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// Copyright (c) 2020, Viktor Larsson
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// * Neither the name of the copyright holder nor the
// names of its contributors may be used to endorse or promote products
// derived from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT HOLDER> BE LIABLE FOR ANY
// DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
// (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
// LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
// ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#include "up4pl.h"
#include "PoseLib/misc/qep.h"
int poselib::up4pl(const std::vector<Eigen::Vector3d> &x, const std::vector<Eigen::Vector3d> &X,
const std::vector<Eigen::Vector3d> &V, CameraPoseVector *output) {
Eigen::Matrix<double, 4, 4> M, C, K;
Eigen::Matrix<double, 3, 4> VX;
for (int i = 0; i < 4; ++i)
VX.col(i) = V[i].cross(X[i]);
M(0, 0) = -V[0](1) * x[0](2) - V[0](2) * x[0](1);
M(0, 1) = V[0](2) * x[0](0) - V[0](0) * x[0](2);
M(0, 2) = V[0](0) * x[0](1) + V[0](1) * x[0](0);
M(0, 3) = VX(1, 0) * x[0](1) - VX(0, 0) * x[0](0) - VX(2, 0) * x[0](2);
M(1, 0) = -V[1](1) * x[1](2) - V[1](2) * x[1](1);
M(1, 1) = V[1](2) * x[1](0) - V[1](0) * x[1](2);
M(1, 2) = V[1](0) * x[1](1) + V[1](1) * x[1](0);
M(1, 3) = VX(1, 1) * x[1](1) - VX(0, 1) * x[1](0) - VX(2, 1) * x[1](2);
M(2, 0) = -V[2](1) * x[2](2) - V[2](2) * x[2](1);
M(2, 1) = V[2](2) * x[2](0) - V[2](0) * x[2](2);
M(2, 2) = V[2](0) * x[2](1) + V[2](1) * x[2](0);
M(2, 3) = VX(1, 2) * x[2](1) - VX(0, 2) * x[2](0) - VX(2, 2) * x[2](2);
M(3, 0) = -V[3](1) * x[3](2) - V[3](2) * x[3](1);
M(3, 1) = V[3](2) * x[3](0) - V[3](0) * x[3](2);
M(3, 2) = V[3](0) * x[3](1) + V[3](1) * x[3](0);
M(3, 3) = VX(1, 3) * x[3](1) - VX(0, 3) * x[3](0) - VX(2, 3) * x[3](2);
C(0, 0) = -2 * V[0](0) * x[0](1);
C(0, 1) = 2 * V[0](0) * x[0](0) + 2 * V[0](2) * x[0](2);
C(0, 2) = -2 * V[0](2) * x[0](1);
C(0, 3) = 2 * VX(2, 0) * x[0](0) - 2 * VX(0, 0) * x[0](2);
C(1, 0) = -2 * V[1](0) * x[1](1);
C(1, 1) = 2 * V[1](0) * x[1](0) + 2 * V[1](2) * x[1](2);
C(1, 2) = -2 * V[1](2) * x[1](1);
C(1, 3) = 2 * VX(2, 1) * x[1](0) - 2 * VX(0, 1) * x[1](2);
C(2, 0) = -2 * V[2](0) * x[2](1);
C(2, 1) = 2 * V[2](0) * x[2](0) + 2 * V[2](2) * x[2](2);
C(2, 2) = -2 * V[2](2) * x[2](1);
C(2, 3) = 2 * VX(2, 2) * x[2](0) - 2 * VX(0, 2) * x[2](2);
C(3, 0) = -2 * V[3](0) * x[3](1);
C(3, 1) = 2 * V[3](0) * x[3](0) + 2 * V[3](2) * x[3](2);
C(3, 2) = -2 * V[3](2) * x[3](1);
C(3, 3) = 2 * VX(2, 3) * x[3](0) - 2 * VX(0, 3) * x[3](2);
K(0, 0) = V[0](2) * x[0](1) - V[0](1) * x[0](2);
K(0, 1) = V[0](0) * x[0](2) - V[0](2) * x[0](0);
K(0, 2) = V[0](1) * x[0](0) - V[0](0) * x[0](1);
K(0, 3) = VX(0, 0) * x[0](0) + VX(1, 0) * x[0](1) + VX(2, 0) * x[0](2);
K(1, 0) = V[1](2) * x[1](1) - V[1](1) * x[1](2);
K(1, 1) = V[1](0) * x[1](2) - V[1](2) * x[1](0);
K(1, 2) = V[1](1) * x[1](0) - V[1](0) * x[1](1);
K(1, 3) = VX(0, 1) * x[1](0) + VX(1, 1) * x[1](1) + VX(2, 1) * x[1](2);
K(2, 0) = V[2](2) * x[2](1) - V[2](1) * x[2](2);
K(2, 1) = V[2](0) * x[2](2) - V[2](2) * x[2](0);
K(2, 2) = V[2](1) * x[2](0) - V[2](0) * x[2](1);
K(2, 3) = VX(0, 2) * x[2](0) + VX(1, 2) * x[2](1) + VX(2, 2) * x[2](2);
K(3, 0) = V[3](2) * x[3](1) - V[3](1) * x[3](2);
K(3, 1) = V[3](0) * x[3](2) - V[3](2) * x[3](0);
K(3, 2) = V[3](1) * x[3](0) - V[3](0) * x[3](1);
K(3, 3) = VX(0, 3) * x[3](0) + VX(1, 3) * x[3](1) + VX(2, 3) * x[3](2);
/*
Eigen::Matrix<double, 3, 8> eig_vecs;
double eig_vals[8];
const int n_roots = qep::qep_sturm(M, C, K, eig_vals, &eig_vecs);
*/
// We know that (1+q^2) is a factor. Dividing by this gives degree 6 poly.
Eigen::Matrix<double, 3, 6> eig_vecs;
double eig_vals[6];
const int n_roots = qep::qep_sturm_div_1_q2(M, C, K, eig_vals, &eig_vecs);
output->clear();
for (int i = 0; i < n_roots; ++i) {
const double q = eig_vals[i];
const double q2 = q * q;
const double inv_norm = 1.0 / (1 + q2);
const double cq = (1 - q2) * inv_norm;
const double sq = 2 * q * inv_norm;
Eigen::Matrix3d R;
R.setIdentity();
R(0, 0) = cq;
R(0, 2) = sq;
R(2, 0) = -sq;
R(2, 2) = cq;
output->emplace_back(R, eig_vecs.col(i));
}
return n_roots;
}
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