See: http://forum.kde.org/viewtopic.php?f=74&t=117764 The problem is that this product does not instanciate the right Translation::operator* overload. The fix consists in having a general overload for MatrixBase<> objects with meta-programming tricks to return the right type (Affine or Vector) with the right implementation more like Transform::operator*.

There are other Transform-related operations/conversions that don't work, e.g. AngleAxisd a; DiagonalMatrix<double,3> d; Affine3d T0 = d; // not ok Affine3d T1 = a * d; // ok Affine3d T2 = a * d.inverse(); // not ok Affine3d T3(a * d.inverse()); // ok (explicit conversion from Matrix3d) Affine3d T4 = a.toRotationMatrix(); // not ok I assume there are more examples. Maybe we should introduce a TransformBase from which all classes which can be converted to a Transform must inherit. Then we implement several Transform * Transform products which must return something derived from TransformBase (with a fall-back to Transform(a) * Transform(b) if no specialization is applicable). Alternatively, instead of TransformBase, introduce a transform_traits struct. That would also avoid having to avoid DiagonalBase (which should not depend on the Geometry module). I would also not limit x to be a vector in Transform * x. If it is a matrix, apply Transform to each column separately: AngleAxisd a; DiagonalMatrix<double,3> d; Matrix<double, 3, 2> m; // essentially, a pair of 3d vectors a * m; // does not work a * d * m; // ok a * (d * m); // does not work a.toRotationMatrix() * m; // ok There is a problem however, when multiplying Translation3d * Matrix3d. The latter could be interpreted as three separate vectors (resulting in 3 vectors) or a linear transformation (resulting in an affine transformation).

(In reply to comment #1) > Alternatively, instead of TransformBase, introduce a transform_traits struct. > That would also avoid having to avoid DiagonalBase (which should not depend on > the Geometry module). Sorry for the messed up last sentence. What I wanted to say is that this way DiagonalBase does not have to inherit from TransformBase (and the diagonal-traits can be defined inside the Geometry module).

Looking at this general issue again, it also seems that the documentation of Transform * MatrixBase is misleading. Among the different possibilities for the rhs, it mentions: "a linear transformation matrix of size Dim x Dim," suggesting that the lhs L should in this case be interpreted as the following affine transformation: L 0 0 1 but, that's not the case as it is interpreted as a collection of Dim column vectors of size Dim+1 completed with 1 for the homogeneous coordinate: L 1 I think that the current behavior is the only one we could do, but then the documentation is wrong, and we also have a serious discrepancy between Translation and Transform: Translation3f T; Matrix3f L; T * Affine3f(L) == Affine3f(T) * Affine3f(L) // OK T * L == T * Affine3f(L) // might look ok at a first glance, but: Affine3f(T) * L != T * L // clearly not OK I don't known how to fix this without breaking existing code, perhaps even silently. This also complicates the generalisation of Translation::operator*. IMO, the "correct" fix would be to add a Linear<> decorator and always see a MatrixBase as a collection of column vectors and never as a rotation, linear or affine transform.

Regarding the doc issue: https://bitbucket.org/eigen/eigen/commits/969affbdd8a

Regarding comment 3: I like the idea of a Linear<> decorator (or we could add Linear, Rotation, ScaledRotation, ... modes to Transform). An idea which at least would not silently break existing code: Transform<...> * MatrixBase<...> results in a Product<Transform, Matrix> object which can only be assigned to another MatrixBase object, but not to a Transform object and also is not multipliable by another Matrix; and Transform * Transform (including Translation/Rotation/...) results in a Product<Transform, Transform> object, which can only be assigned to a transform, or multiplied by either another Transform or a Matrix. Transform<...> T1, T2, T3; // or Translation/Scaling/Rotation/... Matrix M1, M2, M3; T1 = T2 * T3; // ok, works as before T1 = T2 * M1; // compile error! T1 = T2*Affine3d(M1); // ok, M1 is interpreted as linear operator M1 = T1 * M2; // ok, M2 is interpreted as set of vectors M1 = T1 * T2; // does not compile M1 = (T1 * T2) * M2; // ok, T1 and T2 result in a Transform // which is applied to M2 M1 = T1 * (T2 * M2); // ok, same result as above M1 = T1 * (M2 * M3); // ok, M2*M3 is evaluated first, then transformed M1 = (T1 * M2) * M3; // compile error, dubious whether M2 is a // set of vectors or a linear operator M1 = Matrix(T1*M2)*M3; // ok, result of T1*M2 is interpreted as matrix M1 = (T1*M2).matrix()*M3; // same result, without explicit temporary The not compiling cases can give reasonable compile errors and we might even provide a compile time flag to temporarily switch to the old behavior (as we did with EIGEN2_SUPPORT)

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