Hy.
I have a scenegraph.
Each object in the scenegraph is a node and can have a parent(1 or 0 ) for my application i must multiply from the bottom to the top.
Each node have a 3x3 rotation matrix and a 3dvector for the traslation.
I can do node->parent for find the parent node.
i use a loop for iterate from bottom to top and use the parent() function.

1)i do in the loop: currentMatrix =currentNode->parent()->getmatrix3x3->Trasposed() * currentMatrix
then the currentNode becomes : currentNode = currentNode->parent() until the parent == 0.
2)first problem : how i must multiply the translation vectors where each node is? At each position i must draw a mesh , then i must have the correct location.

3)I must use transposed matrix for my project , is correct do the transposition every cicle only for the new matrix?like
currentNode->parent()->getmatrix3x3->Trasposed() * old concatenate matrix?

thanks.

Why don't you use 4x4 matrices? You would have your translation in the matrix and computed with the multiplication.

If you have to multiply by the transpose, create a multTranspose kind of method instead of using a temporary transposed matrix object. You don't need this object, you just have to multiply the matrix components in the transposed direction.

Finally, when you traverse you tree, you can keep a pre-multiplied matrix of all the node from the parent to the root, to avoid your costly loop.