Subdivision surface fitting to a dense mesh using ridges and umbilics

Fitting a sparse surface to approximate vast dense data is of interest for many applications: reverse engineering, recognition and compression, etc. The present work provides an approach to fit a Loop subdivision surface to a dense triangular mesh of arbitrary topology, whilst preserving and aligning the original features. The natural ridge-joined connectivity of umbilics and ridge-crossings is used as the connectivity of the control mesh for subdivision, so that the edges follow salient features on the surface. Furthermore, the chosen features and connectivity characterise the overall shape of the original mesh, since ridges capture extreme principal curvatures and ridges start and end at umbilics. A metric of Hausdorff distance including curvature vectors is proposed and implemented in a distance transform algorithm to construct the connectivity. Ridge-colour matching is introduced as a criterion for edge flipping to improve feature alignment. Several examples are provided to demonstrate the feature-preserving capability of the proposed approach

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

Distance Preserving Graph Simplification

Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph. Specifically, we construct a gate graph from a large graph so that for any "non-local" vertex pair (distance higher than some threshold) in the original graph, their shortest-path distance can be recovered by consecutive "local" walks through the gate vertices in the gate graph. We perform a theoretical investigation on the gate-vertex set discovery problem. We characterize its computational complexity and reveal the upper bound of minimum gate-vertex set using VC-dimension theory. We propose an efficient mining algorithm to discover a gate-vertex set with guaranteed logarithmic bound. We further present a fast technique for pruning redundant edges in a gate graph. The detailed experimental results using both real and synthetic graphs demonstrate the effectiveness and efficiency of our approach.Comment: A short version of this paper will be published for ICDM'11, December 201

Road Graph Simplification for Minimum Cost Flow Problem

V této práci se zaměřujeme na problém výpočtu nejlevnějších toků jako na klíčový problém pro řízení dopravního provozu. Tento problém se řeší pravidelně během dne, tj. nejde o nalezení řešení jednou, ale o dlouhodobý proces, ve kterém se pořád hledá řešení toho samého problémů s různými vstupy. Proto představujeme řešení, které může být úspěšně použito v dlouhodobém horizontu. Předpokládáme, že v poptávce existuje periodický vzor, tj. směr vozidel se obecně opakuje denně. Naše zlepšení je založeno na metodě generování sloupců, která umožňuje opětovné použití cest vozidel z předchozích dnů při vyhledávání řešení. Dosáhli jsme snížení výpočetního času o 40% při zachování optimality řešení.In this work we consider the Minimum Cost Multicommodity Network Flow (MCMNF) problem as a key problem for traffic routing. The routing problem is recurring, it should be solved many times a day on a daily basis. So we present a solution that may be successfully used in the long term. We make use of a periodic demand pattern, i.e. vehicles' directions are in general recurring daily. Our improvement is based on column generation method, that allows us to reuse vehicles paths from previous days in the solution process. We achieved a 40% reduction of computational time, while the optimal solution is preserved

Virasoro Representations on Fusion Graphs

For any non-unitary model with central charge c(2,q) the path spaces associated to a certain fusion graph are isomorphic to the irreducible Virasoro highest weight modules.Comment: 9 pages (2 Figures not included), Bonn-HE-92-2

Derivation of diagnostic models based on formalized process knowledge

© IFAC.Industrial systems are vulnerable to faults. Early and accurate detection and diagnosis in production systems can minimize down-time, increase the safety of the plant operation, and reduce manufacturing costs. Knowledge- and model-based approaches to automated fault detection and diagnosis have been demonstrated to be suitable for fault cause analysis within a broad range of industrial processes and research case studies. However, the implementation of these methods demands a complex and error-prone development phase, especially due to the extensive efforts required during the derivation of models and their respective validation. In an effort to reduce such modeling complexity, this paper presents a structured causal modeling approach to supporting the derivation of diagnostic models based on formalized process knowledge. The method described herein exploits the Formalized Process Description Guideline VDI/VDE 3682 to establish causal relations among key-process variables, develops an extension of the Signed Digraph model combined with the use of fuzzy set theory to allow more accurate causality descriptions, and proposes a representation of the resulting diagnostic model in CAEX/AutomationML targeting dynamic data access, portability, and seamless information exchange

Quad Meshing

Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi-regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this State of the Art Report, we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrization, and remeshing