System for polygon interpolation using instantaneous values in a variable

Abstract

Barycentric coordinates are determined using data readily available in computer graphics systems and defining polygons in world space so as to interpolate such polygons with regard to pixels selected by scan conversion. The barycentric coordinates are employed to interpolate the polygons, for example to accomplish smooth shading or texture mapping. The process of the system involves defining primitive data (e.g. polygons) in a space not subject to nonlinear distortion (e.g. world space), transforming select primitive data to a space that is subject to nonlinear distortion, calculating in the space subject to nonlinear distortion (e.g. screen space) a set of areas (e.g. pixels) within a defined primitive (e.g. polygon) using data transformed to space subject to nonlinear distortion, transforming the set of areas to the space not subject to nonlinear distortion, determining at least one differential value (rate of change) of a variable for the primitive, calculating display data that is not subject to nonlinear distortion and using the differential to provide display data. For example, at a pixel, the rate of change in coordinate value (differential) is determined and utilized in texture mapping to facilitate the selection of levels of fuzziness with regard to picture detail for the pixel. Specifically, the differentials are in the coordinates of the texture du land dv.