Parametric Cubic Spline Interpolation Surface Subdivision

Parametric cubic spline interpolation surface sub-division (PACSIS2), a new subdivision surface modeling (SSM) technique, is established by using parametric cubic spline inter-polation surfaces (PACSIS). The initial polygon mesh (PM) can be arbitrary, or no restriction on polygons or vertex being irregular or extraordinary. At each level, there is a freedom for the number of new points which are selected on the current level PACSIS. The distinction between a traditional surface subdivision scheme and PACSIS2 is that, at each level, the results are either a new and finer polygon quadrilateral mesh or a new PACSIS. The former is a PM but the latter is a pseudo-G<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> continuous surface. At any level of subdivision, the PACSIS2 is G<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> at all vertices of the corresponding PM. At any stage, even on the initial stage, if one prefers, a continuous surface can be established on the PM without recursion. The innovative smooth SSM technique is demonstrated by a variety of examples.