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We present a new shape measure for tetrahedral elements that is optimal in the sense 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. We use this shape measure to… (More)

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… (More)

Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically… (More)

Placement of interior node points is a crucial step in the generation of quality meshes in sweeping algorithms. Two new algorithms were devised for node point placement and implemented in Sweep Tool, the first based on the use of linear transformations between bounding node loops and the second based on smoothing. Examples are given that demonstrate the… (More)

We solve the problem of generating a uniform Poisson-disk sampling that is both <b>maximal</b> and <b>unbiased</b> over bounded non-convex domains. To our knowledge this is the first provably correct algorithm with time and space dependent only on the number of points produced. Our method has two phases, both based on classical dart-throwing. The first… (More)

The Winslow equations from structured elliptic grid generation are adapted to smoothing of two-dimensional unstructured meshes using a finite difference approach. Winslow smoothing on unstructured quadrilateral meshes results in mesh folding less frequently than with traditional Laplacian smoothing.

Sweeping has become the workhorse algorithm for creating conforming hexahedral meshes of complex models. This paper describes progress on the automatic, robust generation of MultiSwept meshes in CUBIT. MultiSweeping extends the class of volumes that may be swept to include those with multiple source and multiple target surfaces. While not yet perfect,… (More)