Eigen 中的 Quaternion

参考网址：
http://eigen.tuxfamily.org/dox-devel/classEigen_1_1Quaternion.html

http://www.cc.gatech.edu/classes/AY2015/cs4496_spring/Eigen.html

Eigen中quaternion的构造函数为
Quaternion (const Scalar &w, const Scalar &x, const Scalar &y, const Scalar &z)，注意w在前。然而在内部存储时eigen将四元数的w放在最后
例如通过Eigen::Vector4d q = q_AB.coeffs();访问时，q中的最后一个元素才是w。

Eigen中用四元数表示向量的旋转
Quaternion：

Eigen::Quaterniond q(2, 0, 1, -3); std::cout << “This quaternion consists of a scalar ” << q.w() << ” and a vector ” << std::endl << q.vec() << std::endl; q.normalize(); std::cout << “To represent rotation, we need to normalize it such that its length is ” << q.norm() << std::endl; Eigen::Vector3d v(1, 2, -1); Eigen::Quaterniond p; p.w() = 0; p.vec() = v; Eigen::Quaterniond rotatedP = q * p * q.inverse(); Eigen::Vector3d rotatedV = rotatedP.vec(); std::cout << “We can now use it to rotate a vector ” << std::endl << v << ” to ” << std::endl << rotatedV << std::endl;

Eigen::Matrix3d R = q.toRotationMatrix(); // convert a quaternion to a 3x3 rotation matrix std::cout << “Compare with the result using an rotation matrix ” << std::endl << R * v << std::endl;

Eigen::Quaterniond a = Eigen::Quterniond::Identity(); Eigen::Quaterniond b = Eigen::Quterniond::Identity(); Eigen::Quaterniond c; // Adding two quaternion as two 4x1 vectors is not supported by the EIgen API. That is, c = a + b is not allowed. We have to do this in a hard way c.w() = a.w() + b.w(); c.x() = a.x() + b.x(); c.y() = a.y() + b.y(); c.z() = a.z() + b.z();