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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2022 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
// 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 Google Inc. 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 THE COPYRIGHT OWNER OR CONTRIBUTORS 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: vitus@google.com (Mike Vitus)
// jodebo_beck@gmx.de (Johannes Beck)
#ifndef CERES_PUBLIC_SPHERE_MANIFOLD_H_
#define CERES_PUBLIC_SPHERE_MANIFOLD_H_
#include <Eigen/Core>
#include <algorithm>
#include <array>
#include <memory>
#include <vector>
#include "ceres/internal/disable_warnings.h"
#include "ceres/internal/export.h"
#include "ceres/internal/householder_vector.h"
#include "ceres/internal/sphere_manifold_functions.h"
#include "ceres/manifold.h"
#include "ceres/types.h"
#include "glog/logging.h"
namespace ceres {
// This provides a manifold on a sphere meaning that the norm of the vector
// stays the same. Such cases often arises in Structure for Motion
// problems. One example where they are used is in representing points whose
// triangulation is ill-conditioned. Here it is advantageous to use an
// over-parameterization since homogeneous vectors can represent points at
// infinity.
//
// The plus operator is defined as
// Plus(x, delta) =
// [sin(0.5 * |delta|) * delta / |delta|, cos(0.5 * |delta|)] * x
//
// The minus operator is defined as
// Minus(x, y) = 2 atan2(nhy, y[-1]) / nhy * hy[0 : size_ - 1]
// with nhy = norm(hy[0 : size_ - 1])
//
// with * defined as an operator which applies the update orthogonal to x to
// remain on the sphere. The ambient space dimension is required to be greater
// than 1.
//
// The class works with dynamic and static ambient space dimensions. If the
// ambient space dimensions is known at compile time use
//
// SphereManifold<3> manifold;
//
// If the ambient space dimensions is not known at compile time the template
// parameter needs to be set to ceres::DYNAMIC and the actual dimension needs
// to be provided as a constructor argument:
//
// SphereManifold<ceres::DYNAMIC> manifold(ambient_dim);
//
// See section B.2 (p.25) in "Integrating Generic Sensor Fusion Algorithms
// with Sound State Representations through Encapsulation of Manifolds" by C.
// Hertzberg, R. Wagner, U. Frese and L. Schroder for more details
// (https://arxiv.org/pdf/1107.1119.pdf)
template <int AmbientSpaceDimension>
class SphereManifold final : public Manifold {
public:
static_assert(
AmbientSpaceDimension == ceres::DYNAMIC || AmbientSpaceDimension > 1,
"The size of the homogeneous vector needs to be greater than 1.");
static_assert(ceres::DYNAMIC == Eigen::Dynamic,
"ceres::DYNAMIC needs to be the same as Eigen::Dynamic.");
SphereManifold();
explicit SphereManifold(int size);
int AmbientSize() const override {
return AmbientSpaceDimension == ceres::DYNAMIC ? size_
: AmbientSpaceDimension;
}
int TangentSize() const override { return AmbientSize() - 1; }
bool Plus(const double* x,
const double* delta,
double* x_plus_delta) const override;
bool PlusJacobian(const double* x, double* jacobian) const override;
bool Minus(const double* y,
const double* x,
double* y_minus_x) const override;
bool MinusJacobian(const double* x, double* jacobian) const override;
private:
static constexpr int TangentSpaceDimension =
AmbientSpaceDimension > 0 ? AmbientSpaceDimension - 1 : Eigen::Dynamic;
using AmbientVector = Eigen::Matrix<double, AmbientSpaceDimension, 1>;
using TangentVector = Eigen::Matrix<double, TangentSpaceDimension, 1>;
using MatrixPlusJacobian = Eigen::Matrix<double,
AmbientSpaceDimension,
TangentSpaceDimension,
Eigen::RowMajor>;
using MatrixMinusJacobian = Eigen::Matrix<double,
TangentSpaceDimension,
AmbientSpaceDimension,
Eigen::RowMajor>;
const int size_{};
};
template <int AmbientSpaceDimension>
SphereManifold<AmbientSpaceDimension>::SphereManifold()
: size_{AmbientSpaceDimension} {
static_assert(
AmbientSpaceDimension != Eigen::Dynamic,
"The size is set to dynamic. Please call the constructor with a size.");
}
template <int AmbientSpaceDimension>
SphereManifold<AmbientSpaceDimension>::SphereManifold(int size) : size_{size} {
if (AmbientSpaceDimension != Eigen::Dynamic) {
CHECK_EQ(AmbientSpaceDimension, size)
<< "Specified size by template parameter differs from the supplied "
"one.";
} else {
CHECK_GT(size_, 1)
<< "The size of the manifold needs to be greater than 1.";
}
}
template <int AmbientSpaceDimension>
bool SphereManifold<AmbientSpaceDimension>::Plus(
const double* x_ptr,
const double* delta_ptr,
double* x_plus_delta_ptr) const {
Eigen::Map<const AmbientVector> x(x_ptr, size_);
Eigen::Map<const TangentVector> delta(delta_ptr, size_ - 1);
Eigen::Map<AmbientVector> x_plus_delta(x_plus_delta_ptr, size_);
const double norm_delta = delta.norm();
if (norm_delta == 0.0) {
x_plus_delta = x;
return true;
}
AmbientVector v(size_);
double beta;
// NOTE: The explicit template arguments are needed here because
// ComputeHouseholderVector is templated and some versions of MSVC
// have trouble deducing the type of v automatically.
internal::ComputeHouseholderVector<Eigen::Map<const AmbientVector>,
double,
AmbientSpaceDimension>(x, &v, &beta);
internal::ComputeSphereManifoldPlus(
v, beta, x, delta, norm_delta, &x_plus_delta);
return true;
}
template <int AmbientSpaceDimension>
bool SphereManifold<AmbientSpaceDimension>::PlusJacobian(
const double* x_ptr, double* jacobian_ptr) const {
Eigen::Map<const AmbientVector> x(x_ptr, size_);
Eigen::Map<MatrixPlusJacobian> jacobian(jacobian_ptr, size_, size_ - 1);
internal::ComputeSphereManifoldPlusJacobian(x, &jacobian);
return true;
}
template <int AmbientSpaceDimension>
bool SphereManifold<AmbientSpaceDimension>::Minus(const double* y_ptr,
const double* x_ptr,
double* y_minus_x_ptr) const {
AmbientVector y = Eigen::Map<const AmbientVector>(y_ptr, size_);
Eigen::Map<const AmbientVector> x(x_ptr, size_);
Eigen::Map<TangentVector> y_minus_x(y_minus_x_ptr, size_ - 1);
// Apply hoseholder transformation.
AmbientVector v(size_);
double beta;
// NOTE: The explicit template arguments are needed here because
// ComputeHouseholderVector is templated and some versions of MSVC
// have trouble deducing the type of v automatically.
internal::ComputeHouseholderVector<Eigen::Map<const AmbientVector>,
double,
AmbientSpaceDimension>(x, &v, &beta);
internal::ComputeSphereManifoldMinus(v, beta, x, y, &y_minus_x);
return true;
}
template <int AmbientSpaceDimension>
bool SphereManifold<AmbientSpaceDimension>::MinusJacobian(
const double* x_ptr, double* jacobian_ptr) const {
Eigen::Map<const AmbientVector> x(x_ptr, size_);
Eigen::Map<MatrixMinusJacobian> jacobian(jacobian_ptr, size_ - 1, size_);
internal::ComputeSphereManifoldMinusJacobian(x, &jacobian);
return true;
}
} // namespace ceres
// clang-format off
#include "ceres/internal/reenable_warnings.h"
// clang-format on
#endif // CERES_PUBLIC_SPHERE_MANIFOLD_H_
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