点云旋转到参考坐标系方向（最小方向包围盒方法）

参考文章：
PCL ——最小包围盒(画出了最小包围盒并求出顶点坐标)
PCL包围盒（详细介绍）
PCL中点云BoundingBox包围盒绘制（基于PCA）
点云学习笔记17——求点云的最小包围盒

下面的代码都是复制上面几篇文章的，纯属做个记录。

引用代码

#include          
VTK_MODULE_INIT(vtkRenderingOpenGL);
VTK_MODULE_INIT(vtkInteractionStyle);
VTK_MODULE_INIT(vtkRenderingFreeType);#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include using namespace std;
typedef pcl::PointXYZ PointType;int main(int argc, char** argv)
{pcl::PointCloud<PointType>::Ptr cloud(new pcl::PointCloud<PointType>());pcl::io::loadPCDFile("C:\\Users\\80hu_mian.pcd", *cloud);
/*利用PCA主元分析法获得点云的三个主方向，获取质心，计算协方差，获得协方差矩阵，求取协方差矩阵的特征值和特长向量，特征向量即为主方向 */Eigen::Vector4f pcaCentroid;pcl::compute3DCentroid(*cloud, pcaCentroid);Eigen::Matrix3f covariance;pcl::computeCovarianceMatrixNormalized(*cloud, pcaCentroid, covariance);Eigen::SelfAdjointEigenSolver<Eigen::Matrix3f> eigen_solver(covariance, Eigen::ComputeEigenvectors);Eigen::Matrix3f eigenVectorsPCA = eigen_solver.eigenvectors();Eigen::Vector3f eigenValuesPCA = eigen_solver.eigenvalues();eigenVectorsPCA.col(2) = eigenVectorsPCA.col(0).cross(eigenVectorsPCA.col(1)); //校正主方向间垂直eigenVectorsPCA.col(0) = eigenVectorsPCA.col(1).cross(eigenVectorsPCA.col(2));eigenVectorsPCA.col(1) = eigenVectorsPCA.col(2).cross(eigenVectorsPCA.col(0));std::cout << "特征值va(3x1):\n" << eigenValuesPCA << std::endl;std::cout << "特征向量ve(3x3):\n" << eigenVectorsPCA << std::endl;std::cout << "质心点(4x1):\n" << pcaCentroid << std::endl;/*// 另一种计算点云协方差矩阵特征值和特征向量的方式:通过pcl中的pca接口，如下，这种情况得到的特征向量相似特征向量pcl::PointCloud::Ptr cloudPCAprojection (new pcl::PointCloud);pcl::PCA pca;pca.setInputCloud(cloudSegmented);pca.project(*cloudSegmented, *cloudPCAprojection);std::cerr << std::endl << "EigenVectors: " << pca.getEigenVectors() << std::endl;//计算特征向量std::cerr << std::endl << "EigenValues: " << pca.getEigenValues() << std::endl;//计算特征值*/Eigen::Matrix4f tm = Eigen::Matrix4f::Identity();Eigen::Matrix4f tm_inv = Eigen::Matrix4f::Identity();tm.block<3, 3>(0, 0) = eigenVectorsPCA.transpose();   //R.tm.block<3, 1>(0, 3) = -1.0f * (eigenVectorsPCA.transpose()) * (pcaCentroid.head<3>());//  -R*ttm_inv = tm.inverse();std::cout << "变换矩阵tm(4x4):\n" << tm << std::endl;std::cout << "逆变矩阵tm'(4x4):\n" << tm_inv << std::endl;pcl::PointCloud<PointType>::Ptr transformedCloud(new pcl::PointCloud<PointType>);pcl::transformPointCloud(*cloud, *transformedCloud, tm);PointType min_p1, max_p1;Eigen::Vector3f c1, c;pcl::getMinMax3D(*transformedCloud, min_p1, max_p1);c1 = 0.5f * (min_p1.getVector3fMap() + max_p1.getVector3fMap());std::cout << "型心c1(3x1):\n" << c1 << std::endl;Eigen::Affine3f tm_inv_aff(tm_inv);pcl::transformPoint(c1, c, tm_inv_aff);Eigen::Vector3f whd, whd1;whd1 = max_p1.getVector3fMap() - min_p1.getVector3fMap();whd = whd1;float sc1 = (whd1(0) + whd1(1) + whd1(2)) / 3;  //点云平均尺度，用于设置主方向箭头大小std::cout << "width1=" << whd1(0) << endl;std::cout << "heght1=" << whd1(1) << endl;std::cout << "depth1=" << whd1(2) << endl;std::cout << "scale1=" << sc1 << endl;const Eigen::Quaternionf bboxQ1(Eigen::Quaternionf::Identity());const Eigen::Vector3f    bboxT1(c1);const Eigen::Quaternionf bboxQ(tm_inv.block<3, 3>(0, 0));const Eigen::Vector3f    bboxT(c);//变换到原点的点云主方向PointType op;op.x = 0.0;op.y = 0.0;op.z = 0.0;Eigen::Vector3f px, py, pz;Eigen::Affine3f tm_aff(tm);pcl::transformVector(eigenVectorsPCA.col(0), px, tm_aff);pcl::transformVector(eigenVectorsPCA.col(1), py, tm_aff);pcl::transformVector(eigenVectorsPCA.col(2), pz, tm_aff);PointType pcaX;pcaX.x = sc1 * px(0);pcaX.y = sc1 * px(1);pcaX.z = sc1 * px(2);PointType pcaY;pcaY.x = sc1 * py(0);pcaY.y = sc1 * py(1);pcaY.z = sc1 * py(2);PointType pcaZ;pcaZ.x = sc1 * pz(0);pcaZ.y = sc1 * pz(1);pcaZ.z = sc1 * pz(2);//初始点云的主方向PointType cp;cp.x = pcaCentroid(0);cp.y = pcaCentroid(1);cp.z = pcaCentroid(2);PointType pcX;pcX.x = sc1 * eigenVectorsPCA(0, 0) + cp.x;pcX.y = sc1 * eigenVectorsPCA(1, 0) + cp.y;pcX.z = sc1 * eigenVectorsPCA(2, 0) + cp.z;PointType pcY;pcY.x = sc1 * eigenVectorsPCA(0, 1) + cp.x;pcY.y = sc1 * eigenVectorsPCA(1, 1) + cp.y;pcY.z = sc1 * eigenVectorsPCA(2, 1) + cp.z;PointType pcZ;pcZ.x = sc1 * eigenVectorsPCA(0, 2) + cp.x;pcZ.y = sc1 * eigenVectorsPCA(1, 2) + cp.y;pcZ.z = sc1 * eigenVectorsPCA(2, 2) + cp.z;//visualizationpcl::visualization::PCLVisualizer viewer;pcl::visualization::PointCloudColorHandlerCustom<PointType> tc_handler(transformedCloud, 0, 255, 0); //转换到原点的点云相关viewer.addPointCloud(transformedCloud, tc_handler, "transformCloud");viewer.addCube(bboxT1, bboxQ1, whd1(0), whd1(1), whd1(2), "bbox1");viewer.setShapeRenderingProperties(pcl::visualization::PCL_VISUALIZER_REPRESENTATION, pcl::visualization::PCL_VISUALIZER_REPRESENTATION_WIREFRAME, "bbox1");viewer.setShapeRenderingProperties(pcl::visualization::PCL_VISUALIZER_COLOR, 0.0, 1.0, 0.0, "bbox1");viewer.addArrow(pcaX, op, 1.0, 0.0, 0.0, false, "arrow_X");viewer.addArrow(pcaY, op, 0.0, 1.0, 0.0, false, "arrow_Y");viewer.addArrow(pcaZ, op, 0.0, 0.0, 1.0, false, "arrow_Z");pcl::visualization::PointCloudColorHandlerCustom<PointType> color_handler(cloud, 255, 0, 0);  //输入的初始点云相关viewer.addPointCloud(cloud, color_handler, "cloud");viewer.addCube(bboxT, bboxQ, whd(0), whd(1), whd(2), "bbox");viewer.setShapeRenderingProperties(pcl::visualization::PCL_VISUALIZER_REPRESENTATION, pcl::visualization::PCL_VISUALIZER_REPRESENTATION_WIREFRAME, "bbox");viewer.setShapeRenderingProperties(pcl::visualization::PCL_VISUALIZER_COLOR, 1.0, 0.0, 0.0, "bbox");viewer.addArrow(pcX, cp, 1.0, 0.0, 0.0, false, "arrow_x");viewer.addArrow(pcY, cp, 0.0, 1.0, 0.0, false, "arrow_y");viewer.addArrow(pcZ, cp, 0.0, 0.0, 1.0, false, "arrow_z");viewer.addCoordinateSystem(0.5f * sc1);viewer.setBackgroundColor(1.0, 1.0, 1.0);while (!viewer.wasStopped()){viewer.spinOnce(100);}return 0;
}

出现报错：

1>D:\PCL\new\pcl\Project1\pcl_test.cpp(97,7): error C2672: “pcl::transformVector”: 未找到匹配的重载函数
1>D:\PCL\new\pcl\Project1\pcl_test.cpp(97,59): error C2784: “void pcl::transformVector(const Eigen::Matrix<_Scalar,3,1,0,3,1> &,Eigen::Matrix<_Scalar,3,1,0,3,1> &,const Eigen::Transform<Scalar,3,2,0> &)”: 未能从“Eigen::Block<Derived,3,1,true>”为“const Eigen::Matrix<_Scalar,3,1,0,3,1> &”推导 模板 参数
1>        with
1>        [
1>            Derived=Eigen::Matrix<float,3,3,0,3,3>
1>        ]

转到该函数的声明：

/** \brief Transform a vector using an affine matrix* \param[in] vector_in the vector to be transformed* \param[out] vector_out the transformed vector* \param[in] transformation the transformation matrix** \note Can be used with \c vector_in = \c vector_out*/template <typename Scalar> inline voidtransformVector (const Eigen::Matrix<Scalar, 3, 1> &vector_in,Eigen::Matrix<Scalar, 3, 1> &vector_out,const Eigen::Transform<Scalar, 3, Eigen::Affine> &transformation){vector_out = transformation.linear () * vector_in;}

报错代码：

	//变换到原点的点云主方向PointType op;op.x = 0.0;op.y = 0.0;op.z = 0.0;Eigen::Vector3f px, py, pz;Eigen::Affine3f tm_aff(tm);pcl::transformVector((eigenVectorsPCA.col(0)), px, tm_aff);pcl::transformVector(eigenVectorsPCA.col(1), py, tm_aff);pcl::transformVector(eigenVectorsPCA.col(2), pz, tm_aff);

是eigenVectorsPCA.col(0))不是Vector3f的数据类型吗？没有找到解决方案

实现代码2：

#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include using PointT = pcl::PointXYZ;int main(int argc, char** argv)
{// 导入点云pcl::PointCloud<PointT>::Ptr original_cloud(new pcl::PointCloud<PointT>());std::string fileName("C:\\Users\\oh_clm\\80hu_mian.pcd");pcl::io::loadPCDFile(fileName, *original_cloud);// PCA：计算主方向Eigen::Vector4f centroid;							// 质心pcl::compute3DCentroid(*original_cloud, centroid);	// 齐次坐标，（c0,c1,c2,1）Eigen::Matrix3f covariance;computeCovarianceMatrixNormalized(*original_cloud, centroid, covariance);		// 计算归一化协方差矩阵// 计算主方向：特征向量和特征值Eigen::SelfAdjointEigenSolver<Eigen::Matrix3f> eigen_solver(covariance, Eigen::ComputeEigenvectors);Eigen::Matrix3f eigen_vectors = eigen_solver.eigenvectors();//Eigen::Vector3f eigen_values = eigen_solver.eigenvalues();eigen_vectors.col(2) = eigen_vectors.col(0).cross(eigen_vectors.col(1));	// 校正主方向间垂直（特征向量方向： (e0, e1, e0 × e1) --- note: e0 × e1 = +/- e2）// 转到参考坐标系，将点云主方向与参考坐标系的坐标轴进行对齐Eigen::Matrix4f transformation(Eigen::Matrix4f::Identity());transformation.block<3, 3>(0, 0) = eigen_vectors.transpose();										// R^(-1) = R^Ttransformation.block<3, 1>(0, 3) = -1.f * (transformation.block<3, 3>(0, 0) * centroid.head<3>());	// t^(-1) = -R^T * tpcl::PointCloud<PointT> transformed_cloud;	// 变换后的点云pcl::transformPointCloud(*original_cloud, transformed_cloud, transformation);pcl::io::savePCDFile("C:\\Users\\oh_clm\\80hu_mian_transform.pcd", transformed_cloud);PointT min_pt, max_pt;						// 沿参考坐标系坐标轴的边界值pcl::getMinMax3D(transformed_cloud, min_pt, max_pt);const Eigen::Vector3f mean_diag = 0.5f * (max_pt.getVector3fMap() + min_pt.getVector3fMap());	// 形心// 参考坐标系到主方向坐标系的变换关系const Eigen::Quaternionf qfinal(eigen_vectors);const Eigen::Vector3f tfinal = eigen_vectors * mean_diag + centroid.head<3>();// 显示结果pcl::visualization::PCLVisualizer viewer;viewer.addPointCloud(original_cloud);viewer.addCoordinateSystem();// 显示点云主方向Eigen::Vector3f whd;		// 3个方向尺寸：宽高深whd = max_pt.getVector3fMap() - min_pt.getVector3fMap();// getVector3fMap:返回Eigen::Mapfloat scale = (whd(0) + whd(1) + whd(2)) / 3;			// 点云平均尺度，用于设置主方向箭头大小PointT cp;			// 箭头由质心分别指向pirncipal_dir_X、pirncipal_dir_Y、pirncipal_dir_Zcp.x = centroid(0);cp.y = centroid(1);cp.z = centroid(2);PointT principal_dir_X;principal_dir_X.x = scale * eigen_vectors(0, 0) + cp.x;principal_dir_X.y = scale * eigen_vectors(1, 0) + cp.y;principal_dir_X.z = scale * eigen_vectors(2, 0) + cp.z;PointT principal_dir_Y;principal_dir_Y.x = scale * eigen_vectors(0, 1) + cp.x;principal_dir_Y.y = scale * eigen_vectors(1, 1) + cp.y;principal_dir_Y.z = scale * eigen_vectors(2, 1) + cp.z;PointT principal_dir_Z;principal_dir_Z.x = scale * eigen_vectors(0, 2) + cp.x;principal_dir_Z.y = scale * eigen_vectors(1, 2) + cp.y;principal_dir_Z.z = scale * eigen_vectors(2, 2) + cp.z;viewer.addArrow(principal_dir_X, cp, 1.0, 0.0, 0.0, false, "arrow_x");		// 箭头附在起点上viewer.addArrow(principal_dir_Y, cp, 0.0, 1.0, 0.0, false, "arrow_y");viewer.addArrow(principal_dir_Z, cp, 0.0, 0.0, 1.0, false, "arrow_z");// 显示包围盒，并设置包围盒属性，以显示透明度viewer.addCube(tfinal, qfinal, whd(0), whd(1), whd(2), "bbox");viewer.setShapeRenderingProperties(pcl::visualization::PCL_VISUALIZER_REPRESENTATION, pcl::visualization::PCL_VISUALIZER_REPRESENTATION_WIREFRAME, "bbox");viewer.setShapeRenderingProperties(pcl::visualization::PCL_VISUALIZER_COLOR, 1.0, 0.0, 0.0, "bbox");while (!viewer.wasStopped()){viewer.spinOnce(100);}return 0;
}

变换结果：