  We develop a theory and an algorithm for constructing minimal-degree
polynomial moving frames for polynomial curves in an affine space. The
algorithm is equivariant under volume-preserving affine transformations of the
ambient space and the parameter shifts. We show that any matrix-completion
algorithm can be turned into an equivariant moving frame algorithm via an
equivariantization procedure that we develop. We prove that if a
matrix-completion algorithm is of minimal degree then so is the resulting
equivariant moving frame algorithm. We propose a novel minimal-degree
matrix-completion algorithm, complementing the existing body of literature on
this topic.
