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...

Ruled surfaces play an important role in many manufacturing and construction applications. In this work, we explore a multidimensional dynamic programming based ruled surface fitting scheme to a given freeform rational surface, S. Considering two initial opposite boundaries of S, sampled into a discrete piecewise linear polyline representation, the ruled surface fitting problem is reduced to a ...

Here we study rank 2 arithmetically Cohen-Macaulay vector bundles on a a ruled surface over a smooth genus q curve, essentially proving their non-existence if q ≥ 2 and the ruled surface is rather balanced.

The μ-basis of a rational ruled surface P(s, t) = P0(s)+tP1(s) is defined in Chen et al. (Comput. Aided Geom. Design 18 (2001) 61) to consist of two polynomials p(x, y, z, s) and q(x, y, z, s) that are linear in x, y, z. It is shown there that the resultant of p and q with respect to s gives the implicit equation of the rational ruled surface; however, the parametric equation P(s, t) of the rat...

In this paper, we classify evolute offsets of a ruled surface in Minkowski 3-space L with constant Gaussian curvature and mean curvature. As a result, we investigate linear Weingarten evolute offsets of a ruled surface in L .

This paper deals with a kind of design of a ruled surface. It combines concepts from the fields of computer aided geometric design and kinematics. A dual unit spherical Bézierlike curve on the dual unit sphere (DUS) is obtained with respect the control points by a new method. So, with the aid of Study [1] transference principle, a dual unit spherical Bézier-like curve corresponds to a ruled sur...