Mesh generation is a useful tool for obtaining discrete descriptors of biological objects represented by images. The generation of meshes with straight sided elements has been fairly well understood. However, in order to match curved shapes that are ubiquitous in nature, meshes with high-order elements are required. Moreover, for the processing of large data sets, automatic meshing procedures a...

The paper proposes a parallel algorithm to compute the eigenvalues and eigenvectors of a real symmetric matrix on a mesh multicomputer. The algorithm uses the one-sided Jacobi method and it is aimed at reducing the communication cost incurred by one-dimensional algorithms found in the literature. The performance of the proposed algorithm on a squared 2D/3D mesh multicomputer is assessed through...

Domain decomposition (DD) methods are important techniques for designing parallel algorithms for solving partial differential equations. Since the decomposition is often performed using automatic mesh partitioning tools, one can in general not make any assumptions on the shape or physical size of the subdomains, especially if local mesh refinement is used. In many of the popular domain decompos...

We present a method for generating three-dimensional unstructured tetrahedral meshes of multi-material images. The method uses an octree as the background grid from which to build the final graded conforming meshes. The algorithm is fast and robust. It produces a small number of mesh elements and provides guaranteed bounds on the smallest dihedral angle and the two-sided Hausdorff distance betw...

We report the cases of two patients diagnosed with Morgagni hernia who presented with nonspecific abdominal symptoms. Both underwent laparoscopic surgery that used a dual-sided mesh, polyvinylidene fluoride (PVDF; Dynamesh IPOM®). The procedures were successful and both patients were discharged with no complications. There was no recurrence in 18 months of follow up.Herein is the report of thes...

A parallel distributed approach to refine a mesh while preserving the curvature of a target geometry is presented. Our approach starts by generating a coarse linear mesh of the computational domain. Second, the former coarse mesh is curved to match the curvature of the target geometry. Then, the curved mesh is partitioned and the subdomain meshes are sent to the slaves. Finally, the curved elem...

Multi-sided surfaces are important in several areas of Computer-Aided Geometric Design, including curve network based design, approximation of triangular meshes, hole filling, and so on. In the majority of surface representations, the boundary constraints entirely determine the interior of these patches, however, frequently there is a need to have additional design freedom for shaping the surfa...

A three-dimensional, medial-axis-based mesh generator is described. First the medial axis of the geometry to be meshed is constructed, then quad-dominant meshes on the medial surface are generated and extruded to the boundary at both sides of the medial surface. The resulting single cell layer is subdivided in direction normal to the boundary, yielding columns of hexahedral and three-sided pris...

We present a novel algorithm for generating three-dimensional unstructured tetrahedral meshes of multi-material images. The algorithm produces meshes with high quality since it provides a guaranteed dihedral angle bound of up to 19.47◦ for the output tetrahedra. In addition, it allows for user-specified guaranteed bounds on the two-sided Hausdorff distance between the boundaries of the mesh and...

In this paper, a new free-form shape deformation approach is proposed. We combine a skeleton-based mesh deformation technique with discrete differential coordinates in order to create natural-looking global shape deformations. Given a triangle mesh, we first extract a skeletal mesh, a two-sided Voronoi-based approximation of the medial axis. Next the skeletal mesh is modified by free-form defor...