= Characteristic map of a subdivision surface
The <characteristic map of a subdivision surface> is the planar limit map obtained from the two independent tangent <eigenvectors> of its local <subdivision matrix>. In the usual stationary setting, a simple constant eigenvalue one, a semisimple double subdominant eigenvalue $0<\lambda<1$, strictly smaller other eigenvalues, and a regular injective characteristic map establish the standard $C^1$ tangent-plane behavior for nondegenerate data. The eigenvalue inequalities alone do not exclude a folded or singular characteristic map. For an alternating scheme these tests must use a full period of refinement.
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