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| /* | ||
| * Copyright (C) 2021 Open Source Robotics Foundation | ||
| * | ||
| * Licensed under the Apache License, Version 2.0 (the "License"); | ||
| * you may not use this file except in compliance with the License. | ||
| * You may obtain a copy of the License at | ||
| * | ||
| * http://www.apache.org/licenses/LICENSE-2.0 | ||
| * | ||
| * Unless required by applicable law or agreed to in writing, software | ||
| * distributed under the License is distributed on an "AS IS" BASIS, | ||
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | ||
| * See the License for the specific language governing permissions and | ||
| * limitations under the License. | ||
| * | ||
| */ | ||
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| #ifndef IGNITION_MATH_EIGEN3_UTIL_HH_ | ||
| #define IGNITION_MATH_EIGEN3_UTIL_HH_ | ||
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| #include <vector> | ||
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| #include <Eigen/Geometry> | ||
| #include <Eigen/Eigenvalues> | ||
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| #include <ignition/math/AxisAlignedBox.hh> | ||
| #include <ignition/math/Matrix3.hh> | ||
| #include <ignition/math/OrientedBox.hh> | ||
| #include <ignition/math/Pose3.hh> | ||
| #include <ignition/math/Quaternion.hh> | ||
| #include <ignition/math/Vector3.hh> | ||
| #include <ignition/math/eigen3/Conversions.hh> | ||
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| namespace ignition | ||
| { | ||
| namespace math | ||
| { | ||
| namespace eigen3 | ||
| { | ||
| /// \brief Get covariance matrix from a set of 3d vertices | ||
| /// https://github.com/isl-org/Open3D/blob/76c2baf9debd460900f056a9b51e9a80de9c0e64/cpp/open3d/utility/Eigen.cpp#L305 | ||
| /// \param[in] _vertices a vector of 3d vertices | ||
| /// \return Covariance matrix | ||
| inline Eigen::Matrix3d covarianceMatrix( | ||
| const std::vector<math::Vector3d> &_vertices) | ||
| { | ||
| if (_vertices.empty()) | ||
| return Eigen::Matrix3d::Identity(); | ||
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| Eigen::Matrix<double, 9, 1> cumulants; | ||
| cumulants.setZero(); | ||
| for (const auto &vertex : _vertices) | ||
| { | ||
| const Eigen::Vector3d &point = math::eigen3::convert(vertex); | ||
| cumulants(0) += point(0); | ||
| cumulants(1) += point(1); | ||
| cumulants(2) += point(2); | ||
| cumulants(3) += point(0) * point(0); | ||
| cumulants(4) += point(0) * point(1); | ||
| cumulants(5) += point(0) * point(2); | ||
| cumulants(6) += point(1) * point(1); | ||
| cumulants(7) += point(1) * point(2); | ||
| cumulants(8) += point(2) * point(2); | ||
| } | ||
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| Eigen::Matrix3d covariance; | ||
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| cumulants /= static_cast<double>(_vertices.size()); | ||
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| covariance(0, 0) = cumulants(3) - cumulants(0) * cumulants(0); | ||
| covariance(1, 1) = cumulants(6) - cumulants(1) * cumulants(1); | ||
| covariance(2, 2) = cumulants(8) - cumulants(2) * cumulants(2); | ||
| covariance(0, 1) = cumulants(4) - cumulants(0) * cumulants(1); | ||
| covariance(1, 0) = covariance(0, 1); | ||
| covariance(0, 2) = cumulants(5) - cumulants(0) * cumulants(2); | ||
| covariance(2, 0) = covariance(0, 2); | ||
| covariance(1, 2) = cumulants(7) - cumulants(1) * cumulants(2); | ||
| covariance(2, 1) = covariance(1, 2); | ||
| return covariance; | ||
| } | ||
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| /// \brief Get the oriented 3d bounding box of a set of 3d | ||
| /// vertices using PCA | ||
| /// http://codextechnicanum.blogspot.com/2015/04/find-minimum-oriented-bounding-box-of.html | ||
| /// \param[in] _vertices a vector of 3d vertices | ||
| /// \return Oriented 3D box | ||
| inline ignition::math::OrientedBoxd verticesToOrientedBox( | ||
| const std::vector<math::Vector3d> &_vertices) | ||
| { | ||
| math::OrientedBoxd box; | ||
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| // Return an empty box if there are no vertices | ||
| if (_vertices.empty()) | ||
| return box; | ||
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| math::Vector3d mean; | ||
| for (const auto &point : _vertices) | ||
| mean += point; | ||
| mean /= static_cast<double>(_vertices.size()); | ||
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| Eigen::Vector3d centroid = math::eigen3::convert(mean); | ||
| Eigen::Matrix3d covariance = covarianceMatrix(_vertices); | ||
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| // Eigen Vectors | ||
| Eigen::SelfAdjointEigenSolver<Eigen::Matrix3d> | ||
| eigenSolver(covariance, Eigen::ComputeEigenvectors); | ||
| Eigen::Matrix3d eigenVectorsPCA = eigenSolver.eigenvectors(); | ||
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| // This line is necessary for proper orientation in some cases. | ||
| // The numbers come out the same without it, but the signs are | ||
| // different and the box doesn't get correctly oriented in some cases. | ||
| eigenVectorsPCA.col(2) = | ||
| eigenVectorsPCA.col(0).cross(eigenVectorsPCA.col(1)); | ||
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| // Transform the original cloud to the origin where the principal | ||
| // components correspond to the axes. | ||
| Eigen::Matrix4d projectionTransform(Eigen::Matrix4d::Identity()); | ||
| projectionTransform.block<3, 3>(0, 0) = eigenVectorsPCA.transpose(); | ||
| projectionTransform.block<3, 1>(0, 3) = | ||
| -1.0f * (projectionTransform.block<3, 3>(0, 0) * centroid); | ||
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| Eigen::Vector3d minPoint(INF_I32, INF_I32, INF_I32); | ||
| Eigen::Vector3d maxPoint(-INF_I32, -INF_I32, -INF_I32); | ||
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| // Get the minimum and maximum points of the transformed cloud. | ||
| for (const auto &point : _vertices) | ||
| { | ||
| Eigen::Vector4d pt(0, 0, 0, 1); | ||
| pt.head<3>() = math::eigen3::convert(point); | ||
| Eigen::Vector4d tfPoint = projectionTransform * pt; | ||
| minPoint = minPoint.cwiseMin(tfPoint.head<3>()); | ||
| maxPoint = maxPoint.cwiseMax(tfPoint.head<3>()); | ||
| } | ||
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| const Eigen::Vector3d meanDiagonal = 0.5f * (maxPoint + minPoint); | ||
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| // quaternion is calculated using the eigenvectors (which determines | ||
| // how the final box gets rotated), and the transform to put the box | ||
| // in correct location is calculated | ||
| const Eigen::Quaterniond bboxQuaternion(eigenVectorsPCA); | ||
| const Eigen::Vector3d bboxTransform = | ||
| eigenVectorsPCA * meanDiagonal + centroid; | ||
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| math::Vector3d size( | ||
| maxPoint.x() - minPoint.x(), | ||
| maxPoint.y() - minPoint.y(), | ||
| maxPoint.z() - minPoint.z() | ||
| ); | ||
| math::Pose3d pose; | ||
| pose.Rot() = math::eigen3::convert(bboxQuaternion); | ||
| pose.Pos() = math::eigen3::convert(bboxTransform); | ||
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| box.Size(size); | ||
| box.Pose(pose); | ||
| return box; | ||
| } | ||
| } | ||
| } | ||
| } | ||
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| #endif |
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