Getting the transformation matrix for a node

To get the default translation, rotation, and scaling (default TRS properties) of a node, call the node’s GetDefaultT(), GetDefaultR(), and GetDefaultS() member functions. All three member functions return vectors of class KFbxVector4. The value of each vector is an offset from the corresponding default TRS property vector for the parent node.

The actual TRS properties for the node at a given point in time depend on:

The node’s default TRS properties.
The limits that apply to the node (see KFbxNode::GetLimits())
The function curves (animation) of the current take (see Animating a Scene).

You can get the node’s actual TRS properties in the scene’s global coordinate system expressed as a transformation matrix (often called the transform) by calling the node’s GetGlobalFromDefaultTake() member function.

See Also

Getting the properties of a node as a point in space
KFbxNode::GetDefaultT()
KFbxNode::GetDefaultR()
KFbxNode::GetDefaultS()

Computing the transformation matrix

Here is how FBX SDK computes the transformation matrix for a node:

Transform = T * Roff * Rp * Rpre * R * Rpost * Rp^-1 * Soff * Sp * S * Sp^-1

Where:	Is:
Transform	Transformation matrix (4 X 4)
T	Translation
Roff	Rotation offset
Rp	Rotation pivot
Rpre	Pre-rotation
R	Rotation
Rpost	Post-rotation
Rp^-1	Inverse of the rotation pivot
Soff	Scaling offset
Sp	Scaling pivot
S	Scaling
Sp^-1	Inverse of the scaling pivot

Notes:

Computations are performed from left to right.
The effect of the formula is that any given vector is first translated, then rotated, then scaled.
The R matrix takes into account the rotation order. Because of the mathematical properties of the matrices, R is the result of one of the possible combinations of Ry, Ry and Rz (each being matrices also). For example, for the default rotation order of XYZ, R = Rx * Ry * Rz