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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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/* | ||
* 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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#include <gtest/gtest.h> | ||
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#include <ignition/math/eigen3/Util.hh> | ||
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using namespace ignition; | ||
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///////////////////////////////////////////////// | ||
/// \brief Test the oriented box converted from a set of vertices | ||
TEST(EigenUtil, verticesToOrientedBox) | ||
{ | ||
std::vector<math::Vector3d> vertices; | ||
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vertices.push_back(math::Vector3d(1, 0, 0.5)); | ||
vertices.push_back(math::Vector3d(2, 0.1, 0.4)); | ||
vertices.push_back(math::Vector3d(2, 1, 3)); | ||
vertices.push_back(math::Vector3d(1.6, 0.3, 0.1)); | ||
vertices.push_back(math::Vector3d(1.5, 0.5, 1)); | ||
vertices.push_back(math::Vector3d(1.4, 1, 3)); | ||
vertices.push_back(math::Vector3d(1, 0.4, 0.7)); | ||
vertices.push_back(math::Vector3d(0.9, 1.3, 0)); | ||
vertices.push_back(math::Vector3d(0.6, 4, 2)); | ||
vertices.push_back(math::Vector3d(0, 3, 3)); | ||
vertices.push_back(math::Vector3d(-1, -2, 4)); | ||
vertices.push_back(math::Vector3d(-2, -2, 0.6)); | ||
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math::OrientedBoxd box = math::eigen3::verticesToOrientedBox( | ||
vertices); | ||
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auto position = box.Pose().Pos(); | ||
auto rotation = box.Pose().Rot(); | ||
auto size = box.Size(); | ||
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double error = 0.1; | ||
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EXPECT_NEAR(size.X(), 3.09, error); | ||
EXPECT_NEAR(size.Y(), 4.39, error); | ||
EXPECT_NEAR(size.Z(), 6.63, error); | ||
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EXPECT_NEAR(position.X(), 0.38, error); | ||
EXPECT_NEAR(position.Y(), 0.47, error); | ||
EXPECT_NEAR(position.Z(), 1.96, error); | ||
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EXPECT_NEAR(rotation.Roll(), -1.66, error); | ||
EXPECT_NEAR(rotation.Pitch(), 0.4, error); | ||
EXPECT_NEAR(rotation.Yaw(), 2.7, error); | ||
} | ||
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///////////////////////////////////////////////// | ||
TEST(EigenUtil, emptyVertices) | ||
{ | ||
std::vector<math::Vector3d> emptyVertices; | ||
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math::OrientedBoxd box = math::eigen3::verticesToOrientedBox( | ||
emptyVertices); | ||
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auto position = box.Pose().Pos(); | ||
auto rotation = box.Pose().Rot(); | ||
auto size = box.Size(); | ||
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EXPECT_DOUBLE_EQ(size.X(), 0); | ||
EXPECT_DOUBLE_EQ(size.Y(), 0); | ||
EXPECT_DOUBLE_EQ(size.Z(), 0); | ||
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EXPECT_DOUBLE_EQ(position.X(), 0); | ||
EXPECT_DOUBLE_EQ(position.Y(), 0); | ||
EXPECT_DOUBLE_EQ(position.Z(), 0); | ||
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EXPECT_DOUBLE_EQ(rotation.Roll(), 0); | ||
EXPECT_DOUBLE_EQ(rotation.Pitch(), 0); | ||
EXPECT_DOUBLE_EQ(rotation.Yaw(), 0); | ||
} | ||
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///////////////////////////////////////////////// | ||
TEST(EigenUtil, simpleBox) | ||
{ | ||
std::vector<math::Vector3d> vertices; | ||
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vertices.push_back(math::Vector3d(-1, -1, -1)); | ||
vertices.push_back(math::Vector3d(-1, 1, -1)); | ||
vertices.push_back(math::Vector3d(1, -1, -1)); | ||
vertices.push_back(math::Vector3d(1, 1, -1)); | ||
vertices.push_back(math::Vector3d(-1, -1, 1)); | ||
vertices.push_back(math::Vector3d(-1, 1, 1)); | ||
vertices.push_back(math::Vector3d(1, -1, 1)); | ||
vertices.push_back(math::Vector3d(1, 1, 1)); | ||
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math::OrientedBoxd box = math::eigen3::verticesToOrientedBox( | ||
vertices); | ||
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auto position = box.Pose().Pos(); | ||
auto rotation = box.Pose().Rot(); | ||
auto size = box.Size(); | ||
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double error = 0.1; | ||
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EXPECT_NEAR(size.X(), 2, error); | ||
EXPECT_NEAR(size.Y(), 2, error); | ||
EXPECT_NEAR(size.Z(), 2, error); | ||
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EXPECT_NEAR(position.X(), 0, error); | ||
EXPECT_NEAR(position.Y(), 0, error); | ||
EXPECT_NEAR(position.Z(), 0, error); | ||
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EXPECT_NEAR(rotation.Roll(), 0, error); | ||
EXPECT_NEAR(rotation.Pitch(), 0, error); | ||
EXPECT_NEAR(rotation.Yaw(), 0, error); | ||
} | ||
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///////////////////////////////////////////////// | ||
TEST(EigenUtil, covarianceTest) | ||
{ | ||
std::vector<math::Vector3d> vertices; | ||
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vertices.push_back(math::Vector3d(1, 0, 0.5)); | ||
vertices.push_back(math::Vector3d(2, 0.1, 0.4)); | ||
vertices.push_back(math::Vector3d(2, 1, 3)); | ||
vertices.push_back(math::Vector3d(1.6, 0.3, 0.1)); | ||
vertices.push_back(math::Vector3d(1.5, 0.5, 1)); | ||
vertices.push_back(math::Vector3d(1.4, 1, 3)); | ||
vertices.push_back(math::Vector3d(1, 0.4, 0.7)); | ||
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Eigen::Matrix3d covariance = math::eigen3::covarianceMatrix( | ||
vertices); | ||
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double error = 0.1; | ||
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EXPECT_NEAR(covariance(0), 0.145714, error); | ||
EXPECT_NEAR(covariance(1), 0.04, error); | ||
EXPECT_NEAR(covariance(2), 0.115714, error); | ||
EXPECT_NEAR(covariance(3), 0.04, error); | ||
EXPECT_NEAR(covariance(4), 0.136327, error); | ||
EXPECT_NEAR(covariance(5), 0.392653, error); | ||
EXPECT_NEAR(covariance(6), 0.115714, error); | ||
EXPECT_NEAR(covariance(7), 0.392653, error); | ||
EXPECT_NEAR(covariance(8), 1.29959, error); | ||
} | ||
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///////////////////////////////////////////////// | ||
TEST(EigenUtil, covarianceEmptyTest) | ||
{ | ||
std::vector<math::Vector3d> vertices; | ||
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Eigen::Matrix3d covariance = math::eigen3::covarianceMatrix( | ||
vertices); | ||
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EXPECT_DOUBLE_EQ(covariance(0), 1); | ||
EXPECT_DOUBLE_EQ(covariance(1), 0); | ||
EXPECT_DOUBLE_EQ(covariance(2), 0); | ||
EXPECT_DOUBLE_EQ(covariance(3), 0); | ||
EXPECT_DOUBLE_EQ(covariance(4), 1); | ||
EXPECT_DOUBLE_EQ(covariance(5), 0); | ||
EXPECT_DOUBLE_EQ(covariance(6), 0); | ||
EXPECT_DOUBLE_EQ(covariance(7), 0); | ||
EXPECT_DOUBLE_EQ(covariance(8), 1); | ||
} |
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