1, H2);
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if (H1) *H1 = composeH1 * invH;
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return result;
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}
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/* ************************************************************************* */
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double Pose3::range(const Point3& point,
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boost::optional<Matrix&> H1,
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boost::optional<Matrix&> H2) const {
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if (!H1 && !H2) return transform_to(point).norm();
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Point3 d = transform_to(point, H1, H2);
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double x = d.x(), y = d.y(), z = d.z(),
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d2 = x * x + y * y + z * z, n = sqrt(d2);
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Matrix D_result_d = Matrix_(1, 3, x / n, y / n, z / n);
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if (H1) *H1 = D_result_d * (*H1);
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if (H2) *H2 = D_result_d * (*H2);
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return n;
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}
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/* ************************************************************************* */
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double Pose3::range(const Pose3& point,
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boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
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double r = range(point.translation(), H1, H2);
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if (H2) {
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Matrix H2_ = *H2 * point.rotation().matrix();
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*H2 = zeros(1, 6);
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insertSub(*H2, H2_, 0, 3);
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}
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return r;
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}
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} // namespace gtsam
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