  This is the second paper devoted to the numerical version of
Signature-inverse Theorem in terms of the underlying joint invariants.
Signature Theorem and its Inverse guarantee any application of differential
invariant signature curves to the invariant recognition of visual objects. We
first show the invalidity of Curvature-inverse and Signature inverse theorems,
meaning non-congruent meshes may have the same joint invariant numerical
curvature or signature. Then by classifying three and five point ordinary
meshes respectively in the Euclidean and affine cases, we look for conditions
in terms of the associated joint invariant signatures which make these theorems
correct. Additionally, we bring forward The Host Theorem to provide a simpler
version of Signature-inverse Theorem for closed ordinary meshes.
