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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.
// Author: Yaqing Ding
// Mark Shachkov
#include "p3p.h"
#include "PoseLib/misc/univariate.h"
#include "p3p_common.h"
namespace poselib {
int p3p(const std::vector<Eigen::Vector3d> &x_copy, const std::vector<Eigen::Vector3d> &X_copy,
std::vector<CameraPose> *output) {
if (output == nullptr) {
return 0;
}
output->clear();
output->reserve(4);
Eigen::Vector3d X01 = X_copy[0] - X_copy[1];
Eigen::Vector3d X02 = X_copy[0] - X_copy[2];
Eigen::Vector3d X12 = X_copy[1] - X_copy[2];
double a01 = X01.squaredNorm();
double a02 = X02.squaredNorm();
double a12 = X12.squaredNorm();
std::array<Eigen::Vector3d, 3> X = {X_copy[0], X_copy[1], X_copy[2]};
std::array<Eigen::Vector3d, 3> x = {x_copy[0], x_copy[1], x_copy[2]};
// Switch X,x so that BC is the largest distance among {X01, X02, X12}
if (a01 > a02) {
if (a01 > a12) {
std::swap(x[0], x[2]);
std::swap(X[0], X[2]);
std::swap(a01, a12);
X01 = -X12;
X02 = -X02;
}
} else if (a02 > a12) {
std::swap(x[0], x[1]);
std::swap(X[0], X[1]);
std::swap(a02, a12);
X01 = -X01;
X02 = X12;
}
const double a12d = 1.0 / a12;
const double a = a01 * a12d;
const double b = a02 * a12d;
const double m01 = x[0].dot(x[1]);
const double m02 = x[0].dot(x[2]);
const double m12 = x[1].dot(x[2]);
// Ugly parameters to simplify the calculation
const double m12sq = -m12 * m12 + 1.0;
const double m02sq = -1.0 + m02 * m02;
const double m01sq = -1.0 + m01 * m01;
const double ab = a * b;
const double bsq = b * b;
const double asq = a * a;
const double m013 = -2.0 + 2.0 * m01 * m02 * m12;
const double bsqm12sq = bsq * m12sq;
const double asqm12sq = asq * m12sq;
const double abm12sq = 2.0 * ab * m12sq;
const double k3_inv = 1.0 / (bsqm12sq + b * m02sq);
const double k2 = k3_inv * ((-1.0 + a) * m02sq + abm12sq + bsqm12sq + b * m013);
const double k1 = k3_inv * (asqm12sq + abm12sq + a * m013 + (-1.0 + b) * m01sq);
const double k0 = k3_inv * (asqm12sq + a * m01sq);
double s;
bool G = univariate::solve_cubic_single_real(k2, k1, k0, s);
Eigen::Matrix3d C;
C(0, 0) = -a + s * (1 - b);
C(0, 1) = -m02 * s;
C(0, 2) = a * m12 + b * m12 * s;
C(1, 0) = C(0, 1);
C(1, 1) = s + 1;
C(1, 2) = -m01;
C(2, 0) = C(0, 2);
C(2, 1) = C(1, 2);
C(2, 2) = -a - b * s + 1;
std::array<Eigen::Vector3d, 2> pq = compute_pq(C);
double d0, d1, d2;
CameraPose pose;
output->clear();
Eigen::Matrix3d XX;
XX << X01, X02, X01.cross(X02);
XX = XX.inverse().eval();
Eigen::Vector3d v1, v2;
Eigen::Matrix3d YY;
int n_sols = 0;
for (int i = 0; i < 2; ++i) {
// [p0 p1 p2] * [1; x; y] = 0, or [p0 p1 p2] * [d2; d0; d1] = 0
double p0 = pq[i](0);
double p1 = pq[i](1);
double p2 = pq[i](2);
// here we run into trouble if p0 is zero,
// so depending on which is larger, we solve for either d0 or d1
// The case p0 = p1 = 0 is degenerate and can be ignored
bool switch_12 = std::abs(p0) <= std::abs(p1);
if (switch_12) {
// eliminate d0
double w0 = -p0 / p1;
double w1 = -p2 / p1;
double ca = 1.0 / (w1 * w1 - b);
double cb = 2.0 * (b * m12 - m02 * w1 + w0 * w1) * ca;
double cc = (w0 * w0 - 2 * m02 * w0 - b + 1.0) * ca;
double taus[2];
if (!root2real(cb, cc, taus[0], taus[1]))
continue;
for (double tau : taus) {
if (tau <= 0)
continue;
// positive only
d2 = std::sqrt(a12 / (tau * (tau - 2.0 * m12) + 1.0));
d1 = tau * d2;
d0 = (w0 * d2 + w1 * d1);
if (d0 < 0)
continue;
refine_lambda(d0, d1, d2, a01, a02, a12, m01, m02, m12);
v1 = d0 * x[0] - d1 * x[1];
v2 = d0 * x[0] - d2 * x[2];
YY << v1, v2, v1.cross(v2);
Eigen::Matrix3d R = YY * XX;
output->emplace_back(R, d0 * x[0] - R * X[0]);
++n_sols;
}
} else {
double w0 = -p1 / p0;
double w1 = -p2 / p0;
double ca = 1.0 / (-a * w1 * w1 + 2 * a * m12 * w1 - a + 1);
double cb = 2 * (a * m12 * w0 - m01 - a * w0 * w1) * ca;
double cc = (1 - a * w0 * w0) * ca;
double taus[2];
if (!root2real(cb, cc, taus[0], taus[1]))
continue;
for (double tau : taus) {
if (tau <= 0)
continue;
d0 = std::sqrt(a01 / (tau * (tau - 2.0 * m01) + 1.0));
d1 = tau * d0;
d2 = w0 * d0 + w1 * d1;
if (d2 < 0)
continue;
refine_lambda(d0, d1, d2, a01, a02, a12, m01, m02, m12);
v1 = d0 * x[0] - d1 * x[1];
v2 = d0 * x[0] - d2 * x[2];
YY << v1, v2, v1.cross(v2);
Eigen::Matrix3d R = YY * XX;
output->emplace_back(R, d0 * x[0] - R * X[0]);
++n_sols;
}
}
if (n_sols > 0 && G)
break;
}
return output->size();
}
} // namespace poselib
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