You can dedent this sector a level. We usually put public:, protected: and private: on the same level as class to save on indentation.

If you skip new, this will be created on the heap instead of the stack, which appears to be what you're going for. Dereferencing and assigning to a member variable like this copies from the heap allocated object onto a stack allocated object, meaning the dynamic allocation itself was wasted effort.

Otherwise, if you want this to live on the heap, make the transform member variable into a std::shared_ptr<Transform>.

Also, we usually avoid inline comments, in favor of putting them above the line instead. This is so we don't make the code too wide. You'll want to adjust that throughout.

This would be an error, as transform is type Transformation, not LayerInstance (the type of cpy). I think you meant this...

For the sake of consistency, you should choose one of these two names for use in both classes: either perform_transformation or do_transformation. When choosing function names, especially for public member functions, you want to minimize the learning curve and memory load for the user. Always assume someone else will be using your class(es).

One thing you could do to ensure the matrix chosen always matches DIMENSION is to put a typedef right here. That will save you further refactoring if you ever need to move from Matrix3d or something else. (It also reduces the possibility of error.)

If you do this, be sure to change Matrix3d to TransformMatrix throughout.

Oh. Ha, I just spotted the initialization list. My mistake! That can actually be used for this ....I think. You'll have to double-check that the tests still pass with this change.