Research and Advances

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.

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Research and Advances

Texture and reflection in computer generated images

In 1974 Catmull developed a new algorithm for rendering images of bivariate surface patches. This paper describes extensions of this algorithm in the areas of texture simulation and lighting models. The parametrization of a patch defines a coordinate system which is used as a key for mapping patterns onto the surface. The intensity of the pattern at each picture element is computed as a weighted average of regions of the pattern definition function. The shape and size of this weighting function are chosen using digital signal processing theory. The patch rendering algorithm allows accurate computation of the surface normal to the patch at each picture element, permitting the simulation of mirror reflections. The amount of light coming from a given direction is modeled in a similar manner to the texture mapping and then added to the intensity obtained from the texture mapping. Several examples of images synthesized using these new techniques are included.

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