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Techniques are presented for navigating between adjacent triangles of greater or equal size in a hierarchical triangle mesh where the triangles are obtained by a recursive quadtree-like subdivision of the underlying space into four equilateral triangles. These techniques are useful in a number of applications, including finite element analysis, ray tracing,… (More)

Techniques are presented for moving between adjacent tetrahedra in a tetrahedral mesh. The tetrahedra result from a recursive decomposition of a cube into six initial congruent tetrahedra. A new technique is presented f o r labeling the triangular faces. The labeling enables the implementation of a binary-like decomposition of each tetrahedron which is… (More)

The paper deals with the problem of analyzing and visualizing large-size volume data sets. To this aim, we consider mul-tiresolution representations based on a decomposition of the field domain into tetrahedral cells. We compare two types of multires-olution representations that differ on the rule applied to refine an initial coarse mesh: one is based on… (More)

- Michael Lee, Hanan Samet
- 1998

Techniques are presented for moving between adjacent triangles of equal size in a hierarchical representation for spherical data that is projected onto the faces of an icosahedron. The faces of the icosahedron are represented by a triangular quadtree. The operations are analogous to those used for a quadtree representation of data on the two-dimensional… (More)

We consider a recursive decomposition of a four-dimensional hypercube into a hierarchy of nested 4-dimensional simplexes, that we call pentatopes. The paper presents an algorithm for finding the neighbors of a pentatope along its five tetrahedral faces in constant time. To this aim, we develop a labeling technique for nested pentatopes that enables their… (More)

Two new pentaketides, including a new benzofuran-1-one derivative (1) and a new isochromen-1-one (5), and seven new benzoic acid derivatives, including two new benzopyran derivatives (2a, b), a new benzoxepine derivative (3), two new chromen-4-one derivatives (4b, 7) and two new benzofuran derivatives (6a, b), were isolated, together with the previously… (More)

- Michael Lee, Elizabeth Love, Elizabeth Wascher, Sivaram K. Narayan
- 2006

A magic square M is an n-by-n array of numbers whose rows, columns, and the two diagonals sum to µ called the magic sum. If all the diagonals including broken diagonals sum to µ then the magic square is said to be pandiagonal. A regular magic square satisfies the condition that the entries symmetrically placed with respect to the center sum to 2µ n. If the… (More)

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