Using graphs of bivariate functions to locally represent and modify surfaces.

Computer Aided Geometric Design, 10:453--463, 1993.

This article develops methods for locally representing and manipulating curved surfaces as graphs of scalar algebraic functions in two variables. Based on two propositions, one from differential geometry and one from algebraic geometry, any surface can be approximated and locally represented as such a function. This representation offers many advantages in terms of its display in computer graphics, the evaluation of its geometric properties and the calculation of intersections with lines and other surfaces. One can locally manipulate the surface, using its intrinsic geometric measures as well as other external constraints. The formulation is extremely fast and allows interactive surface manipulation and display to occur in real or close-to-real time.