！！！实现环境：pcl1.8.0+vs2015+win10
大致过程：
1、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));2、利用1中获得的主方向和质心，将输入点云转换至原点，且主方向与坐标系方向重回，建立变换到原点的点云的包围盒。
3、给输入点云设置主方向和包围盒，通过输入点云到原点点云变换的逆变换实现。
4、完整代码：
#include <vtkAutoInit.h>
VTK_MODULE_INIT(vtkRenderingOpenGL);
VTK_MODULE_INIT(vtkInteractionStyle);
VTK_MODULE_INIT(vtkRenderingFreeType);
#include <iostream>
#include <string>
#include <pcl/io/pcd_io.h>
#include <pcl/point_cloud.h>
#include <pcl/point_types.h>
#include <Eigen/Core>
#include <pcl/common/transforms.h>
#include <pcl/common/common.h>
#include <pcl/visualization/pcl_visualizer.h>
using namespace std;
typedef pcl::PointXYZ PointType;
int main(int argc, char **argv)
{
pcl::PointCloud<PointType>::Ptr cloud(new pcl::PointCloud<PointType>());
std::cout << "请输入需要显示的点云文件名：";
std::string fileName("rabbit");
getline(cin, fileName);
fileName += ".pcd";
//std::string fileName(argv[1]);
pcl::io::loadPCDFile(fileName, *cloud);
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<pcl::PointXYZ>::Ptr cloudPCAprojection (new pcl::PointCloud<pcl::PointXYZ>);
pcl::PCA<pcl::PointXYZ> 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*t
tm_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;
//visualization
pcl::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;
}
注：如有问题请批评指正。
参考资料：
[1] Finding oriented bounding box of a cloud
[2] 计算点云的最小BBOX