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.