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Motivated by the discretization problem in isogeometric analysis, we consider the challenge of segmenting a contractible boundary-represented solid into a small number of topological hexahedra. A satisfactory segmentation of a solid must eliminate non-convex edges because they prevent regular parameterizations. Our method works by searching a sufficiently… (More)

• Segmentation of a 3D solid without non-convex edges into topological hexahedra. • Method is based on the edge graph of the solid. • Decomposition is done by means of simple combinatorial and geometric criteria. • Number of resulting topological hexahedra is small. a b s t r a c t We present a novel technique for segmenting a three-dimensional solid with a… (More)

- Michael Pauley, Shreya Bhattarai, Philip Schrader, Seyed Hassan Alavi, Neil Gillespie
- 2011

Geodesics are a generalisation of straight lines to Riemannian manifolds and other spaces equipped with an affine connection. Interpolation and approximation problems motivate analogous generalisations of cubic polynomials. There are several approaches. Cubic polynomials in Euclidean space are critical points of the mean norm-squared acceleration,… (More)

The finite flag-transitive linear spaces which have an insoluble automorphism group were given a precise description in [BDD + 90], and their classification has recently been completed (see [Lie98] and [Sax02]). However, the remaining case where the automorphism group is a subgroup of one-dimensional affine transformations has not been classified and bears… (More)

- John Bamberg, Anton Betten, Philippe Cara, Jan De Beule, Michel Lavrauw, Maska Law +3 others
- 2009

A linear space is an incidence structure of points and lines having the property that there is exactly one line incident with any two given points. Finite linear spaces can be used to make experimental designs and error correcting codes. The collineations of a linear space are the bijections from the linear space to itself which preserve incidence. A linear… (More)

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