Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement

The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application. In this paper, we design an algorithm to address all three optimization goals simultaneously. The user specifies desired bounds on approximation error {\delta}, minimal interior angle {\theta} and maximum mesh complexity N (number of vertices). Since such a desired mesh might not even exist, our optimization framework treats only the approximation error bound {\delta} as a hard constraint and the other two criteria as optimization goals. More specifically, we iteratively perform carefully prioritized local operators, whenever they do not violate the approximation error bound and improve the mesh otherwise. In this way our optimization framework greedily searches for the coarsest mesh with minimal interior angle above {\theta} and approximation error bounded by {\delta}. Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that our approach delivers high-quality meshes with implicitly preserved features and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.Comment: 14 pages, 20 figures. Submitted to IEEE Transactions on Visualization and Computer Graphic

Применение сервис-ориентированной архитектуры при интеграции систем управления технологическими процессами

Отражен опыт применения сервис-ориентированной архитектуры при создании автоматизированных систем управления технологическими процессами и их интеграции на ОАО "НПК "Уралвагонзавод"

Subdivide and Conquer: Adapting Non-Manifold Subdivision Surfaces to Surface-Based Representation and Reconstruction of Complex Geological Structures

Methods from the field of computer graphics are the foundation for the representation of geological structures in the form of geological models. However, as many of these methods have been developed for other types of applications, some of the requirements for the representation of geological features may not be considered, and the capacities and limitations of different algorithms are not always evident. In this work, we therefore review surface-based geological modelling methods from both a geological and computer graphics perspective. Specifically, we investigate the use of NURBS (non-uniform rational B-splines) and subdivision surfaces, as two main parametric surface-based modelling methods, and compare the strengths and weaknesses of the two approaches. Although NURBS surfaces have been used in geological modelling, subdivision surfaces as a standard method in the animation and gaming industries have so far received little attention—even if subdivision surfaces support arbitrary topologies and watertight boundary representation, two aspects that make them an appealing choice for complex geological modelling. It is worth mentioning that watertight models are an important basis for subsequent process simulations. Many complex geological structures require a combination of smooth and sharp edges. Investigating subdivision schemes with semi-sharp creases is therefore an important part of this paper, as semi-sharp creases characterise the resistance of a mesh structure to the subdivision procedure. Moreover, non-manifold topologies, as a challenging concept in complex geological and reservoir modelling, are explored, and the subdivision surface method, which is compatible with non-manifold topology, is described. Finally, solving inverse problems by fitting the smooth surfaces to complex geological structures is investigated with a case study. The fitted surfaces are watertight, controllable with control points, and topologically similar to the main geological structure. Also, the fitted model can reduce the cost of modelling and simulation by using a reduced number of vertices in comparison with the complex geological structure

Quadrilateral surface mesh generation for animation and simulation

Besides triangle meshes, quadrilateral meshes are the most prominent discrete representation of surfaces embedded in 3D. Especially in sophisticated applications like for instance animation and simulation, they are often preferred due to their tensor-product nature, which induces several practical advantages. In contrast to their wide area of application, the available generation algorithms for high-quality quadrilateral meshes are still nonsatisfying compared to their triangle mesh counterparts. The main reason consists in the intrinsically more difficult topology, which requires global instead of local considerations. This thesis is devoted to novel algorithms that are specifically designed for the practical requirements in animation and simulation. First we will discuss important quality criteria, stemming from these applications. It turns out that, although the goal of both application areas is quite diverse, the quality criteria, which characterize a high-quality quad mesh, are identical. Apart from topological regularity, applications benefit from quadrilaterals with low distortion, well chosen curvature alignment to achieve good approximation and a coarse patch-structure in order to enable powerful mapping techniques as well as multi-level solver. Based on mixed-integer optimization and graph theory we propose carefully designed algorithms that are able to generate high-quality quadmeshes with the aforementioned properties in a fully automatic manner. Furthermore, the designer or engineer is still equipped with maximal control by the possibility of interactively influencing the automatic solution by means of additional high-level constraints

Quadrilateral surface mesh generation for animation and simulation

Besides triangle meshes, quadrilateral meshes are the most prominent discrete representation of surfaces embedded in 3D. Especially in sophisticated applications like for instance animation and simulation, they are often preferred due to their tensor-product nature, which induces several practical advantages. In contrast to their wide area of application, the available generation algorithms for high-quality quadrilateral meshes are still nonsatisfying compared to their triangle mesh counterparts. The main reason consists in the intrinsically more difficult topology, which requires global instead of local considerations. This thesis is devoted to novel algorithms that are specifically designed for the practical requirements in animation and simulation. First we will discuss important quality criteria, stemming from these applications. It turns out that, although the goal of both application areas is quite diverse, the quality criteria, which characterize a high-quality quad mesh, are identical. Apart from topological regularity, applications benefit from quadrilaterals with low distortion, well chosen curvature alignment to achieve good approximation and a coarse patch-structure in order to enable powerful mapping techniques as well as multi-level solver. Based on mixed-integer optimization and graph theory we propose carefully designed algorithms that are able to generate high-quality quadmeshes with the aforementioned properties in a fully automatic manner. Furthermore, the designer or engineer is still equipped with maximal control by the possibility of interactively influencing the automatic solution by means of additional high-level constraints

Expansion Cones: A Progressive Volumetric Mapping Framework

Volumetric mapping is a ubiquitous and difficult problem in Geometry Processing and has been the subject of research in numerous and various directions. While several methods show encouraging results, the field still lacks a general approach with guarantees regarding map bijectivity. Through this work, we aim at opening the door to a new family of methods by providing a novel framework based on the concept of progressive expansion. Starting from an initial map of a tetrahedral mesh whose image may contain degeneracies but no inversions, we incrementally adjust vertex images to expand degenerate elements. By restricting movement to so-called expansion cones, it is done in such a way that the number of degenerate elements decreases in a strictly monotonic manner, without ever introducing any inversion. Adaptive local refinement of the mesh is performed to facilitate this process. We describe a prototype algorithm in the realm of this framework for the computation of maps from ball-topology tetrahedral meshes to convex or star-shaped domains. This algorithm is evaluated and compared to state-of-the-art methods, demonstrating its benefits in terms of bijectivity. We also discuss the associated cost in terms of sometimes significant mesh refinement to obtain the necessary degrees of freedom required for establishing a valid mapping. Our conclusions include that while this algorithm is only of limited immediate practical utility due to efficiency concerns, the general framework has the potential to inspire a range of novel methods improving on the efficiency aspect