449 lines
15 KiB
C++
449 lines
15 KiB
C++
/**
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BSD 3-Clause License
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This file is part of the Basalt project.
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https://gitlab.com/VladyslavUsenko/basalt-headers.git
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Copyright (c) 2019, Vladyslav Usenko and Nikolaus Demmel.
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All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are met:
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* Redistributions of source code must retain the above copyright notice, this
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list of conditions and the following disclaimer.
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* Redistributions in binary form must reproduce the above copyright notice,
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this list of conditions and the following disclaimer in the documentation
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and/or other materials provided with the distribution.
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* Neither the name of the copyright holder nor the names of its
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contributors may be used to endorse or promote products derived from
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this software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
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FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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@file
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@brief Implementation of double sphere camera model
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*/
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#pragma once
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#include <basalt/camera/camera_static_assert.hpp>
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#include <basalt/utils/sophus_utils.hpp>
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namespace basalt {
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using std::sqrt;
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/// @brief Double Sphere camera model
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///
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/// \image html ds.png
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/// This model has N=6 parameters \f$ \mathbf{i} = \left[f_x, f_y, c_x, c_y,
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/// \xi, \alpha \right]^T \f$ with \f$ \xi \in [-1,1], \alpha \in [0,1] \f$. See
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/// \ref project and \ref unproject functions for more details.
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template <typename Scalar_ = double>
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class DoubleSphereCamera {
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public:
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using Scalar = Scalar_;
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static constexpr int N = 6; ///< Number of intrinsic parameters.
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using Vec2 = Eigen::Matrix<Scalar, 2, 1>;
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using Vec4 = Eigen::Matrix<Scalar, 4, 1>;
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using VecN = Eigen::Matrix<Scalar, N, 1>;
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using Mat24 = Eigen::Matrix<Scalar, 2, 4>;
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using Mat2N = Eigen::Matrix<Scalar, 2, N>;
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using Mat42 = Eigen::Matrix<Scalar, 4, 2>;
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using Mat4N = Eigen::Matrix<Scalar, 4, N>;
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/// @brief Default constructor with zero intrinsics
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DoubleSphereCamera() { param_.setZero(); }
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/// @brief Construct camera model with given vector of intrinsics
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///
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/// @param[in] p vector of intrinsic parameters [fx, fy, cx, cy, xi, alpha]
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explicit DoubleSphereCamera(const VecN& p) { param_ = p; }
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/// @brief Cast to different scalar type
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template <class Scalar2>
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DoubleSphereCamera<Scalar2> cast() const {
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return DoubleSphereCamera<Scalar2>(param_.template cast<Scalar2>());
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}
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/// @brief Camera model name
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///
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/// @return "ds"
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static std::string getName() { return "ds"; }
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/// @brief Project the point and optionally compute Jacobians
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///
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/// Projection function is defined as follows:
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/// \f{align}{
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/// \pi(\mathbf{x}, \mathbf{i}) &=
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/// \begin{bmatrix}
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/// f_x{\frac{x}{\alpha d_2 + (1-\alpha) (\xi d_1 + z)}}
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/// \\ f_y{\frac{y}{\alpha d_2 + (1-\alpha) (\xi d_1 + z)}}
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/// \\ \end{bmatrix}
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/// +
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/// \begin{bmatrix}
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/// c_x
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/// \\ c_y
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/// \\ \end{bmatrix},
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/// \\ d_1 &= \sqrt{x^2 + y^2 + z^2},
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/// \\ d_2 &= \sqrt{x^2 + y^2 + (\xi d_1 + z)^2}.
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/// \f}
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/// A set of 3D points that results in valid projection is expressed as
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/// follows: \f{align}{
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/// \Omega &= \{\mathbf{x} \in \mathbb{R}^3 ~|~ z > -w_2 d_1 \}
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/// \\ w_2 &= \frac{w_1+\xi}{\sqrt{2w_1\xi + \xi^2 + 1}}
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/// \\ w_1 &= \begin{cases} \frac{\alpha}{1-\alpha}, & \mbox{if } \alpha
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/// \le 0.5 \\ \frac{1-\alpha}{\alpha} & \mbox{if } \alpha > 0.5
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/// \end{cases}
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/// \f}
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///
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/// @param[in] p3d point to project
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/// @param[out] proj result of projection
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/// @param[out] d_proj_d_p3d if not nullptr computed Jacobian of projection
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/// with respect to p3d
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/// @param[out] d_proj_d_param point if not nullptr computed Jacobian of
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/// projection with respect to intrinsic parameters
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/// @return if projection is valid
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template <class DerivedPoint3D, class DerivedPoint2D,
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class DerivedJ3D = std::nullptr_t,
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class DerivedJparam = std::nullptr_t>
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inline bool project(const Eigen::MatrixBase<DerivedPoint3D>& p3d,
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Eigen::MatrixBase<DerivedPoint2D>& proj,
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DerivedJ3D d_proj_d_p3d = nullptr,
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DerivedJparam d_proj_d_param = nullptr) const {
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checkProjectionDerivedTypes<DerivedPoint3D, DerivedPoint2D, DerivedJ3D,
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DerivedJparam, N>();
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const typename EvalOrReference<DerivedPoint3D>::Type p3d_eval(p3d);
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const Scalar& fx = param_[0];
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const Scalar& fy = param_[1];
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const Scalar& cx = param_[2];
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const Scalar& cy = param_[3];
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const Scalar& xi = param_[4];
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const Scalar& alpha = param_[5];
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const Scalar& x = p3d_eval[0];
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const Scalar& y = p3d_eval[1];
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const Scalar& z = p3d_eval[2];
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const Scalar xx = x * x;
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const Scalar yy = y * y;
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const Scalar zz = z * z;
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const Scalar r2 = xx + yy;
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const Scalar d1_2 = r2 + zz;
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const Scalar d1 = sqrt(d1_2);
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const Scalar w1 = alpha > Scalar(0.5) ? (Scalar(1) - alpha) / alpha
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: alpha / (Scalar(1) - alpha);
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const Scalar w2 =
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(w1 + xi) / sqrt(Scalar(2) * w1 * xi + xi * xi + Scalar(1));
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const bool is_valid = (z > -w2 * d1);
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const Scalar k = xi * d1 + z;
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const Scalar kk = k * k;
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const Scalar d2_2 = r2 + kk;
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const Scalar d2 = sqrt(d2_2);
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const Scalar norm = alpha * d2 + (Scalar(1) - alpha) * k;
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const Scalar mx = x / norm;
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const Scalar my = y / norm;
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proj[0] = fx * mx + cx;
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proj[1] = fy * my + cy;
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if constexpr (!std::is_same_v<DerivedJ3D, std::nullptr_t>) {
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BASALT_ASSERT(d_proj_d_p3d);
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const Scalar norm2 = norm * norm;
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const Scalar xy = x * y;
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const Scalar tt2 = xi * z / d1 + Scalar(1);
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const Scalar d_norm_d_r2 = (xi * (Scalar(1) - alpha) / d1 +
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alpha * (xi * k / d1 + Scalar(1)) / d2) /
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norm2;
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const Scalar tmp2 =
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((Scalar(1) - alpha) * tt2 + alpha * k * tt2 / d2) / norm2;
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d_proj_d_p3d->setZero();
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(*d_proj_d_p3d)(0, 0) = fx * (Scalar(1) / norm - xx * d_norm_d_r2);
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(*d_proj_d_p3d)(1, 0) = -fy * xy * d_norm_d_r2;
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(*d_proj_d_p3d)(0, 1) = -fx * xy * d_norm_d_r2;
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(*d_proj_d_p3d)(1, 1) = fy * (Scalar(1) / norm - yy * d_norm_d_r2);
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(*d_proj_d_p3d)(0, 2) = -fx * x * tmp2;
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(*d_proj_d_p3d)(1, 2) = -fy * y * tmp2;
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} else {
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UNUSED(d_proj_d_p3d);
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}
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if constexpr (!std::is_same_v<DerivedJparam, std::nullptr_t>) {
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BASALT_ASSERT(d_proj_d_param);
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const Scalar norm2 = norm * norm;
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(*d_proj_d_param).setZero();
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(*d_proj_d_param)(0, 0) = mx;
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(*d_proj_d_param)(0, 2) = Scalar(1);
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(*d_proj_d_param)(1, 1) = my;
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(*d_proj_d_param)(1, 3) = Scalar(1);
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const Scalar tmp4 = (alpha - Scalar(1) - alpha * k / d2) * d1 / norm2;
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const Scalar tmp5 = (k - d2) / norm2;
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(*d_proj_d_param)(0, 4) = fx * x * tmp4;
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(*d_proj_d_param)(1, 4) = fy * y * tmp4;
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(*d_proj_d_param)(0, 5) = fx * x * tmp5;
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(*d_proj_d_param)(1, 5) = fy * y * tmp5;
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} else {
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UNUSED(d_proj_d_param);
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}
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return is_valid;
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}
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/// @brief Unproject the point and optionally compute Jacobians
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///
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/// The unprojection function is computed as follows: \f{align}{
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/// \pi^{-1}(\mathbf{u}, \mathbf{i}) &=
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/// \frac{m_z \xi + \sqrt{m_z^2 + (1 - \xi^2) r^2}}{m_z^2 + r^2}
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/// \begin{bmatrix}
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/// m_x \\ m_y \\m_z
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/// \\ \end{bmatrix}-\begin{bmatrix}
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/// 0 \\ 0 \\ \xi
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/// \\ \end{bmatrix},
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/// \\ m_x &= \frac{u - c_x}{f_x},
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/// \\ m_y &= \frac{v - c_y}{f_y},
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/// \\ r^2 &= m_x^2 + m_y^2,
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/// \\ m_z &= \frac{1 - \alpha^2 r^2}{\alpha \sqrt{1 - (2 \alpha - 1)
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/// r^2}
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/// + 1 - \alpha},
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/// \f}
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///
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/// The valid range of unprojections is \f{align}{
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/// \Theta &= \begin{cases}
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/// \mathbb{R}^2 & \mbox{if } \alpha \le 0.5
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/// \\ \{ \mathbf{u} \in \mathbb{R}^2 ~|~ r^2 \le \frac{1}{2\alpha-1} \} &
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/// \mbox{if} \alpha > 0.5 \end{cases}
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/// \f}
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///
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/// @param[in] proj point to unproject
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/// @param[out] p3d result of unprojection
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/// @param[out] d_p3d_d_proj if not nullptr computed Jacobian of unprojection
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/// with respect to proj
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/// @param[out] d_p3d_d_param point if not nullptr computed Jacobian of
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/// unprojection with respect to intrinsic parameters
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/// @return if unprojection is valid
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template <class DerivedPoint2D, class DerivedPoint3D,
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class DerivedJ2D = std::nullptr_t,
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class DerivedJparam = std::nullptr_t>
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inline bool unproject(const Eigen::MatrixBase<DerivedPoint2D>& proj,
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Eigen::MatrixBase<DerivedPoint3D>& p3d,
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DerivedJ2D d_p3d_d_proj = nullptr,
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DerivedJparam d_p3d_d_param = nullptr) const {
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checkUnprojectionDerivedTypes<DerivedPoint2D, DerivedPoint3D, DerivedJ2D,
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DerivedJparam, N>();
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const typename EvalOrReference<DerivedPoint2D>::Type proj_eval(proj);
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const Scalar& fx = param_[0];
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const Scalar& fy = param_[1];
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const Scalar& cx = param_[2];
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const Scalar& cy = param_[3];
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const Scalar& xi = param_[4];
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const Scalar& alpha = param_[5];
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const Scalar mx = (proj_eval[0] - cx) / fx;
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const Scalar my = (proj_eval[1] - cy) / fy;
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const Scalar r2 = mx * mx + my * my;
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const bool is_valid =
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!static_cast<bool>(alpha > Scalar(0.5) &&
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(r2 >= Scalar(1) / (Scalar(2) * alpha - Scalar(1))));
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const Scalar xi2_2 = alpha * alpha;
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const Scalar xi1_2 = xi * xi;
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const Scalar sqrt2 = sqrt(Scalar(1) - (Scalar(2) * alpha - Scalar(1)) * r2);
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const Scalar norm2 = alpha * sqrt2 + Scalar(1) - alpha;
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const Scalar mz = (Scalar(1) - xi2_2 * r2) / norm2;
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const Scalar mz2 = mz * mz;
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const Scalar norm1 = mz2 + r2;
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const Scalar sqrt1 = sqrt(mz2 + (Scalar(1) - xi1_2) * r2);
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const Scalar k = (mz * xi + sqrt1) / norm1;
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p3d.setZero();
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p3d[0] = k * mx;
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p3d[1] = k * my;
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p3d[2] = k * mz - xi;
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if constexpr (!std::is_same_v<DerivedJ2D, std::nullptr_t> ||
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!std::is_same_v<DerivedJparam, std::nullptr_t>) {
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const Scalar norm2_2 = norm2 * norm2;
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const Scalar norm1_2 = norm1 * norm1;
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const Scalar d_mz_d_r2 = (Scalar(0.5) * alpha - xi2_2) *
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(r2 * xi2_2 - Scalar(1)) /
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(sqrt2 * norm2_2) -
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xi2_2 / norm2;
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const Scalar d_mz_d_mx = 2 * mx * d_mz_d_r2;
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const Scalar d_mz_d_my = 2 * my * d_mz_d_r2;
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const Scalar d_k_d_mz =
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(norm1 * (xi * sqrt1 + mz) - 2 * mz * (mz * xi + sqrt1) * sqrt1) /
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(norm1_2 * sqrt1);
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const Scalar d_k_d_r2 =
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(xi * d_mz_d_r2 +
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Scalar(0.5) / sqrt1 *
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(Scalar(2) * mz * d_mz_d_r2 + Scalar(1) - xi1_2)) /
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norm1 -
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(mz * xi + sqrt1) * (Scalar(2) * mz * d_mz_d_r2 + Scalar(1)) /
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norm1_2;
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const Scalar d_k_d_mx = d_k_d_r2 * 2 * mx;
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const Scalar d_k_d_my = d_k_d_r2 * 2 * my;
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constexpr int SIZE_3D = DerivedPoint3D::SizeAtCompileTime;
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Eigen::Matrix<Scalar, SIZE_3D, 1> c0, c1;
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c0.setZero();
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c0[0] = (mx * d_k_d_mx + k);
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c0[1] = my * d_k_d_mx;
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c0[2] = (mz * d_k_d_mx + k * d_mz_d_mx);
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c0 /= fx;
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c1.setZero();
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c1[0] = mx * d_k_d_my;
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c1[1] = (my * d_k_d_my + k);
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c1[2] = (mz * d_k_d_my + k * d_mz_d_my);
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c1 /= fy;
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if constexpr (!std::is_same_v<DerivedJ2D, std::nullptr_t>) {
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BASALT_ASSERT(d_p3d_d_proj);
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d_p3d_d_proj->col(0) = c0;
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d_p3d_d_proj->col(1) = c1;
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} else {
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UNUSED(d_p3d_d_proj);
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}
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if constexpr (!std::is_same_v<DerivedJparam, std::nullptr_t>) {
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BASALT_ASSERT(d_p3d_d_param);
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const Scalar d_k_d_xi1 = (mz * sqrt1 - xi * r2) / (sqrt1 * norm1);
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const Scalar d_mz_d_xi2 =
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((Scalar(1) - r2 * xi2_2) *
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(r2 * alpha / sqrt2 - sqrt2 + Scalar(1)) / norm2 -
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Scalar(2) * r2 * alpha) /
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norm2;
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const Scalar d_k_d_xi2 = d_k_d_mz * d_mz_d_xi2;
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d_p3d_d_param->setZero();
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(*d_p3d_d_param).col(0) = -c0 * mx;
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(*d_p3d_d_param).col(1) = -c1 * my;
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(*d_p3d_d_param).col(2) = -c0;
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(*d_p3d_d_param).col(3) = -c1;
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(*d_p3d_d_param)(0, 4) = mx * d_k_d_xi1;
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(*d_p3d_d_param)(1, 4) = my * d_k_d_xi1;
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(*d_p3d_d_param)(2, 4) = mz * d_k_d_xi1 - 1;
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(*d_p3d_d_param)(0, 5) = mx * d_k_d_xi2;
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(*d_p3d_d_param)(1, 5) = my * d_k_d_xi2;
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(*d_p3d_d_param)(2, 5) = mz * d_k_d_xi2 + k * d_mz_d_xi2;
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} else {
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UNUSED(d_p3d_d_param);
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UNUSED(d_k_d_mz);
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}
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} else {
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UNUSED(d_p3d_d_proj);
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UNUSED(d_p3d_d_param);
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}
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return is_valid;
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}
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/// @brief Set parameters from initialization
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///
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/// Initializes the camera model to \f$ \left[f_x, f_y, c_x, c_y, 0, 0.5
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/// \right]^T \f$
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///
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/// @param[in] init vector [fx, fy, cx, cy]
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inline void setFromInit(const Vec4& init) {
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param_[0] = init[0];
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param_[1] = init[1];
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param_[2] = init[2];
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param_[3] = init[3];
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param_[4] = 0;
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param_[5] = 0.5;
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}
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/// @brief Increment intrinsic parameters by inc and clamp the values to the
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/// valid range
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///
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/// @param[in] inc increment vector
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void operator+=(const VecN& inc) {
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param_ += inc;
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param_[4] = std::clamp(param_[4], Scalar(-1), Scalar(1));
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param_[5] = std::clamp(param_[5], Scalar(0), Scalar(1));
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}
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/// @brief Returns a const reference to the intrinsic parameters vector
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///
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/// The order is following: \f$ \left[f_x, f_y, c_x, c_y, \xi, \alpha
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/// \right]^T \f$
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/// @return const reference to the intrinsic parameters vector
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const VecN& getParam() const { return param_; }
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/// @brief Projections used for unit-tests
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static Eigen::aligned_vector<DoubleSphereCamera> getTestProjections() {
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Eigen::aligned_vector<DoubleSphereCamera> res;
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VecN vec1;
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vec1 << 0.5 * 805, 0.5 * 800, 505, 509, 0.5 * -0.150694, 0.5 * 1.48785;
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res.emplace_back(vec1);
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return res;
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}
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW
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private:
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VecN param_;
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};
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} // namespace basalt
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