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A simple and systematic method is described for calculating the integral of a polynomial function over an arbitrary nonconvex polyhedron. First a general formula is presented for direct evaluation of… (More)
An adaptive forward differencing algorithm is presented for rapid rendering of cubic curves and bicubic surfaces. This method adjusts the forward difference step size so that approximately one pixel… (More)
We present several techniques for implementing Phong shading in hardware for bicubic patches. Patches are shaded, not by subdividing into polygons, but by drawing many curves close together leaving… (More)
For use in obtaining rational cubic functions x/w, y/w and z/w coordinates, the apparatus comprises means 18, for emulating a truncated version of the Taylor series:- and means 20, 22, 24 multiplying… (More)
This thesis seeks to establish mathematical principles and to provide efficient solutions to various time consuming operations in computer-aided geometric design. It contains a discussion of three… (More)