Template-based quadrilateral mesh generation from imaging data

This paper describes a novel template-based meshing approach for generating good quality quadrilateral meshes from 2D digital images. This approach builds upon an existing image-based mesh generation technique called Imeshp, which enables us to create a segmented triangle mesh from an image without the need for an image segmentation step. Our approach generates a quadrilateral mesh using an indirect scheme, which converts the segmented triangle mesh created by the initial steps of the Imesh technique into a quadrilateral one. The triangle-to-quadrilateral conversion makes use of template meshes of triangles. To ensure good element quality, the conversion step is followed by a smoothing step, which is based on a new optimization-based procedure. We show several examples of meshes generated by our approach, and present a thorough experimental evaluation of the quality of the meshes given as examples.

Rankamaite from the Urubu pegmatite, Itinga, Minas Gerais, Brazil: Crystal chemistry and Rietveld refinement

A new occurrence of rankamaite is here described at the Urubu pegmatite, Itinga municipality, Minas Gerais, Brazil. The mineral forms cream-white botryoidal aggregates of acicular to fibrous crystals, intimately associated with simpsonite, thoreaulite, cassiterite, quartz, elbaite, albite, and muscovite. The average of six chemical analyses obtained by electron microprobe is (range in parentheses, wt%): Na(2)O 2.08 (1.95-2.13), K(2)O 2.61 (2.52-2.74), Al(2)O(3) 1.96 (1.89-2.00), Fe(2)O(3) 0.01 (0.00-0.03), TiO(2) 0.02 (0.00-0.06), Ta(2)O(5) 81.04 (79.12-85.18), Nb(2)O(5) 9.49 (8.58-9.86), total 97.21 (95.95-101.50). The chemical formula derived from this analysis is (Na(1.55)K(1.28))(Sigma 2.83)(Ta(8.45)Nb(1.64)Al(0.89)Fe(0.01)(3+)Ti(0.01))(Sigma 11.00)[O(25.02)(OH)(5.98)](Sigma 31.00). Rankamaite is an orthorhombic ""tungsten bronze"" (OTB), crystallizing in the space group Cmmm. Its unit-cell parameters refined from X-ray diffraction powder data are: a = 17.224(3), b = 17.687(3), c = 3.9361(7) angstrom, V = 1199.1(3) angstrom(3), Z = 2. Rietveld refinement of the powder data was undertaken using the structure of LaTa(5)O(14) as a starting model for the rankamaite structure. The structural formula obtained with the Rietveld analyses is: (Na(2.21)K(1.26))Sigma(3.37)(Ta(9.12)NB(1.30) Al(0.59))(Sigma 11.00)[O(26.29)(OH)(4.71)](Sigma 31.00). The tantalum atoms are coordinated by six and seven oxygen atoms in the form of distorted TaO(6) octahedra and TaO(2) pentagonal bipyramids, respectively. Every pentagonal bipyramid shares edges with four octahedra, thus forming Ta(5)O(14) units. The potassium atom is in an 11-fold coordination, whereas one sodium atom is in a 10-fold and the other is in a 12-fold coordination. Raman and infrared spectroscopy were used to investigate the room-temperature spectra of rankamaite.