= Subdivision matrix
{title2=$S$}
A local <subdivision matrix> maps the <control points> in a refinement-invariant neighborhood to the refined neighborhood. Row sums one express constant reproduction. Its constant <eigenvector> has <eigenvalue> one; remaining <eigenvalues> govern decay of shape modes. Near an <extraordinary subdivision vertex>, tangent modes and a <characteristic map of a subdivision surface> are needed to test geometric smoothness, beyond simple convergence.
Back to article page
