Geometric Modelling by Recursively Cutting Vertices

In this paper, a new method for curve and surface modelling is introduced which generates curves and surfaces by recursively cutting and grinding polygons and polyhedra. It is a generalization of the existing corner-cutting methods. A lot of properties, such as geometric continuity, representation, shape-preserving, and the algorithm are studied which show that such curves and surfaces are suitable for geometric designs in CAD, computer graphics and their application fields.