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Scan line methods for displaying parametrically defined surfaces

This paper presents three scan line methods for drawing pictures 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 way 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. In this paper, three different methods for doing the numerical inversion are presented along with an overview of scan line methods.