A Smooth Surface Based on Biquadratic Patches

Abstract

A representation for arbitrary C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> surfaces, using biquadratic patches, is described. The key to this simplification is the introduction of extra knots into the system. Using this representation, the polynomial equation for ray tracing is at most eight degree, in contrast to bicubic, which leads to an eighteenth degree polynomial. The scheme was implemented in the SynthaVision system, where ray tracing is used to generate images.