Curve evaluation and interrogation on surfaces

This paper presents a coherent computational framework to efficiently, and more so robustly, evaluate, interrogate, and compute a whole variety of cha racteristic curves on freeform parametric rational surfaces represented as (piecewise) polynomial or rational functions. These characteristic curves a re expressed as zero sets of bivariate rational functions and include silho uette curves and isoclines. from a prescribed viewing direction and/or poin t, reflection lines and reflection ovals, and highlight lines. This zero se t formulation allows for a better treatment of singular cases while these c haracteristic curves are crucial for various applications, from visualizati on through interrogation to design and manufacturing. (C) 2001 Academic Pre ss.