First, we apply Thurston’s construction of pseudo-Anosov homeomorphisms to grid graphs and obtain translation surfaces whose Veech groups are commensurable to (m, n,∞) triangle groups. Many (if not all) of the surfaces we construct were first discovered by Bouw and Möller, however our treatment of the surfaces differs. We construct these surfaces by gluing together polygons in two ways. We use ...

In this work we extend the Weierstrass representation for maximal spacelike surfaces in the 3-dimensional Lorentz–Minkowski space to spacelike surfaces whose mean curvature is proportional to its Gaussian curvature (linear Weingarten surfaces of maximal type). We use this representation in order to study the Gaussian curvature and the Gauss map of such surfaces when the immersion is complete, p...

In this paper are studied the nets of principal curvature lines on surfaces embedded in Euclidean 3−space near their end points, at which the surfaces tend to infinity. This is a natural complement and extension to smooth surfaces of the work of Garcia and Sotomayor (1996), devoted to the study of principal curvature nets which are structurally stable –do not change topologically– under small p...

Magnetic abrasive finishing can be classified as a non-traditional super finishing method for finishing surfaces with different shapes and working materials like flat plates, shafts, bearings parts, screws, tubes and many other mechanical parts that need good surface finishing properties. MAF is effective in polishing, cleaning, deburring and burnishing metal parts. The most important parameter...

Translation surfaces arise in complex analysis, the classification of surface diffeomorphisms and the study of polygonal billiards. In recent years there have been some notable advances in understanding their properties. In particular Calta and McMullen have made significant advances in understanding translation structures in genus 2. This paper is motivated by our desire to reformulate and ext...

This paper presents a general 8th-order PDE method to generate Bézier surfaces from the boundary with position and tangent vector information. We extend the work on generating biharmonic Bézier surfaces by Monterde to generating Bézier surfaces based on a general 4th-order PDE. And further the results are extended to generate tetraharmonic Bézier surfaces by a general 8th-order PDE. The solutio...

Moving least squares (MLS) surfaces representation directly defines smooth surfaces from point cloud data, on which the differential geometric properties of point set can be conveniently estimated. Nowadays, the MLS surfaces have been widely applied in the processing and rendering of point-sampled models and increasingly adopted as the standard definition of point set surfaces. We classify the ...

Many engineering objects have surfaces that are critical to their performance. Analysis codes are used to design these surfaces for efficient performance. The iterative procedure of design followed by analysis requires the ability to generate and modify such surfaces rapidly. In the work described in the paper, surfaces which blend together bifurcated inlets are generated. A functional blendino...

In this paper we present a method for generating Bézier surfaces from the boundary information based on a general 4th-order PDE. This is a generalisation of our previous work on harmonic and biharmonic Bézier surfaces whereby we studied the Bézier solutions for Laplace and the standard biharmonic equation, respectively. Here we study the Bézier solutions of the Euler–Lagrange equation associate...