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2D Piecewise Algebraic Splines for Implicit Modeling

<26> Geometric modelling using piecewise algebraic curves and surfaces has both theoretical and practical implications in computational geometry, computer graphics, and computer aided geometrical reconstruction. In this article, we developed a theoretically elegant and practically useful 2D spline technique. To the best of our knowledge, it is the only technique in the world that allows one to construct from any given polygonal net, to any required degree of smoothness, a set of 2D piecewise algebraic spline basis functions, which possess the desirable properties of non-negativity, partition of unity, convex-hull and additivity.