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Eigen矩阵的平移,旋转,缩放

news 来源：原创 2025/5/7 6:48:08

#include <Eigen/Core>
#include <Eigen/Dense>

平移

x轴

	// 原始点或对象的坐标Eigen::Vector3d original_point(1.0, 2.0, 3.0);std::cout << "original_point: " << std::endl << original_point << std::endl;// x 轴上的平移量double tx = 2.0;// 构造平移矩阵Eigen::Matrix4d translation_matrix = Eigen::Matrix4d::Identity();translation_matrix(0, 3) = tx;std::cout << "translation_matrix: " << std::endl << translation_matrix << std::endl;// 1 0 0 2// 0 1 0 0// 0 0 1 0// 0 0 0 1// 应用平移变换Eigen::Vector4d homogenous_point(original_point.x(), original_point.y(), original_point.z(), 1.0);Eigen::Vector4d transformed_point = translation_matrix * homogenous_point;std::cout << "Transformed point after translation along x-axis: " << transformed_point.transpose().block<1, 3>(0, 0) << std::endl;

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y轴

	// 原始点或对象的坐标Eigen::Vector3d original_point(1.0, 2.0, 3.0);// y 轴上的平移量double ty = -1.0;// 构造平移矩阵Eigen::Matrix4d translation_matrix = Eigen::Matrix4d::Identity();translation_matrix(1, 3) = ty;std::cout << "translation_matrix: " << std::endl << translation_matrix << std::endl;// 1  0  0   0// 0  1  0  -1// 0  0  1   0// 0  0  0   1// 应用平移变换Eigen::Vector4d homogenous_point(original_point.x(), original_point.y(), original_point.z(), 1.0);Eigen::Vector4d transformed_point = translation_matrix * homogenous_point;// 输出结果std::cout << "Original point: " << original_point.transpose() << std::endl;std::cout << "Transformed point after translation along y-axis: " << transformed_point.transpose().block<1, 3>(0, 0) << std::endl;

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z轴

	// 原始点或对象的坐标Eigen::Vector3d original_point(1.0, 2.0, 3.0);// z 轴上的平移量double tz = 0.5;// 构造平移矩阵Eigen::Matrix4d translation_matrix = Eigen::Matrix4d::Identity();translation_matrix(2, 3) = tz;std::cout << "translation_matrix: " << std::endl << translation_matrix << std::endl;// 1   0   0   0// 0   1   0   0// 0   0   1  0.5// 0   0   0   1// 应用平移变换Eigen::Vector4d homogenous_point(original_point.x(), original_point.y(), original_point.z(), 1.0);Eigen::Vector4d transformed_point = translation_matrix * homogenous_point;// 输出结果std::cout << "Original point: " << original_point.transpose() << std::endl;std::cout << "Transformed point after translation along y-axis: " << transformed_point.transpose().block<1, 3>(0, 0) << std::endl;

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旋转

x轴

	#define M_PI 3.14159265358979323846// 原始点或对象的坐标Eigen::Vector3d original_point(0.0, 1.0, 0.0);// 绕 x 轴顺时针旋转角度（弧度）double angle = M_PI / 4.0; // 45 度 绕 x 轴逆时针旋转角度（弧度）//double angle = -M_PI / 4.0; // -45 度// 构造旋转矩阵Eigen::Matrix3d rotation_matrix;rotation_matrix = Eigen::AngleAxisd(angle, Eigen::Vector3d::UnitX());// 应用旋转变换Eigen::Vector3d rotated_point = rotation_matrix * original_point;// 输出结果std::cout << "Original point: " << original_point.transpose() << std::endl;std::cout << "Rotated point after clockwise rotation around x-axis: " << rotated_point.transpose() << std::endl;

y轴

	#define M_PI 3.14159265358979323846// 原始点或对象的坐标Eigen::Vector3d original_point(0.0, 1.0, 0.0); 绕 y 轴顺时针旋转角度（弧度）//double angle = M_PI / 3.0; // 60 度// 绕 y 轴逆时针旋转角度（弧度）double angle = -M_PI / 3.0; // -60 度// 构造旋转矩阵Eigen::Matrix3d rotation_matrix;rotation_matrix = Eigen::AngleAxisd(angle, Eigen::Vector3d::UnitY());// 应用旋转变换Eigen::Vector3d rotated_point = rotation_matrix * original_point;// 输出结果std::cout << "Original point: " << original_point.transpose() << std::endl;std::cout << "Rotated point after clockwise rotation around y-axis: " << rotated_point.transpose() << std::endl;

z轴

	#define M_PI 3.14159265358979323846// 原始点或对象的坐标Eigen::Vector3d original_point(0.0, 1.0, 0.0); 绕 z 轴顺时针旋转角度（弧度）//double angle = M_PI / 6.0; // 30 度// 绕 z 轴逆时针旋转角度（弧度）double angle = -M_PI / 6.0; // -30 度// 构造旋转矩阵Eigen::Matrix3d rotation_matrix;rotation_matrix = Eigen::AngleAxisd(angle, Eigen::Vector3d::UnitZ());// 应用旋转变换Eigen::Vector3d rotated_point = rotation_matrix * original_point;// 输出结果std::cout << "Original point: " << original_point.transpose() << std::endl;std::cout << "Rotated point after clockwise rotation around z-axis: " << rotated_point.transpose() << std::endl;