We present an algorithm for ray–tetrahedron intersection. The algorithm uses Plücker coordinates to represent the ray and the edges of the tetrahedron and employs a robust and efficient test to determine the intersection. The algorithm is highly optimized and provides a significant performance increase over related algorithms.

aminocarboxylic acids, such as 2-aminobenzoic acid, react easily with [ir(cod)(pme3)3]cl, (cod=1,5-cyclooctadiene), in thf to produce hydridoaminocarboxylato iridium(iii) complexes in high yields. these octahedral complexes are formed via oxidative addition reaction of the o-h bond of the carboxylic group with the central metal. the starting iridium(i) complex losses the cod molecule, the chlor...

A discrete Fourier analysis on the dodecahedron is studied, from which results on a tetrahedron is deduced by invariance. The results include Fourier analysis in trigonometric functions, interpolation and cubature formulas on these domains. In particular, a trigonometric Lagrange interpolation on the tetrahedron is shown to satisfy an explicit compact formula and the Lebesgue constant of the in...

A DNA tetrahedron is employed for efficient delivery of doxorubicin into drug-resistant breast cancer cells. The drug delivered with the DNA nanoconstruct is considerably cytotoxic, whereas free doxorubicin is virtually non-cytotoxic for the drug-resistant cells. Thus, the DNA tetrahedron, made of the inherently natural and biocompatible material, can be a good candidate for the drug carrier to...

The Sierpinski tetrahedron is two-dimensional with respect to fractal dimensions though it is realized in threedimensional space, and it has square projections in three orthogonal directions. We study its generalizations and present two-dimensional fractals with many square projections. One is generated from a hexagonal bipyramid which has square projections not in three but in six directions. ...

A generalised tetrahedron group is the colimit of a triangle of groups whose vertex groups are generalised triangle groups and whose edge groups are finite cyclic. We prove an improved Spelling Theorem for generalised triangle groups which enables us to compute the precise Gersten-Stallings angles of this triangle of groups, and hence obtain a classification of generalised tetrahedron groups ac...

We report progress in constructing Boltzmann weights for integrable 3dimensional lattice spin models. We show that a large class of vertex solutions to the modified tetrahedron equation can be conveniently parameterized in terms of N -th roots of theta-functions on the Jacobian of a compact algebraic curve. Fay’s identity guarantees the Fermat relations and the classical equations of motion for...

We present a method to adapt a tetrahedron mesh together with a surface mesh with respect to a size criterion. Both surface and tetrahedron mesh adaptation are carried out simultaneously and no CAD is required to adapt the surface mesh. The adaptation procedure consists in splitting or removing interior and surface edges in order to enforce a given size criterion. The enrichment process is base...

One of the challenges of Volume Modelling is the definition of theoretical frameworks to support object manipulation and representation. Opposite to what is seen in the field of surface modelling, few satisfactory tools have been presented that ensure topological robustness to volumetric models. In this paper we offer one such mathematical framework for volumetric model definition based on tetr...

SUMMARY We present a new shape measure for tetrahedral elements that is optimal in that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. Using this shape measure, we formulate two optimization objective funct...