Spectral-based mesh segmentation

In design and manufacturing, mesh segmentation is required for FACE construction in boundary representation (BRep), which in turn is central for featurebased design, machining, parametric CAD and reverse engineering, among others -- Although mesh segmentation is dictated by geometry and topology, this article focuses on the topological aspect (graph spectrum), as we consider that this tool has not been fully exploited -- We preprocess the mesh to obtain a edgelength homogeneous triangle set and its Graph Laplacian is calculated -- We then produce a monotonically increasing permutation of the Fiedler vector (2nd eigenvector of Graph Laplacian) for encoding the connectivity among part feature submeshes -- Within the mutated vector, discontinuities larger than a threshold (interactively set by a human) determine the partition of the original mesh -- We present tests of our method on large complex meshes, which show results which mostly adjust to BRep FACE partition -- The achieved segmentations properly locate most manufacturing features, although it requires human interaction to avoid over segmentation -- Future work includes an iterative application of this algorithm to progressively sever features of the mesh left from previous submesh removals

Triangular mesh parameterization with trimmed surfaces

Given a 2manifold triangular mesh \(M \subset {\mathbb {R}}^3\), with border, a parameterization of \(M\) is a FACE or trimmed surface \(F=\{S,L_0,\ldots, L_m\}\) -- \(F\) is a connected subset or region of a parametric surface \(S\), bounded by a set of LOOPs \(L_0,\ldots ,L_m\) such that each \(L_i \subset S\) is a closed 1manifold having no intersection with the other \(L_j\) LOOPs -- The parametric surface \(S\) is a statistical fit of the mesh \(M\) -- \(L_0\) is the outermost LOOP bounding \(F\) and \(L_i\) is the LOOP of the ith hole in \(F\) (if any) -- The problem of parameterizing triangular meshes is relevant for reverse engineering, tool path planning, feature detection, redesign, etc -- Stateofart mesh procedures parameterize a rectangular mesh \(M\) -- To improve such procedures, we report here the implementation of an algorithm which parameterizes meshes \(M\) presenting holes and concavities -- We synthesize a parametric surface \(S \subset {\mathbb {R}}^3\) which approximates a superset of the mesh \(M\) -- Then, we compute a set of LOOPs trimming \(S\), and therefore completing the FACE \(F=\ {S,L_0,\ldots ,L_m\}\) -- Our algorithm gives satisfactory results for \(M\) having low Gaussian curvature (i.e., \(M\) being quasi-developable or developable) -- This assumption is a reasonable one, since \(M\) is the product of manifold segmentation preprocessing -- Our algorithm computes: (1) a manifold learning mapping \(\phi : M \rightarrow U \subset {\mathbb {R}}^2\), (2) an inverse mapping \(S: W \subset {\mathbb {R}}^2 \rightarrow {\mathbb {R}}^3\), with \ (W\) being a rectangular grid containing and surpassing \(U\) -- To compute \(\phi\) we test IsoMap, Laplacian Eigenmaps and Hessian local linear embedding (best results with HLLE) -- For the back mapping (NURBS) \(S\) the crucial step is to find a control polyhedron \(P\), which is an extrapolation of \(M\) -- We calculate \(P\) by extrapolating radial basis functions that interpolate points inside \(\phi (M)\) -- We successfully test our implementation with several datasets presenting concavities, holes, and are extremely nondevelopable -- Ongoing work is being devoted to manifold segmentation which facilitates mesh parameterization

Development of a Coupling Model for Fluid-Structure Interaction using the Mesh-free Finite Element Method and the Lattice Boltzmann Method

In the presented thesis work, the meshfree method with distance fields was coupled with the lattice Boltzmann method to obtain solutions of fluid-structure interaction problems. The thesis work involved development and implementation of numerical algorithms, data structure, and software. Numerical and computational properties of the coupling algorithm combining the meshfree method with distance fields and the lattice Boltzmann method were investigated. Convergence and accuracy of the methodology was validated by analytical solutions. The research was focused on fluid-structure interaction solutions in complex, mesh-resistant domains as both the lattice Boltzmann method and the meshfree method with distance fields are particularly adept in these situations. Furthermore, the fluid solution provided by the lattice Boltzmann method is massively scalable, allowing extensive use of cutting edge parallel computing resources to accelerate this phase of the solution process. The meshfree method with distance fields allows for exact satisfaction of boundary conditions making it possible to exactly capture the effects of the fluid field on the solid structure.

Niche segregation between immature and adult seabirds: Does progressive maturation play a role?

In long-lived species with slow maturation, prebreeders often represent a large percentage of the individuals alive at any moment, but their ecology is still understudied. Recent studies have found prebreeding seabirds to differ in their isotopic (and trophic) niche from adult breeders attending the same nesting colonies. These differences have been hypothesized to be linked to the less-developed foraging performance of younger and less-experienced immatures or perhaps to their inferior competitive abilities. Such differences from adults would wane as individuals mature (“the progressive ontogenetic shift hypothesis”) and could underpin the prolonged breeding deferral until adulthood displayed by those species. This study documents a marked difference in the nitrogen and carbon isotopic ratios measured in the whole blood of immatures and breeders in 2 pelagic seabird species (Cory’s shearwaters, Calonectris borealis, and black-browed albatrosses, Thalassarche melanophris) nesting in contrasting environments. However, blood isotopic values did not present a relationship with prebreeder age, suggesting no gradual ontogenetic shift from an immature toward an adult isotopic niche. Furthermore, isotopic signatures of sabbatical adults could not be separated from those of immatures attending the same colonies, but were clearly segregated from adult breeders. These results suggest that isotopic differentiation between immatures and breeders is mainly linked to a factor unrelated to previous experience and hence probably unrelated to a hypothetical gradual improvement of foraging competence or competitive abilities. Any ecological differentiation between breeders and nonbreeders is more likely related to the severity of the central-place foraging constraints and to the energetic requirements of reproduction (“the reproductive constraint hypothesis”).

Size selectivity of diamond and square mesh cod ends for four by-catch species in the crustacean fishery off the Portuguese south coast

The effects of an increase in cod end mesh size from 55 to 60 and 70 mm and a change of mesh configuration from 55 mm diamond to 55 turn square mesh on the size selectivity of four by-catch species (the red shrimp Aristeus antennatus, the European hake Merluccius merluccius, the horse mackerel Trachurus trachurus and the blue whiting Micromesistius poutassou) commonly captured in the crustacean fishery off the Portuguese south coast, were evaluated. Selectivity parameters for blue whiting, the most abundant species in the catches, were estimated taking into account between-haul variation, while for the remaining species, captured in much lower quantities, the selectivity estimates were based on pooled data by length class for all hauls within the same cod end. Length at 50% retention, L-50, was found to increase with mesh size and with the change in mesh configuration for all the studied species. For blue whiting trawling depth and cod end catch were found to play a role in between-haul variation by increasing L-50 as well. The results suggest that an increase in the current minimum mesh size of 55-70 mm would be advisable to be compatible with the minimum landing sizes (MLSs) of 29 mm carapace length and 27 cm total length for red shrimp and hake, respectively, while it would greatly reduce the amount of discards, particularly those for blue whiting, that accounted for approximately 50% of the total catch weight. Horse mackerel was the only species for which the use of a larger mesh size would result in a significant escapement of individuals above the MLS of 15 cm. (C) 2002 Elsevier Science B.V. All rights reserved.

Size selectivity of diamond and square mesh cod ends for rose shrimp (Parapenaeus longirostris) and Norway lobster (Nephrops norvegicus) off the Portuguese south coast

The effects of an increase in cod end mesh size from 55 to 60 and 70 mm and a change of mesh configuration from diamond to square mesh on the size selectivity for rose shrimp Parapenaeus longirostris and Norway lobster Nephrops norvegicus captured off the Portuguese south coast were evaluated. The results were analysed taking into account between-haul variation in selectivity, and indicate a significant increase in L-50 for rose shrimp with an increase in mesh size or with the use of a square mesh cod end, while for Norway lobster only mesh configuration was found to affect this parameter. Two other important external variables were identified; the trawling depth and the cod end catch, which influence between-haul variation, by increasing the selection range for rose shrimp and Norway lobster, respectively. The results obtained suggest that an increase in the current minimum mesh size of 55 mm would be advisable for rose shrimp in order to respect the minimum landing size of 24 mm carapace length presently established for this species. Moreover, trawling for rose shrimp should be avoided at depths above 200 m, in order to avoid catches consisting almost exclusively of juveniles. Such an increase in mesh size would have a minor impact in terms of losses of individuals above the minimum landing size for Norway lobster and would contribute to reducing the amount of discards in this fishery. (C) 2002 Elsevier Science B.V. All rights reserved.

A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement

We propose an alternative crack propagation algo- rithm which effectively circumvents the variable transfer procedure adopted with classical mesh adaptation algo- rithms. The present alternative consists of two stages: a mesh-creation stage where a local damage model is employed with the objective of defining a crack-conforming mesh and a subsequent analysis stage with a localization limiter in the form of a modified screened Poisson equation which is exempt of crack path calculations. In the second stage, the crack naturally occurs within the refined region. A staggered scheme for standard equilibrium and screened Poisson equa- tions is used in this second stage. Element subdivision is based on edge split operations using a constitutive quantity (damage). To assess the robustness and accuracy of this algo- rithm, we use five quasi-brittle benchmarks, all successfully solved.