In encoding, simplifying, amalgamating and intersecting cartographic features, it is useful to know the precision of locational data being processed. It is suggested that representing spatial phenomena in a hierarchical tessellated framework can facilitate documenting the certainty of coordinates and in dealing with its consequences. Objects thus encoded can identify the precision with which th...

Rapid Prototyping technologies are able of generating physical objects from CAD models. An important aspect of these technologies is the achieved surface quality of manufactured parts. The surface quality is strongly associated with the layered manufacturing. The surface roughness which depends by the staircase effect is a consequence of the layered manufacturing. The staircase effect vary acco...

A multiscale computational model coupling atomistic molecular dynamics simulations with continuum elasticity was used for studying craters formed on Si surfaces by Ar cluster impacts, with energies of 20–50 eV/atom. The results were confirmed by atomic force microscopy/transmission electron microscopy. They show that on a Si (1 0 0), craters are nearly triangular in cross-section, with the face...

Since the introduction of techniques for isosurface extraction from volumetric datasets, one of the hardest problems has been to reduce the number of generated triangles (or polygons). This paper presents an algorithm that considerably reduces the number of triangles generated by a Marching Cubes algorithm, while presenting very close or shorter running times. The algorithm first assumes discre...

An algorithm for surface reconstruction from a polyhedron with arbitrary topology consisting of triangular faces is presented. The rst variant of the algorithm constructs a curve network consisting of cubic B ezier curves meeting with tangent plane continuity at the vertices. This curve network is extended to a smooth surface by replacing each of the networks facets with a split patch consistin...

The classical game of Peg Solitaire has uncertain origins, but was certainly popular by the time of LOUIS XIV, and was described by LEIBNIZ in 1710. The modern mathematical study of the game dates to the 1960s, when the solitaire cone was first described by BOARDMAN and CONWAY. Valid inequalities over this cone, known as pagoda functions, were used to show the infeasibility of various peg games...

The construction of dimethylenebis(eicosyldimethylammonium bromide) surfactant-directed gold nanoparticles (NPs) has been accomplished via a one-pot thermal reduction of HAuCl4 with trisodium citrate. The effect of cationic twin-tail surfactants, dimethylenebis(hexadecyldimethylammonium bromide) (16-2-16), dimethylenebis(octadecyldimethylammonium bromide) (18-2-18) and dimethylenebis(eicosyldim...

A method is presented for approximating a curved surface by developable rigid origami; polyhedral shape which can be developed to plane without deformation of its facets. Form generation starts from triangulated surface, and an optimization problem solved obtain polyhedron satisfies the geometric conditions developability. The degrees freedom origami mechanism with only triangular facets are of...

Several CAD applications require a surface model of an object consisting of a mesh of triangular facets. In this paper, a new algorithm for triangulation of trimmed surfaces is presented. The algorithm generates a triangulation that approximates the initial surface within a predefined tolerance. The approximation is conformal, without cracks in edges: a closed polyhedron is obtained in the case...

Triangular and hexagonal shaped noble metal (Au, Ag, Pt, Pd) nanodisks were synthesized on the top facets of ZnO nanorods via simple deposition-annealing method. Other metals (Ni, Cu, Cr, Pb, Al) only formed irregular shaped nanostructures on ZnO nanorods. The morphology, elemental composition, as well as growth mechanism of the metal nanodisks/ZnO nanorod composite materials were studied. The ...