Smooth appearance for polygonal surfaces

Abstract

Current shading methods for polygonal approximations to smooth surfaces reveal the polygon edges by lack of smoothness in the shading, highlights, texture, reflection lines, intersections, profiles, and shadows. These defects are eliminated here by interpolating the perspective depth in screen coordinates with aC1 piecewise-polynomial function, defined over triangles in the screen plane. The three eye-space components of the surface normal, and the two texture parameters, are separately interpolated with similarC1 functions. For smooth intersections, the depth comparison test of Watkins' scan-line algorithm is replaced by a simple test which uses closed-form solutions to polynomials of degree 2, 3, or 4. When the scan lines arise from scan planes containing the eye and the light source, a version of the shadow volume algorithm can also generate smooth cast shadows.