PCL_PCA－最⼩包围盒（画出最⼩包围盒顶点）
1.包围盒简介
包围盒也叫外接最⼩矩形，是⼀种求解离散点集最优包围空间的算法，基本思想是⽤体积稍⼤且特性简单的⼏何体（称为包围盒）来近似地代替复杂的⼏何对象。
常见的包围盒算法有AABB包围盒、包围球、⽅向包围盒OBB以及固定⽅向凸包FDH。碰撞检测问题在虚拟现实、计算机辅助设计与制造、游戏及机器⼈等领域有着⼴泛的应⽤，甚⾄成为关键技术。⽽包围盒算法是进⾏碰撞⼲涉初步检测的重要⽅法之⼀。
在此借助于PCL点云库寻找点云的最⼩包围盒，代码参考⽹上代码，因为⼯程需要包围盒的顶点坐标或偏转⾓度,⽹上代码都只画出了最⼩包围盒没有求出顶点坐标，所以⾃⼰折腾了很久终于把顶点坐标求出，下⾯将代码放出来供⼤家参考.
2.原理简述
最⼩包围盒的计算过程⼤致如下:
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。
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。
最⼩包围盒顶点计算的过程⼤致如下:
1.输⼊点云转换⾄远点后，求得变换后点云的最⼤最⼩x,y,z轴的坐标，此时(max.x,max.y,max.z),(max.x,min.y,max.z),(max.x,max.y,min.z), (min.x,max.y,max.z),(min.x,max.y,min.z),(min.x,min.y,max.z),(min.x,min.y,max.z),(min.x,min.y,min.z)
即为变换后点云的包围盒，也是原始输⼊点云包围盒顶点坐标经过变化后的坐标.
2.将上述求得的８个包围盒坐标逆变换回输⼊点云的坐标系，即得到原始输⼊点云的包围盒顶点坐标.
3.详细代码
#include <iostream>
#include <pcl/ModelCoefficients.h>
#include <pcl/io/pcd_io.h>
#include <pcl/filters/project_inliers.h>
#include <pcl/filters/extract_indices.h>
#include <pcl/sample_connsus/method_types.h>
#include <pcl/sample_connsus/model_types.h>
#include <pcl/gmentation/sac_gmentation.h>
#include <pcl/visualization/cloud_viewer.h>
#include <pcl/point_types.h>
#include <pcl/filters/voxel_grid.h>
#include <pcl/filters/passthrough.h>
#include <pcl/features/normal_3d.h>
#include <pcl/filters/radius_outlier_removal.h>
#include <pcl/kdtree/kdtree_flann.h>
#include <pcl/gmentation/extract_clusters.h>
#include <Eigen/Core>
#include <pcl/common/transforms.h>
#include <pcl/common/common.h>
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#include <pcl/common/time.h>
#include <pcl/common/angles.h>
#include <pcl/registration/transformation_estimation_svd.h>
using namespace std;
typedef pcl::PointXYZ PointType;
typedef struct myPointType
{
double x; //mm world coordinate x
double y; //mm world coordinate y
double z; //mm world coordinate z
int num; //point num
backpack
};
// Get N bits of the string from back to front.
char* Substrend(char*str,int n)
{
char *substr=(char*)malloc(n+1);
int length=strlen(str);
if(n>=length)
{
strcpy(substr,str);
return substr;
}
int k=0;
for(int i=length-n;i<length;i++)
{
substr[k]=str[i];
k++;
}
substr[k]='\0';
return substr;
}
int main(int argc, char **argv)
{
/
/ create point cloud
pcl::PointCloud<PointType>::Ptr cloud(new pcl::PointCloud<PointType>());
// load data
char* fileType;
if(argc>1)
{
fileType = Substrend(argv[1],3);
}
if(!strcmp(fileType,"pcd"))
{
// load pcd file
pcl::io::loadPCDFile(argv[1], *cloud);
}
el if(!strcmp(fileType,"txt"))
{
// load txt data file
int number_Txt;
myPointType txtPoint;
vector<myPointType> points;
FILE *fp_txt;
学姐英文fp_txt = fopen(argv[1], "r");
if(fp_txt)
{
while(fscanf(fp_txt, "%lf %lf %lf", &txtPoint.x, &txtPoint.y, &txtPoint.z)!= EOF) {
points.push_back(txtPoint);
}
}
el
std::cout <<"txt数据加载失败！"<< endl;
number_Txt = points.size();
cloud->width = number_Txt;
cloud->height = 1;
cloud->is_den =fal;
cloud-&size(cloud->width * cloud->height);
for(size_t i = 0; i < cloud->points.size(); ++i)
{
cloud->points[i].x = points[i].x;
cloud->points[i].y = points[i].y;
cloud->points[i].z = 0;
}
}
el
{
std::cout <<"plea input data file name"<<endl;
return 0;
}
// start calculating time
pcl::StopWatch time;
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();仍想结婚的女人电视剧
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.tInputCloud(cloudSegmented);
pca.project(*cloudSegmented, *cloudPCAprojection);
std::cerr << std::endl <<"EigenVectors: "<< EigenVectors()<< std::endl;//计算特征向量
std::cerr << std::endl <<"EigenValues: "<< EigenValues()<< std::endl;//计算特征值
*/
Eigen::Matrix4f tm = Eigen::Matrix4f::Identity();zap
Eigen::Matrix4f tm_inv = Eigen::Matrix4f::Identity();
tm.block<3, 3>(0, 0)= anspo(); //R.
tm.block<3, 1>(0, 3)= -1.0f * (anspo()) *(pcaCentroid.head<3>());// -R*t
tm_inv = tm.inver();
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*(Vector3fMap() + Vector3fMap());
std::cout <<"型⼼c1(3x1):\n"<< c1 << std::endl;
Eigen::Affine3f tm_inv_aff(tm_inv);
Eigen::Affine3f tm_inv_aff(tm_inv);
pcl::transformPoint(c1, c, tm_inv_aff);
Eigen::Vector3f whd, whd1;
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whd1 = Vector3fMap() - Vector3fMap();
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::l(0), px, tm_aff);
pcl::l(1), py, tm_aff);
pcl::l(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);
囧记单词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;
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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;
//Rectangular vertex
pcl::PointCloud<PointType>::Ptr transVertexCloud(new pcl::PointCloud<PointType>);//存放变换后点云包围盒的6个顶点 pcl::PointCloud<PointType>::Ptr VertexCloud(new pcl::PointCloud<PointType>);//存放原来点云中包围盒的6个顶点
transVertexCloud->width = 6;
transVertexCloud->height = 1;
transVertexCloud->is_den =fal;
moqtransVertexCloud-&size(transVertexCloud->width * transVertexCloud->height);
transVertexCloud-&size(transVertexCloud->width * transVertexCloud->height);
transVertexCloud->points[0].x = max_p1.x;
transVertexCloud->points[0].y = max_p1.y;
transVertexCloud->points[0].z = max_p1.z;
transVertexCloud->points[1].x = max_p1.x;
transVertexCloud->points[1].y = max_p1.y;
transVertexCloud->points[1].z = min_p1.z;
transVertexCloud->points[2].x = max_p1.x;
transVertexCloud->points[2].y = min_p1.y;
transVertexCloud->points[2].z = min_p1.z;
transVertexCloud->points[3].x = min_p1.x;
transVertexCloud->points[3].y = max_p1.y;
transVertexCloud->points[3].z = max_p1.z;
transVertexCloud->points[4].x = min_p1.x;
transVertexCloud->points[4].y = min_p1.y;
transVertexCloud->points[4].z = max_p1.z;
transVertexCloud->points[5].x = min_p1.x;
transVertexCloud->points[5].y = min_p1.y;
transVertexCloud->points[5].z = min_p1.z;
pcl::transformPointCloud(*transVertexCloud, *VertexCloud, tm_inv);
// 逆变换回来的⾓度
cout << whd1(0)<<" "<< whd1(1)<<" "<< whd1(2)<< endl;
auto euler = RotationMatrix().eulerAngles(0, 1, 2);
std::cout <<"Euler from quaternion in roll, pitch, yaw"<< std::endl << euler/3.14*180 << std::endl<<std::endl;
//Output time consumption
std::cout <<"运⾏时间"<< Time()<<"ms"<< std::endl;
//visualization
pcl::visualization::PCLVisualizer viewer;
pcl::visualization::PointCloudColorHandlerCustom<PointType> tc_handler(transformedCloud, 0, 255, 0); //设置点云颜⾊
//Visual transformed point cloud
viewer.addPointCloud(transformedCloud, tc_handler, "transformCloud");
viewer.addCube(bboxT1, bboxQ1, whd1(0), whd1(1), whd1(2), "bbox1");
viewer.tShapeRenderingProperties(pcl::visualization::PCL_VISUALIZER_REPRESENTATION, pcl::visualization::PCL_VISUALIZER_REPRESENTATIO N_WIREFRAME, "bbox1");
viewer.tShapeRenderingProperties(pcl::visualization::PCL_VISUALIZER_COLOR, 0.0, 1.0, 0.0, "bbox1");
viewer.addArrow(pcaX, op, 1.0, 0.0, 0.0, fal, "arrow_X");
viewer.addArrow(pcaY, op, 0.0, 1.0, 0.0, fal, "arrow_Y");
viewer.addArrow(pcaZ, op, 0.0, 0.0, 1.0, fal, "arrow_Z");
pcl::visualization::PointCloudColorHandlerCustom<PointType> color_handler(cloud, 255, 0, 0);
viewer.addPointCloud(cloud, color_handler, "cloud");
viewer.addCube(bboxT, bboxQ, whd(0), whd(1), whd(2), "bbox");
viewer.tShapeRenderingProperties(pcl::visualization::PCL_VISUALIZER_REPRESENTATION, pcl::visualization::PCL_VISUALIZER_REPRESENTATIO N_WIREFRAME, "bbox");
viewer.tShapeRenderingProperties(pcl::visualization::PCL_VISUALIZER_COLOR, 1.0, 0.0, 0.0, "bbox");
viewer.addArrow(pcX, cp, 1.0, 0.0, 0.0, fal, "arrow_x");
viewer.addArrow(pcY, cp, 0.0, 1.0, 0.0, fal, "arrow_y");
viewer.addArrow(pcZ, cp, 0.0, 0.0, 1.0, fal, "arrow_z");
viewer.addCoordinateSystem(0.5f*sc1);
viewer.tBackgroundColor(0.0, 0.0, 0.0);
viewer.addPointCloud(VertexCloud, "temp_cloud");
viewer.tPointCloudRenderingProperties (pcl::visualization::PCL_VISUALIZER_POINT_SIZE, 10, "t
emp_cloud");
while(!viewer.wasStopped())
{
viewer.spinOnce();
}
making outreturn 0;
}
