Ahmed H. Mahmoud

Improving spatial coverage while preserving the blue noise of point sets

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 a domain point and a sample, i.e. its Voronoi cell aspect ratios 2@b^i are small. It is well known that maximizing one of these properties destroys the other: uniform random points have no aspect ratio bound, and the vertices of an equilateral triangular tiling have no randomness. However, we show that there is a lot of room in the middle to get good values for both. Maximal Poisson-disk sampling provides @b=1 and blue noise. We show that a standard optimization technique can improve the well-spacedness while preserving randomness. Given a random point set, our Opt-@b^i algorithm iterates over the points, and for each point locally optimizes its Voronoi cell aspect ratio 2@b^i. It can improve @b^i to a large fraction of the theoretical bound given by a structured tiling: improving from 1.0 to around 0.8, about half-way to 0.58, while preserving most of the randomness of the original set. In terms of both @b and randomness, the output of Opt-@b^i compares favorably to alternative point improvement techniques, such as centroidal Voronoi tessellation with a constant density function, which do not target @b directly. We demonstrate the usefulness of our output through meshing and filtering applications. An open problem is constructing from scratch a WBD distribution with a guarantee of @b<1.

Disk density tuning of a maximal random packing

We introduce an algorithmic framework for tuning the spatial density of disks in a maximal random packing, without changing the sizing function or radii of disks. Starting from any maximal random packing such as a Maximal Poisson‐disk Sampling (MPS), we iteratively relocate, inject (add), or eject (remove) disks, using a set of three successively more‐aggressive local operations. We may achieve a user‐defined density, either more dense or more sparse, almost up to the theoretical structured limits. The tuned samples are conflict‐free, retain coverage maximality, and, except in the extremes, retain the blue noise randomness properties of the input. We change the density of the packing one disk at a time, maintaining the minimum disk separation distance and the maximum domain coverage distance required of any maximal packing. These properties are local, and we can handle spatially‐varying sizing functions. Using fewer points to satisfy a sizing function improves the efficiency of some applications. We apply the framework to improve the quality of meshes, removing non‐obtuse angles; and to more accurately model fiber reinforced polymers for elastic and failure simulations.

All-quad meshing without cleanup

We present an all-quad meshing algorithm for general domains. We start with a strongly balanced quadtree. In contrast to snapping the quadtree corners onto the geometric domain boundaries, we move them away from the geometry. Then we intersect the moved grid with the geometry. The resulting polygons are converted into quads with midpoint subdivision. Moving away avoids creating any flat angles, either at a quadtree corner or at a geometryquadtree intersection. We are able to handle two-sided domains, and more complex topologies than prior methods. The algorithm is provably correct and robust in practice. It is cleanup-free, meaning we have angle and edge length bounds without the use of any pillowing, swapping, or smoothing. Thus, our simple algorithm is fast and predictable. This paper has better quality bounds, and the algorithm is demonstrated over more complex domains, than our prior version.

Small community hospitals programs affiliation with university programs; "lessons Learned" in 28-year successful affiliation

OBJECTIVE Community hospitals affiliation with university hospitals in post graduate surgical education is essential for the 2 types of training programs. Many factors affect the success of the affiliation process. Additionally, various pitfalls and challenges are encountered. The goal of this work is to study the lessons learned in 28 years successful affiliation. DESIGN/SETTING small community hospital affiliation with university program for 28 years. PARTICIPANTS surgery residency programs in small community hospital and university hospital. RESULTS successful affiliation for 28 years between community hospital and university program.

A Constrained Resampling Strategy for Mesh Improvement

In many geometry processing applications, it is required to improve an initial mesh in terms of multiple quality objectives. Despite the availability of several mesh generation algorithms with provable guarantees, such generated meshes may only satisfy a subset of the objectives. The conflicting nature of such objectives makes it challenging to establish similar guarantees for each combination, e.g., angle bounds and vertex count. In this paper, we describe a versatile strategy for mesh improvement by interpreting quality objectives as spatial constraints on resampling and develop a toolbox of local operators to improve the mesh while preserving desirable properties. Our strategy judiciously combines smoothing and transformation techniques allowing increased flexibility to practically achieve multiple objectives simultaneously. We apply our strategy to both planar and surface meshes demonstrating how to simplify Delaunay meshes while preserving element quality, eliminate all obtuse angles in a complex mesh, and maximize the shortest edge length in a Voronoi tessellation far better than the state‐of‐the‐art.

Review of Heterotopic Thyroid Autotransplantation

Total thyroidectomy is increasingly accepted for the management of bilateral benign thyroid disorders. Postoperatively, patients require lifelong levothyroxine replacement therapy to avoid postoperative hypothyroidism, which besides the burden of compliance, has been proven to be associated with several long-term side effects. Heterotopic thyroid autotransplantation was proposed several decades ago to avoid the need for life-long postoperative replacement therapy with maintaining the autoregulatory mechanism of thyroxin production inside the body according to its needs. Available data regarding this topic in literature is relatively poor. Before applying thyroid autotransplantation on humans, several studies have been done on animals, where the autologous transplantations were found to be successful in almost all the cases, proved by follow up postoperative 8-week measurements of thyroid hormones and histopathological examination of the removed autografts. Regarding the clinical application, few trials have been done using cryopreserved in vivo, in vitro or immediately autotransplanted thyroid autografts. Satisfactory results were obtained, however, the number of these studies and the number of patients per each study was very low. Besides the study methodologies were not so consistent.

Exercises in High-Dimensional Sampling: Maximal Poisson-Disk Sampling and k -d Darts

We review our recent progress on efficient algorithms for generating well-spaced samples of high dimensional data, and for exploring and characterizing these data, the underlying domain, and functions over the domain. To our knowledge, these techniques have not yet been applied to computational topology, but the possible connections are worth considering. In particular, computational topology problems often have difficulty in scaling efficiently, and these sampling techniques have the potential to drastically reduce the size of the data over which these computational topology algorithms must operate. We summarize the definition of these sample distributions; algorithms for generating them in low, moderate, and high dimensions; and applications in mesh generation, rendering, motion planning and simulation.

Sampling Conditions for Conforming Voronoi Meshing by the VoroCrust Algorithm

We study the problem of decomposing a volume bounded by a smooth surface into a collection of Voronoi cells. Unlike the dual problem of conforming Delaunay meshing, a principled solution to this problem for generic smooth surfaces remained elusive. VoroCrust leverages ideas from α-shapes and the power crust algorithm to produce unweighted Voronoi cells conforming to the surface, yielding the first provably-correct algorithm for this problem. Given an ϵ-sample on the bounding surface, with a weak σ-sparsity condition, we work with the balls of radius δ times the local feature size centered at each sample. The corners of this union of balls are the Voronoi sites, on both sides of the surface. The facets common to cells on opposite sides reconstruct the surface. For appropriate values of ϵ, σ and δ, we prove that the surface reconstruction is isotopic to the bounding surface. With the surface protected, the enclosed volume can be further decomposed into an isotopic volume mesh of fat Voronoi cells by generating a bounded number of sites in its interior. Compared to state-of-the-art methods based on clipping, VoroCrust cells are full Voronoi cells, with convexity and fatness guarantees. Compared to the power crust algorithm, VoroCrust cells are not filtered, are unweighted, and offer greater flexibility in meshing the enclosed volume by either structured grids or random samples.

VoroCrust Illustrated: Theory and Challenges (Multimedia Exposition).

Over the past decade, polyhedral meshing has been gaining popularity as a better alternative to tetrahedral meshing in certain applications. Within the class of polyhedral elements, Voronoi cells are particularly attractive thanks to their special geometric structure. What has been missing so far is a Voronoi mesher that is sufficiently robust to run automatically on complex models. In this video, we illustrate the main ideas behind the VoroCrust algorithm, highlighting both the theoretical guarantees and the practical challenges imposed by realistic inputs.

Heterotopic thyroid autotransplantation: A preliminary clinical study

Thyroid autotransplantation offers an attractive alternative to subtotal thyroidectomy and replacement therapy. However, it has not been sufficiently clinically investigated.