We classify ruled minimal surfaces in R3 with density ez. It is showed that there is no noncylindrical ruled minimal surface and there is a family of cylindrical ruled minimal surfaces in R3 with density ez. It is also proved that all translation minimal surfaces are ruled. AMS Subject Classification (2000): Primary 53C25; Secondary 53A10; 49Q05

A projective algebraic surface which is homeomorphic to a ruled surface over a curve of genus g ≥ 1 is itself a ruled surface over a curve of genus g. In this note, we prove the analogous result for projective algebraic manifolds of dimension 4 in case g ≥ 2.

To achieve high precision and high productivity in machining sculptured surfaces, a new architecture for a five-axis CNC interpolator for machining ruled surfaces was developed and demonstrated on a milling machine. The objective of the five-axis interpolator is to continuously maintain the milling cutter axis in parallel with the straight lines of the ruled surface. The cutter position and ori...

We investigate how to define a triangulated ruled surface interpolating two polygonal directrices that will meet a variety of optimization objectives which originate from many CAD/CAM and geometric modeling applications. This optimal triangulation problem is formulated as a combinatorial search problem whose search space however has the size tightly factorial to the numbers of points on the two...

Ruled surface design and its applications are widely used in CAGD(Computer Aid Geometric Design) and industrial areas. In this paper, the hyperbolic paraboloid is a particular ruled surface, which is drawn by using the dual De Casteljau algorithm [15]. The characteristics of the hyperbolic paraboloid are analysed in order to match the requirement of the dual De Casteljau algorithm. A new method...

In this paper, using [E. Kasap, _ I. Aydemir, N. Kuruoğlu, Erratum to: ‘‘Ruled surfaces with timelike rulings’’ [Appl. Math. Comput. 147 (2004) 241–253], Applied Mathematics and Computation 168 (2005) 1461–1468 [2]], some mistakes which are related to the classification maximal ruled surfaces with timelike rulings in the last section of [Applied Mathematics and Computation 147 (2004) 241–253 [1...

A first order invariant of ruled surfaces of E3 is the socalled distribution parameter d in a generator. It is defined as the limit of the quotient of the distance and the angle of the generator and its neighbour. Ruled surfaces with constant parameter of distribution are of special interest and have been studied by many authors. H. Brauner could prove that the only nontrivial cubic ruled surfa...

In this paper, a new representational model is introduced for the rational family of ruled surfaces in Computer Graphics. The surface parameterization is constructed using the NURBS basis functions and line geometry. The ruled surface is defined by interpolating directly dual unit vectors representing lines, which is a single parametric surface and its shape depends on the control lines. All th...