RATIONAL RULED SURFACES AND THEIR OFFSETS

In this paper, geometric design problems for rational ruled surfaces a re studied. We investigate a line geometric control structure and its connection to the standard tensor product B-spline representation, the use of the Klein model of line space, and algorithms for geometry pro cessing. The main part of the paper is devoted to both classical and ' 'circular'' offsets of rational ruled surfaces. These surfaces arise i n NC milling. Excluding developable surfaces and, for circular offsets , certain conoidal ruled surfaces, we show that both offset types of r ational ruled surfaces are rational. In particular, we describe simple tool paths which are rational quartics. (C) 1996 Academic Press, Inc.