Fast Spherical Drawing of Triangulations: An Experimental Study of Graph Drawing Tools

We consider the problem of computing a spherical crossing-free geodesic drawing of a planar graph: this problem, as well as the closely related spherical parameterization problem, has attracted a lot of attention in the last two decades both in theory and in practice, motivated by a number of applications ranging from texture mapping to mesh remeshing and morphing. Our main concern is to design and implement a linear time algorithm for the computation of spherical drawings provided with theoretical guarantees. While not being aesthetically pleasing, our method is extremely fast and can be used as initial placer for spherical iterative methods and spring embedders. We provide experimental comparison with initial placers based on planar Tutte parameterization. Finally we explore the use of spherical drawings as initial layouts for (Euclidean) spring embedders: experimental evidence shows that this greatly helps to untangle the layout and to reach better local minima

A novel explicit design method for complex thin-walled structures based on embedded solid moving morphable components

In this article, a novel explicit approach for designing complex thin-walled structures based on the Moving Morphable Component (MMC) method is proposed, which provides a unified framework to systematically address various design issues, including topology optimization, reinforced-rib layout optimization, and sandwich structure design problems. The complexity of thin-walled structures mainly comes from flexible geometries and the variation of thickness. On the one hand, the geometric complexity of thin-walled structures leads to the difficulty in automatically describing material distribution (e.g., reinforced ribs). On the other hand, thin-walled structures with different thicknesses require various hypotheses (e.g., Kirchhoff-Love shell theory and Reissner-Mindlin shell theory) to ensure the precision of structural responses. Whereas for cases that do not fit the shell hypothesis, the precision loss of response solutions is nonnegligible in the optimization process since the accumulation of errors will cause entirely different designs. Hence, the current article proposes a novel embedded solid component to tackle these challenges. The geometric constraints that make the components fit to the curved thin-walled structure are whereby satisfied. Compared with traditional strategies, the proposed method is free from the limit of shell assumptions of structural analysis and can achieve optimized designs with clear load transmission paths at the cost of few design variables and degrees of freedom for finite element analysis (FEA). Finally, we apply the proposed method to several representative examples to demonstrate its effectiveness, efficiency, versatility, and potential to handle complex industrial structures

A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake

We present a generic algorithm for numbering and then efficiently iterating over the data values attached to an extruded mesh. An extruded mesh is formed by replicating an existing mesh, assumed to be unstructured, to form layers of prismatic cells. Applications of extruded meshes include, but are not limited to, the representation of three-dimensional high aspect ratio domains employed by geophysical finite element simulations. These meshes are structured in the extruded direction. The algorithm presented here exploits this structure to avoid the performance penalty traditionally associated with unstructured meshes. We evaluate the implementation of this algorithm in the Firedrake finite element system on a range of low compute intensity operations which constitute worst cases for data layout performance exploration. The experiments show that having structure along the extruded direction enables the cost of the indirect data accesses to be amortized after 10–20 layers as long as the underlying mesh is well ordered. We characterize the resulting spatial and temporal reuse in a representative set of both continuous-Galerkin and discontinuous-Galerkin discretizations. On meshes with realistic numbers of layers the performance achieved is between 70 and 90 % of a theoretical hardware-specific limit

A Quantitative Steinitz Theorem for Plane Triangulations

We give a new proof of Steinitz's classical theorem in the case of plane triangulations, which allows us to obtain a new general bound on the grid size of the simplicial polytope realizing a given triangulation, subexponential in a number of special cases. Formally, we prove that every plane triangulation $G$ with $n$ vertices can be embedded in $\mathbb{R}^2$ in such a way that it is the vertical projection of a convex polyhedral surface. We show that the vertices of this surface may be placed in a $4n^3 \times 8n^5 \times \zeta(n)$ integer grid, where $\zeta(n) \leq (500 n^8)^{\tau(G)}$ and $\tau(G)$ denotes the shedding diameter of $G$, a quantity defined in the paper.Comment: 25 pages, 6 postscript figure

Development of Physical Connectors To Assemble Unfolded Planar Panels for the Construction of Large Shapes

In this work, I propose to identify and construct physical counterparts of the links in geometric data structures that are used in shape modeling. These physical connections will be used to construct large shapes from unfolded polygonal meshes that are represented by geometric data structures. I will implement physical connectors as an extension to a unfolding system that has been developing in our laboratory at Texas A&M University. Using these connectors, any unfolded shape can be constructed by using laser-cut developable panels based on corresponding data structures. This approach is particularly suitable to construct complicated sculptural and architectural shapes from anisotropic materials that can only be bent in one direction

Emerging CFD technologies and aerospace vehicle design

With the recent focus on the needs of design and applications CFD, research groups have begun to address the traditional bottlenecks of grid generation and surface modeling. Now, a host of emerging technologies promise to shortcut or dramatically simplify the simulation process. This paper discusses the current status of these emerging technologies. It will argue that some tools are already available which can have positive impact on portions of the design cycle. However, in most cases, these tools need to be integrated into specific engineering systems and process cycles to be used effectively. The rapidly maturing status of unstructured and Cartesian approaches for inviscid simulations makes suggests the possibility of highly automated Euler-boundary layer simulations with application to loads estimation and even preliminary design. Similarly, technology is available to link block structured mesh generation algorithms with topology libraries to avoid tedious re-meshing of topologically similar configurations. Work in algorithmic based auto-blocking suggests that domain decomposition and point placement operations in multi-block mesh generation may be properly posed as problems in Computational Geometry, and following this approach may lead to robust algorithmic processes for automatic mesh generation

Development of an automated design tool for FEM-based characterization of solid and hollow microneedles

Microneedle design for biomedical applications, such as transdermal drug delivery, vaccination and transdermal biosensing, has lately become a rapidly growing research field. In this sense, finite element analysis has been extendedly used by microneedle designers to determine the most suitable structural parameters for their prototypes, and also to predict their mechanical response and efficiency during the insertion process. Although many proposals include computer-aided tools to build geometrical models for mechanical analysis, there is a lack of software utilities intended to automate the design process encompassing geometrical modeling, simulation setup and postprocessing of results. This work proposes a novel MATLAB-based design tool for microneedle arrays that permits personalized selection of the basic characteristics of a mechanical model. The tool automatically exports the selected options to an ANSYS batch file, including instructions to run a static and a linear buckling analysis. Later, the subsequent simulation results can be retrieved for on-screen display and potential postprocessing. In addition, this work reviews recent proposals (2018-2022) about finite element model characterization of microneedles to establish the minimum set of features that any tool intended for automating a design process should provide.This research was funded by the Spanish “Consejería de Universidades, Igualdad, Cultura y Deporte del Gobierno de Cantabria” under the project VP47 Bloodless Antithrombotic Therapy Monitoring System (BATMS

Modeling of an automatic CAD-based feature recognition and retrieval system for group technology application

In recent time, many researches have come up with new different approaches and means for Computer-Aided Design (CAD) and Computer-Aided Manufacturing (CAM) integration. Computer-Aided Process Planning (CAPP) is considered to be a bridge that connects these both technologies. CAPP may involve such an important technique as automatic feature extraction - a procedure that is engaged in process plans generation to be used in producing a designed part. Also in terms of CAD, the feature extraction procedure facilitates a cooperative design and process planning within the entire product development process. The main objective of the thesis is to present a new automatic feature extraction and classification system that is able to process mechanical rotational and non-rotational parts from the Opitz Code System point of view. The implemented system takes Standard for Exchange of Product data (STEP) - a neutral product representation format as input and extracts features of parts required for further manufacturing. The STEP format is used to provide geometrical and topological information about machining parts. A methodology to extract shape features was developed based on these geometrical and topological data. As output, the proposed system codes the extracted part features to Opitz Code System. CAD product files were taken from official manufacturers of mechanical parts in order to evaluate the developed system

Multilayer representation for geological information systems

En esta tesis se propone el uso de la Representación de Terrenos Basada en Stacks (SBRT, de sus siglas en inglés) para datos geológicos volumétricos. Esta estructura de datos codifica estructuras geológicas representadas como stacks utilizando una compacta representación de datos. A continuación, hemos formalizado la SBRT con un esquema basado en la teoría de geo-átomos para proporcionar una definición precisa y determinar sus propiedades. Esta tesis también introduce una nueva estructura de datos llamada QuadStack, mejorando los resultados de compresión proporcionados por la SBRT al aprovechar la redundancia de información que a menudo se encuentra en los datos distribuidos por capas. También se han proporcionado métodos de visualización para estas representaciones basados en el conocido algoritmo de visualización raycasting. Al mantener los datos en todo momento en la memoria de la GPU de forma compacta, los métodos propuestos son lo suficientemente rápidos como para proporcionar velocidades de visualización interactivas.In this thesis we propose the use of the Stack-Based Representation of Terrains (SBRT) for volumetric geological data. This data structure encodes geological structures represented as stacks using a compact data representation. The SBRT is further formalized with a framework based on the geo-atom theory to provide a precise definition and determine its properties. Also, we introduce QuadStacks, a novel data structure that improves the compression results provided by the SBRT, by exploiting in its data arrangement the redundancy often found in layered dataset. This thesis also provides direct visualization methods for the SBR and QuadStacks based on the well-known raycasting algorithm. By keeping the whole dataset in the GPU in a compact way, the methods are fast enough to provide real-time frame rates.Tesis Univ. Jaén. Departamento de Informática. Leída el 19 de septiembre de 2019