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- Lori A. Diachin, Patrick M. Knupp
- IMR
- 1999

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)

- Patrick M. Knupp
- SIAM J. Scientific Computing
- 2001

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)

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)

- Mohamed S. Ebeida, Andrew A. Davidson, Anjul Patney, Patrick M. Knupp, Scott A. Mitchell, John D. Owens
- ACM Trans. Graph.
- 2011

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)

- Patrick M. Knupp
- IMR
- 1999

- Patrick M. Knupp
- IMR
- 1998

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)

- Patrick M. Knupp
- Engineering with Computers
- 1998

The Winslow equations from structured elliptic grid generation are adapted to smoothing of two-dimensional unstructured meshes using a finite difference approach. We use a local mapping from a uniform N-valent logical mesh to a local physical subdomain. Taylor Series expansions are then applied to compute the derivatives which appear in the Winslow… (More)

- Lori A. Diachin, Patrick M. Knupp, Todd S. Munson, Suzanne M. Shontz
- Engineering with Computers
- 2006

We compare inexact Newton and block coordinate descent optimization methods for improving the quality of a mesh by repositioning the vertices, where the overall quality is measured by the harmonic mean of the mean-ratio metric. The effects of problem size, element size heterogeneity, and various vertex displacement schemes on the performance of these… (More)

- Mohamed S. Ebeida, Muhammad A. Awad, +4 authors Li-Yi Wei
- Computer-Aided Design
- 2014

We explore the notion of a Well-spaced Blue-noise Distribution (WBD) of points, which combines two desirable properties. First, the point distribution is random, as measured by its spectrum having blue noise. Second, it is well-spaced in the sense that the minimum separation distance between samples is large compared to the maximum coverage distance between… (More)