Patrick M. Knupp

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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 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(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)
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)
A procedure is presented to improve the quality of surface meshes while maintaining the essential characteristics of the discrete surface. The surface characteristics are preserved by repositioning mesh vertices in a series of element-based local parametric spaces such that the vertices remain on the original discrete surface. The movement of the mesh(More)