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.
Sánchez-Reyes, J. (1995). Quasinonparametric surfaces. Computer-Aided Design, 27(4), 263–275. https://doi.org/10.1016/0010-4485(95)91136-9