Recent research has produced results on subdivision in arbitrary manifolds. These results can be applied to the manifold of lines and thus we can create subdivision schemes especially for ruled surfaces. We present different methods for refining discrete models of ruled surfaces: An algorithm combining subdivision and projection to the manifold of lines in Euclidean three-space. A further algor...

The ruled surface is a typical modeling surface in computer aided geometric design. It is usually given in the standard parametric form. However, it can also be in the forms than the standard one. For these forms, it is necessary to determine and find the standard form. In this paper, we present algorithms to determine whether a given implicit surface is a rational ruled surface. A parametrizat...

In a recent works Liu and Wang 2008; 2007 study the Mannheim partner curves in the three dimensional space. In this paper, we extend the theory of the Mannheim curves to ruled surfaces and define two ruled surfaces which are offset in the sense of Mannheim. It is shown that, every developable ruled surface have a Mannheim offset if and only if an equation should be satisfied between the geodesi...