For non-uniform control polygons, a parameterized four-point interpolation curve ternary subdivision scheme is proposed, and its convergence continuity are demonstrated. Following subdivision, surface on regular quadrilateral meshes proposed by applying the tensor product method. Analyses were conducted updating rules of parameters, proving that limit continuous. In this paper, we present novel...

Does every Boolean tautology have a short propositional-calculus proof? Here, a propositionalcalculus (i.e. Frege) proof is any proof starting from a set of axioms and deriving new Boolean formulas using a fixed set of sound derivation rules. Establishing any super-polynomial size lower bound on Frege proofs (in terms of the size of the formula proved) is a major open problem in proof complexit...