A transformation is well-defined by a set of three control vectors if and only if the source points are not collinear. (In particular, the degenerate situation where two or more source points are identical will not produce a well-defined transformation). A well-defined transformation exists and is unique. If the control vectors are not well-defined, the system of equations defining the transformation matrix entries is not solvable, and no transformation can be determined.
No such restriction applies to the destination points. However, if the destination points are collinear or non-unique, a non-invertible transformations will be generated.
This technique of recovering a transformation from its effect on known points is used in the Bilinear Interpolated Triangulation algorithm for warping planar surfaces.
null if the control vectors do not determine a well-defined transformation.