Curved support structures and meshes with spherical vertex stars

The computation and construction of curved beams along freeform skins pose many challenges. We show how to use surfaces of constant mean curvature (CMC) to compute beam networks with beneficial properties, both aesthetically and from a fabrication perspective. To explore variations of such networks we introduce a new discretization of CMC surfaces as quadrilateral meshes with spherical vertex stars and right node angles. The computed non-CMC surface variations can be seen as a path in design space - exploring possible solutions in a neighborhood, or represent an actual erection sequence exploiting elastic material behavior

Relativistic MHD with Adaptive Mesh Refinement

This paper presents a new computer code to solve the general relativistic magnetohydrodynamics (GRMHD) equations using distributed parallel adaptive mesh refinement (AMR). The fluid equations are solved using a finite difference Convex ENO method (CENO) in 3+1 dimensions, and the AMR is Berger-Oliger. Hyperbolic divergence cleaning is used to control the $\nabla\cdot {\bf B}=0$ constraint. We present results from three flat space tests, and examine the accretion of a fluid onto a Schwarzschild black hole, reproducing the Michel solution. The AMR simulations substantially improve performance while reproducing the resolution equivalent unigrid simulation results. Finally, we discuss strong scaling results for parallel unigrid and AMR runs.Comment: 24 pages, 14 figures, 3 table

Searchable Sky Coverage of Astronomical Observations: Footprints and Exposures

Sky coverage is one of the most important pieces of information about astronomical observations. We discuss possible representations, and present algorithms to create and manipulate shapes consisting of generalized spherical polygons with arbitrary complexity and size on the celestial sphere. This shape specification integrates well with our Hierarchical Triangular Mesh indexing toolbox, whose performance and capabilities are enhanced by the advanced features presented here. Our portable implementation of the relevant spherical geometry routines comes with wrapper functions for database queries, which are currently being used within several scientific catalog archives including the Sloan Digital Sky Survey, the Galaxy Evolution Explorer and the Hubble Legacy Archive projects as well as the Footprint Service of the Virtual Observatory.Comment: 11 pages, 7 figures, submitted to PAS

Higher-order block-structured hex meshing of tubular structures

Numerical simulations of the cardiovascular system are growing in popularity due to the increasing availability of computational power, and their proven contribution to the understanding of pathodynamics and validation of medical devices with in-silico trials as a potential future breakthrough. Such simulations are performed on volumetric meshes reconstructed from patient-specific imaging data. These meshes are most often unstructured, and result in a brutally large amount of elements, significantly increasing the computational complexity of the simulations, whilst potentially adversely affecting their accuracy. To reduce such complexity, we introduce a new approach for fully automatic generation of higher-order, structured hexahedral meshes of tubular structures, with a focus on healthy blood vessels. The structures are modeled as skeleton-based convolution surfaces. From the same skeleton, the topology is captured by a block-structure, and the geometry by a higher-order surface mesh. Grading may be induced to obtain tailored refinement, thus resolving, e.g., boundary layers. The volumetric meshing is then performed via transfinite mappings. The resulting meshes are of arbitrary order, their elements are of good quality, while the spatial resolution may be as coarse as needed, greatly reducing computing time. Their suitability for practical applications is showcased by a simulation of physiological blood flow modelled by a generalised Newtonian fluid in the human aorta

Generic implementation of CAD models for nuclear simulation

The goal of this project is to utilize the preexisting framework of GADRAS to simulate the radiation leakage from arbitrary CAD models without sacrificing speed or accuracy. The proposed solution is to use STL files to define models. Then, a three-dimension binning structure is created to contain all the elements of the file. This results in preservation of speed, without adding higher performance hardware requirements. Finally, the discretization is performed using a three-dimension framework to utilize GADRAS’ refinement algorithm. The combination of these two enhancements results in an absolute error within 10% for standard conditions, and 20% for edge case conditions. The addition of arbitrary models will simplify the modeling process for complex shapes, allow for more flexible models, and allow for creation of models that are simply impossible in the current framework.Mechanical Engineerin

A Revisit of Shape Editing Techniques: from the Geometric to the Neural Viewpoint

3D shape editing is widely used in a range of applications such as movie production, computer games and computer aided design. It is also a popular research topic in computer graphics and computer vision. In past decades, researchers have developed a series of editing methods to make the editing process faster, more robust, and more reliable. Traditionally, the deformed shape is determined by the optimal transformation and weights for an energy term. With increasing availability of 3D shapes on the Internet, data-driven methods were proposed to improve the editing results. More recently as the deep neural networks became popular, many deep learning based editing methods have been developed in this field, which is naturally data-driven. We mainly survey recent research works from the geometric viewpoint to those emerging neural deformation techniques and categorize them into organic shape editing methods and man-made model editing methods. Both traditional methods and recent neural network based methods are reviewed

Surface Reconstruction From 3D Point Clouds

The triangulation of a point cloud of a 3D object is a complex problem, since it depends on the complexity of the shape of such object, as well as on the density of points generated by a specific scanner. In the literature, there are essentially two approaches to the reconstruction of surfaces from point clouds: interpolation and approximation. In general, interpolation approaches are associated with simplicial methods; that is, methods that directly generate a triangle mesh from a point cloud. On the other hand, approximation approaches generate a global implicit function — that represents an implicit surface — from local shape functions, then generating a triangulation of such implicit surface. The simplicial methods are divided into two families: Delaunay and mesh growing. Bearing in mind that the first of the methods presented in this dissertation falls under the category of mesh growing methods, let us focus our attention for now on these methods. One of the biggest problems with these methods is that, in general, they are based on the establishment of dihedral angle bounds between adjacent triangles, as needed to make the decision on which triangle to add to the expansion mesh front. Typically, other bounds are also used for the internal angles of each triangle. In the course of this dissertation, we will see how this problem was solved. The second algorithm introduced in this dissertation is also a simplicial method but does not fit into any of the two families mentioned above, which makes us think that we are in the presence of a new family: triangulation based on the atlas of charts or triangle stars. This algorithm generates an atlas of the surface that consists of overlapping stars of triangles, that is, one produces a total surface coverage, thus solving one of the common problems of this family of direct triangulation methods, which is the appearance of holes or incomplete triangulation of the surface. The third algorithm refers to an implicit method, but, unlike other implicit methods, it uses an interpolation approach. That is, the local shape functions interpolate the points of the cloud. It is, perhaps, one of a few implicit methods that we can find in the literature that interpolates all points of the cloud. Therefore, one of the biggest problems of the implicit methods is solved, which has to do with the smoothing of the surface sharp features resulting from the blending of the local functions into the global function. What is common to the three methods is the interpolation approach, either in simple or implicit methods, that is, the linearization of the surface subject to reconstruction. As will be seen, the linearization of the neighborhood of each point allows us to solve several problems posed to the surface reconstruction algorithms, namely: point sub‐sampling, non‐uniform sampling, as well as sharp features.A triangulação de uma nuvem de pontos de um objeto 3D é um problema complexo, uma vez que depende da complexidade da forma desse objeto, assim como da densidade dos pontos extraídos desse objeto através de um scanner 3D particular. Na literatura, existem essencialmente duas abordagens na reconstrução de superfícies a partir de nuvens de pontos: interpolação e aproximação. Em geral, as abordagens de interpolação estão associadas aos métodos simpliciais, ou seja, a métodos que geram diretamente uma malha de triângulos a partir de uma nuvem de pontos. Por outro lado, as abordagens de aproximação estão habitualmente associadas à geração de uma função implícita global —que representa uma superfície implícita— a partir de funções locais de forma, para em seguida gerar uma triangulação da dita superfície implícita. Os métodos simpliciais dividem‐se em duas famílias: triangulação de Delaunay e triangulação baseada em crescimento progressivo da triangulação (i.e., mesh growing). Tendo em conta que o primeiro dos métodos apresentados nesta dissertação se enquadra na categoria de métodos de crescimento progressivo, foquemos a nossa atenção por ora nestes métodos. Um dos maiores problemas destes métodos é que, em geral, se baseiam no estabelecimento de limites de ângulos diédricos (i.e., dihedral angle bounds) entre triângulos adjacentes, para assim tomar a decisão sobre qual triângulo acrescentar à frente de expansão da malha. Tipicamente, também se usam limites para os ângulos internos de cada triângulo. No decorrer desta dissertação veremos como é que este problema foi resolvido. O segundo algoritmo introduzido nesta dissertação também é um método simplicial, mas não se enquadra em nenhuma das duas famílias acima referidas, o que nos faz pensar que estaremos na presença de uma nova família: triangulação baseada em atlas de vizinhanças sobrepostas (i.e., atlas of charts) ou estrelas de triângulos (i.e., triangle star). Este algoritmo gera um atlas da superfície que é constituído por estrelas sobrepostas de triângulos, ou seja, produz‐se a cobertura total da superfície, resolvendo assim um dos problemas comuns desta família de métodos de triangulação direta que é o do surgimento de furos ou de triangulação incompleta da superfície. O terceiro algoritmo refere‐se a um método implícito, mas, ao invés de grande parte dos métodos implícitos, utiliza uma abordagem de interpolação. Ou seja, as funções locais de forma interpolam os pontos da nuvem. É, talvez, um dos poucos métodos implícitos que podemos encontrar na literatura que interpola todos os pontos da nuvem. Desta forma resolve‐se um dos maiores problemas dos métodos implícitos que é o do arredondamento de forma resultante do blending das funções locais que geram a função global, em particular ao longo dos vincos da superfície (i.e., sharp features). O que é comum aos três métodos é a abordagem de interpolação, quer em métodos simpliciais quer em métodos implícitos, ou seja a linearização da superfície sujeita a reconstrução. Como se verá, a linearização da vizinhança de cada ponto permite‐nos resolver vários problemas colocados aos algoritmos de reconstrução de superfícies, nomeadamente: sub‐amostragem de pontos (point sub‐sampling), amostragem não uniforme (non‐uniform sampling), bem como formas vincadas (sharp features)

Multi-touch Detection and Semantic Response on Non-parametric Rear-projection Surfaces

The ability of human beings to physically touch our surroundings has had a profound impact on our daily lives. Young children learn to explore their world by touch; likewise, many simulation and training applications benefit from natural touch interactivity. As a result, modern interfaces supporting touch input are ubiquitous. Typically, such interfaces are implemented on integrated touch-display surfaces with simple geometry that can be mathematically parameterized, such as planar surfaces and spheres; for more complicated non-parametric surfaces, such parameterizations are not available. In this dissertation, we introduce a method for generalizable optical multi-touch detection and semantic response on uninstrumented non-parametric rear-projection surfaces using an infrared-light-based multi-camera multi-projector platform. In this paradigm, touch input allows users to manipulate complex virtual 3D content that is registered to and displayed on a physical 3D object. Detected touches trigger responses with specific semantic meaning in the context of the virtual content, such as animations or audio responses. The broad problem of touch detection and response can be decomposed into three major components: determining if a touch has occurred, determining where a detected touch has occurred, and determining how to respond to a detected touch. Our fundamental contribution is the design and implementation of a relational lookup table architecture that addresses these challenges through the encoding of coordinate relationships among the cameras, the projectors, the physical surface, and the virtual content. Detecting the presence of touch input primarily involves distinguishing between touches (actual contact events) and hovers (near-contact proximity events). We present and evaluate two algorithms for touch detection and localization utilizing the lookup table architecture. One of the algorithms, a bounded plane sweep, is additionally able to estimate hover-surface distances, which we explore for interactions above surfaces. The proposed method is designed to operate with low latency and to be generalizable. We demonstrate touch-based interactions on several physical parametric and non-parametric surfaces, and we evaluate both system accuracy and the accuracy of typical users in touching desired targets on these surfaces. In a formative human-subject study, we examine how touch interactions are used in the context of healthcare and present an exploratory application of this method in patient simulation. A second study highlights the advantages of touch input on content-matched physical surfaces achieved by the proposed approach, such as decreases in induced cognitive load, increases in system usability, and increases in user touch performance. In this experiment, novice users were nearly as accurate when touching targets on a 3D head-shaped surface as when touching targets on a flat surface, and their self-perception of their accuracy was higher