A scan line algorithm for displaying parametrically defined surfaces

A scan line algorithm for drawing picture of parametrically defined surfaces using a bivariate Newton-Raphson solution of the defining equations to keep the algorithm general enough to apply to a wide variety of functional forms.

Abstract

This paper presents a scan line algorithm for drawing picture of parametrically defined surfaces. A scan line algorithm is characterized by the order in which it generates the picture elements of the image. These are generated left to right, top to bottom in much the same was as a picture is scanned out on a TV screen. Parametrically defined surfaces are those generated by a set of bivariate functions defining the X, Y and Z position of points on the surface. The primary driving mechanism behind such an algorithm is the inversion of the functions used to define the surface. To keep the algorithm general enough to apply to a wide variety of functional forms, this inversion is done numerically. It is only required to provide mechanism for evaluating the function and its derivatives at any parametric location.