如何將affine2d變換應用到3d矩陣塊上？

Question

我有一個矩陣（x，y，z每列），只想執行二維變換到x和y軸，忽略z。似乎affine2d不能與塊相乘，是否有任何其他方式使其工作？

Eigen::matrix<double, 3, 4> x3d; 
x3d << 
    1, 2, 3, 4, 
    2, 3, 4, 5, 
    1, 1, 1, 1; 
auto x2d = x3d.topRows(2); 
Eigen::Affine2d T = Eigen::Translation2d(1, 2) * Eigen::Scaling(1., 2.); 
x2d = T*x2d; 

輸出錯誤：

> /home/lei/Work/SurfTomo/./include/Eigen/src/Geometry/Transform.h:1361:5: 
> error: static_assert failed "YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES" 
>  EIGEN_STATIC_ASSERT(OtherRows==Dim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES); 
> ^     ~~~~~~~~~~~~~~ /home/lei/Work/SurfTomo/./include/Eigen/src/Core/util/StaticAssert.h:32:40: 
> note: expanded from macro 'EIGEN_STATIC_ASSERT' 
>  #define EIGEN_STATIC_ASSERT(X,MSG) static_assert(X,#MSG); 
>          ^   ~ /home/lei/Work/SurfTomo/./include/Eigen/src/Geometry/Transform.h:442:77: 
> note: in instantiation of member function 
>  'Eigen::internal::transform_right_product_impl<Eigen::Transform<double, 
> 2, 2, 0>, Eigen::Block<Eigen::Matrix<double, 3, 4, 0, 3, 4>, -1, 4, 
>  false>, 2, 4>::run' requested here { return internal::transform_right_product_impl<Transform, 
> OtherDerived>::run(*this,other.derived()); } 
>                   ^/home/lei/Work/SurfTomo/test/test_3dto2d.cc:27:10: note: in 
> instantiation of function template specialization 
> 'Eigen::Transform<double, 2, 2, 
>  0>::operator*<Eigen::Block<Eigen::Matrix<double, 3, 4, 0, 3, 4>, -1, 4, false> >' requested here x2d = T*x2d; 
>  ^1 error generated. 

我發現下面的代碼就可以解決這個問題，但我不明白爲什麼它的工作原理。

x2d = T * x2d.colwise().homogeneous(); 

Answer 1

當Eigen::Affine2d乘以徵想知道，在編譯時其他矩陣的行（因爲取決於不同的代碼路徑採取的數量和運行時檢查可以使顯著的開銷在這裏）。

只需創建使用

auto x2d = x3d.topRows<2>();