The concept of nonparametric surfaces is extended to the definition of quasinonparametric surfaces. These surfaces project one to one onto the plane z = 0 and are built up over the area between two curves that are single-valued, either in Cartesian or in polar coordinates. In the Cartesian case, a subset of nonrational B-spline surfaces is used. The scheme in polar coordinates exhibits all the positive properties of the B-spline tensor-product approach, and yields a piecewise rational Bézier surface. The main interest of this representation is that there exists a very simple point membership classification algorithm for the volume defined between two quasinonparametric patches. Therefore, such a volume can be incorporated as a primitive into a CSG solid-modelling system. © 1995.
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