将Eigen中的多个变换组合成一个变换矩阵(Combining multiple transformations in Eigen into one transformation matrix)

我在Eigen中进行了几次转换（ Eigen::Vector3f ）和旋转（ Eigen::Quaternionf ）。我想按照我选择的顺序将所有这些转换组合成一个4x4转换矩阵Eigen::Matrix4f 。

例如，我想在A，B，C，D，E的顺序中应用以下转换：

Eigen::Vector3f translation_A; Eigen::Quaternionf rotation_B; Eigen::Quaternionf rotation_C; Eigen::Quaternionf rotation_D; Eigen::Vector3f translation_E;

实现这个最简单的方法是什么？到目前为止，我一直将它们分别应用于我的最终数据，如下所示：

pcl::transformPointCloud(*cloud_in, *cloud_out, translation_A, IDENTITY_QUATERNION); pcl::transformPointCloud(*cloud_out, *cloud_out, ZERO_TRANSLATION, rotation_B); pcl::transformPointCloud(*cloud_out, *cloud_out, ZERO_TRANSLATION, rotation_C); pcl::transformPointCloud(*cloud_out, *cloud_out, ZERO_TRANSLATION, rotation_D); pcl::transformPointCloud(*cloud_out, *cloud_out, translation_E, IDENTITY_QUATERNION);

...但是必须有一个简单的（内置的）方法将这些使用Eigen的转换组合到最终的4x4转换矩阵中。

I have several transformations in Eigen, in the form of translations (Eigen::Vector3f) and rotations (Eigen::Quaternionf). I would like to combine all these transformations, in an order of my choosing, into a 4x4 transformation matrix Eigen::Matrix4f.

For example, I would like to apply the following transformations in the order A, B, C, D, E:

Eigen::Vector3f translation_A; Eigen::Quaternionf rotation_B; Eigen::Quaternionf rotation_C; Eigen::Quaternionf rotation_D; Eigen::Vector3f translation_E;

What is the simplest way of achieving this? I have so far been applying them individually to my final data like so:

pcl::transformPointCloud(*cloud_in, *cloud_out, translation_A, IDENTITY_QUATERNION); pcl::transformPointCloud(*cloud_out, *cloud_out, ZERO_TRANSLATION, rotation_B); pcl::transformPointCloud(*cloud_out, *cloud_out, ZERO_TRANSLATION, rotation_C); pcl::transformPointCloud(*cloud_out, *cloud_out, ZERO_TRANSLATION, rotation_D); pcl::transformPointCloud(*cloud_out, *cloud_out, translation_E, IDENTITY_QUATERNION);

...but there must be a simple (built-in?) way of combining these transformations using Eigen, into a final 4x4 transformation matrix.

最满意答案

Eigen文档中有一个很好的教程：这里

在你的情况下，这应该看起来像：

Eigen::Vector3f trans_vec_A; //note that you have to create a Translation because multiplying a //Transform with a vector will _apply_ the transform to the vector Eigen::Translation<float,3> translation_A(trans_vec_A); Eigen::Quaternionf rotation_B; Eigen::Quaternionf rotation_C; Eigen::Quaternionf rotation_D; Eigen::Vector3f trans_vec_E; Eigen::Translation<float,3> translation_E(trans_vec_E); Eigen::Transform<float,3,Affine> combined = translation_A * rotation_B * rotation_C * rotation_D * translation_E;

注意

combined = A*B*C*D*E

所以combined应用于矢量v是

combined*v = A*B*C*D*E*v = A*(B*(C*(D*(E*v))))

即首先应用E ，然后应用D ，依此类推。在我看来，这是正确的顺序，但这可能是一个品味问题。

There is a good tutorial in the Eigen docs: here

In your case, this should look like:

Eigen::Vector3f trans_vec_A; //note that you have to create a Translation because multiplying a //Transform with a vector will _apply_ the transform to the vector Eigen::Translation<float,3> translation_A(trans_vec_A); Eigen::Quaternionf rotation_B; Eigen::Quaternionf rotation_C; Eigen::Quaternionf rotation_D; Eigen::Vector3f trans_vec_E; Eigen::Translation<float,3> translation_E(trans_vec_E); Eigen::Transform<float,3,Affine> combined = translation_A * rotation_B * rotation_C * rotation_D * translation_E;

Note that

combined = A*B*C*D*E

so combined applied to a vector v is

combined*v = A*B*C*D*E*v = A*(B*(C*(D*(E*v))))

that is, E is applied first, then D, and so on. In my mind, this is the correct order, but that may be a matter of taste.

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