Analysis of an Efficient Homogeneous Tensor Representation of Surfaces for Computer Display

There has been growing interest in the interactive construction of free-form surfaces using displays to view and control the design process. Application of computer graphics in this area requires a wise decision as to the class of surfaces to be considered and careful selection of an appropriate mathematical representation for them. We present and analyze such a representation, placing emphasis both on its mathematical properties and on the implications for the associated computer algorithms. The primary goal of this research was to enable the efficient and rapid presentation of true perspective views of a moving object while permitting convenient means to specify the desired surfaces. Within this context it is desirable that the mathematical representation chosen be capable of handling as wide a variety of surfaces as possible. In particular, the algorithms encompass as simple cases such surfaces as cones, spheres, toroids, and saddle surfaces, without recourse to lengthy trigonometric functions.