ruled surfaces of degree 2m, whose shape is guided by m ϩ 1 control lines and m frame lines. This is an advantage In this paper, geometric design problems for rational ruled surfaces are studied. We investigate a line geometric control over the method of Ravani and Wang, which results in structure and its connection to the standard tensor product Bsurfaces of degree 3m from the same data.
spline representation, the use of the Klein model of line space,
Recently, Sederberg and Saito [3] studied the Be ´zier and algorithms for geometry processing. The main part of the representation of planar sections of rational ruled surfaces. paper is devoted to both classical and ''circular'' offsets of In our approach, the Klein model suggests a very simple rational ruled surfaces. These surfaces arise in NC milling. algorithm for the computation of the control points of Excluding developable surfaces and, for circular offsets, certain planar section curves. Its geometric interpretation based conoidal ruled surfaces, we show that both offset types of ratioon control null polarities also provides new geometric innal ruled surfaces are rational. In particular, we describe simple sight into planar sections and, dual to that, contours for tool paths which are rational quartics.