Twofold adaptive partition of unity implicits

Partition of Unity Implicits (PUI) has been recently introduced for surface reconstruction from point clouds. In this work, we propose a PUI method that employs a set of well-observed solutions in order to produce geometrically pleasant results without requiring time consuming or mathematically overloaded computations. One feature of our technique is the use of multivariate orthogonal polynomials in the least-squares approximation, which allows the recursive refinement of the local fittings in terms of the degree of the polynomial. However, since the use of high-order approximations based only on the number of available points is not reliable, we introduce the concept of coverage domain. In addition, the method relies on the use of an algebraically defined triangulation to handle two important tasks in PUI: the spatial decomposition and an adaptive polygonization. As the spatial subdivision is based on tetrahedra, the generated mesh may present poorly-shaped triangles that are improved in this work by means a specific vertex displacement technique. Furthermore, we also address sharp features and raw data treatment. A further contribution is based on the PUI locality property that leads to an intuitive scheme for improving or repairing the surface by means of editing local functions.

Lead and aluminum bonding in Pb-Al metaphosphate glasses

The bonding properties of cations in phosphate glasses determine many short- and medium-range structural features in the glass network, hence influencing bulk properties. In this work, Pb-Al-metaphosphate glasses (1 - x)Pb-(PO(3))(2)center dot xAI(PO(3))(3) with 0 <= - x <= 1 were analyzed to determine the effect of the substitution of Pb by Al on the glass structure in the metaphosphate composition. The glass transition temperature and density were measured as a function of the Al concentration. The vibrational and structural properties were probed by Raman spectroscopy and nuclear magnetic resonance of (31)P, (27)Al, and (207)Pb. Aluminum incorporates homogeneously in the glass creating a stiffer and less packed network. The average coordination number for Al decreases from 5.9 to 5.0 as x increases from 0.1 to 1, indicating more covalent Al-O bonds. The coordination number of Pb in these glasses is greater than 8, showing an increasing ionic behavior for compositions richer in Al. A quantitative analysis of the phosphate speciation shows definite trends in the bonding of AlO(n) groups and phosphate tetrahedra. In glasses with x < 0.48, phosphate groups share preferentially only one nonbridging O corner with an AlO(n) coordination polyhedron. For x > 0.48 more than one nonbridging O can be linked to AlO(n) polyhedra. There is no corner sharing of O between AlO(n) and PbO(n) polyhedra nor between AlO(n) themselves throughout the compositional range. The PbO(n) coordination polyhedra show considerable nonbridging O sharing, with each O participating in the coordination sphere of at least two Pb. The bonding preferences determined for Al are consistent with the behavior observed in Na-Al and Ca-Al metaphosphates, indicating this may be a general behavior for ternary phosphate glasses.

Crystal structure of the (Mg,Fe)[UO2(P,As)O-4](2) center dot 10H(2)O solid solution - A novel mineral variety of saleeite

The crystal structure of a novel variety {[(Mg0.81Fe0.19)(H2O)(6)](H2O)(4)}{(UO2)[(P0.67As0.33)O-4]}(2) of the mineral saleeite is determined using X-ray diffraction (Bruker Smart diffractometer, lambda MoK alpha, graphite monochromator, 2 theta(max) = 56.62 degrees, R = 0.0321 for 2317 reflections, T = 100 K). The main crystal data are as follows: a = 6.952(6) angstrom, b = 19.865(5) , angstrom, c = 6.969(2) angstrom, beta = 90.806(4)degrees, space group P12(l)/n1, Z = 2, and P-calcd = 3.34 g/cm(3). It is shown that the structure is formed by alternating (along the [010] direction) anionic layers, which are composed of uranium bipyramids and T(P,As) tetrahedra, and cation layers consisting of M(Mg, Fe) octahedra and water molecules, which are joined through a system of asymmetric hydrogen bonds. The hydrogen atoms are located, the scheme of hydrogen bonds is established, and their geometric characteristics are calculated.