Recursive subdivision of polygonal complexes and its applications in computer-aided geometric design

Abstract A method for subdividing polygonal complexes and identifying conditions to control their limit curves is presented. A polygonal complex is a sequence of panels where every two adjacent panels share one edge only. We formulate this problem and establish a general theory which has a number of applications in CAGD such as the generation of subdivision surfaces through predefined arbitrary network of curves. This is a further extension of the capability of these surfaces making them more attractive and more practical in surface modeling and computer graphics. One of the main advantages of the proposed scheme is that the regions of the surface between the interpolated curves do not have to be rectangular—a limitation of existing tensor-product based CAD systems.

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