SMOOTH PIECEWISE BIQUARTIC SURFACES FROM QUADRILATERAL CONTROL POLYHEDRA WITH ISOLATED N-SIDED FACES

The modelling of surfaces by piecewise bipolynomial patches has important applications in computer-aided design and computer graphics. However, existing methods do not always work for control polyhedra with arbitrary topology. A method is proposed that uses only piecewise biquartics which will work for control polyhedra with mostly quadrilateral faces and isolated n-sided faces (n not equal 4). The surfaces are modelled by converting the control points to Bezier points for each patch using a blending matrix. The blending matrices are constructed from generalized biquartic B-spline blending functions. The domain of definition of these is a nonplanar rectangular surface mesh in 3D Euclidean space. The rectangular mesh consists of rectangular faces whose vertices can have an arbitrary number of edges. The construction of the generalized biquartic B-spline blending functions is described. The resulting surface is geometrically smooth around the extraordinary vertices and parametrically smooth otherwise. Furthermore, free parameters are available for manipulating the shape of the surface locally around the extraordinary points.