Rational blending surfaces between quadrics

Using tools from classical line geometry and the theory of kinematic mappings, it is possible to define an intrinsic control structure for NURBS curves and surfaces on the sphere, the cylinder and on any projectively equivalent quadratic surface. These methods are further used to construct exact C blends between these surfaces, such that interactive design of trim lines and surface tension is possible. The lowest possible degree of a blend that can be achieved with this method is (4, 3).