Abstract
A method is given for the construction of piecewise surfaces that can be parameterized as single-valued surfaces in spherical coordinates. The main advantage of this representation is that, contrary to general NURBS-bounded primitives, there exists a very simple Point Membership Classification algorithm for the volume defined between two of these surfaces. Therefore, such a volume can be incorporated as a primitive into a CSG solid-modelling system. The chief ingredients for the construction of such surfaces are single-valued spline curves in polar coordinates and single-valued curves on coordinate cones, which are combined following a B-spline scheme. The resulting surfaces are composed of rational Bézier patches belonging to a certain subset, and which join with specified continuity conditions. These spherical spline surfaces exhibit all the positive properties of the B-spline tensor-product approach, including local control or convex hull.
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