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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 the integral of a polynomial over a 3-D simplex. An integral over a polyhedron can then be easily calculated by using the central projection method and… (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 is generated along an ordinary or rational cubic curve for each forward difference step. The adjustment involves a simple linear transformation on the… (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 no pixel gaps. Each curve is drawn using an adaptive forward difference algorithm which generates the coordinates as well as the shading parameters as cubic… (More)

- G. Elber, J. M. Lane, S. Lien, M. Shantz, Nadia Magnenat, Daniel Thalmann +1 other
- 1985

12 Figure 10: Six steps in coarse to ne rendering using adaptive isocurves. A new algorithm is presented that automatically computes an adaptive v alid coverage of a surface using isocurves. The existing capability to eeciently render curves combined with the almost optimal isocurves extraction method presented here makes isocurves rendering of surfaces a… (More)

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