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Sharpen&bend: Recovering curved sharp edges in triangle meshes produced by feature-insensitive sampling

IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2005年第2期11卷 181-192页

作者： Attene, M Falcidieno, B Rossignac, J Spagnuolo, M CNR Ist Matemat Applicata & Tecnol Informat Sez Genova I-16149 Genoa Italy Georgia Inst Technol Coll Comp IRIS GVU TSRB Atlanta GA 30332 USA

Various acquisition, analysis, visualization, and compression approaches sample surfaces of 3D shapes in a uniform fashion without any attempt to align the samples with sharp edges or to adapt the sampling density to the surface curvature. Consequently, triangle meshes that interpolate these samples usually chamfer sharp features and exhibit a relatively large error in their vicinity. We present two new filters that improve the quality of these resampled models. EdgeSharpener restores the sharp edges by splitting the chamfer edges and forcing the new vertices to lie on intersections of planes extending the smooth surfaces incident upon these chamfers. Bender refines the resulting triangle mesh using an interpolating subdivision scheme that preserves the sharpness of the recovered sharp edges while bending their polyline approximations into smooth curves. A combined Sharpen&Bend postprocessing significantly reduces the error produced by feature-insensitive sampling processes. For example, we have observed that the mean-squared distortion introduced by the SwingWrapper remeshing-based compressor can often be reduced by 80 percent executing EdgeSharpener alone after decompression. For models with curved regions, this error may be further reduced by an additional 60 percent if we follow the EdgeSharpening phase by Bender.

关键词： computer graphics computational geometry and object modeling boundary representations geometric algorithms languages and systems

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Learning object models from semistructured Web documents

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2006年第3期18卷 334-349页

作者： Ye, SR Chua, TS Natl Univ Singapore Dept Comp Sci Singapore 117543 Singapore

This paper presents an automated approach to learning object models by means of useful object data extracted from data-intensive semistructured web documents such as product descriptions. modeling intensive data on the Web involves the following three phrases: First, we identify the object region covering the descriptions of object data when irrelevant contents from the web documents are excluded. Second, we partition the contents of different object data appearing in the object region and construct object data using hierarchical XML outputs. Third, we induce the abstract object model from the analogous object data. This model will match the corresponding object data from a Web site more precisely and comprehensively than the existing handcrafted ontologies. The main contribution of this study is in developing a fully automated approach to extract object data and object model from semistructured web documents using kernel-based matching and View Syntax interpretation. Our system, OnModer, can automatically construct object data and induce object models from complicated web documents, such as the technical descriptions of personal computers and digital cameras downloaded from manufacturers' and vendors' sites. A comparison with the available hand-crafted ontologies and tests on an open corpus demonstrate that our framework is effective in extracting meaningful and comprehensive models.

关键词： Web mining machine learning intelligent web services and Semantic Web web text analysis knowledge acquisition ontology design computational geometry and object modeling DOM

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Interpolation over arbitrary topology meshes using a two-phase subdivision scheme

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2006年第3期12卷 301-310页

作者： Zheng, JM Cai, YY Nanyang Technol Univ Sch Comp Engn Singapore 639798 Singapore Nanyang Technol Univ Sch Mech & Aerosp Engn Singapore 639798 Singapore

The construction of a smooth surface interpolating a mesh of arbitrary topological type is an important problem in many graphics applications. This paper presents a two-phase process, based on a topological modification of the control mesh and a subsequent Catmull-Clark subdivision, to construct a smooth surface that interpolates some or all of the vertices of a mesh with arbitrary topology. It is also possible to constrain the surface to have specified tangent planes at an arbitrary subset of the vertices to be interpolated. The method has the following features: 1) It is guaranteed to always work and the computation is numerically stable, 2) there is no need to solve a system of linear equations and the whole computation complexity is O(K) where K is the number of the vertices, and 3) each vertex can be associated with a scalar shape handle for local shape control. These features make interpolation using Catmull-Clark surfaces simple and, thus, make the new method itself suitable for interactive free- form shape design.

关键词： computer graphics computational geometry and object modeling curve, surface, solid, and object representations computer-aided engineering computer-aided design

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Sensor Selection in Arbitrary Dimensions

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2008年第4期5卷 651-660页

作者： Isler, Volkan Magdon-Ismail, Malik Rensselaer Polytech Inst Dept Comp Sci Troy NY 12180 USA

We address the sensor selection problem which arises in tracking and localization applications. In sensor selection, the goal is to select a small number of sensors whose measurements provide a good estimate of a target's state (such as location). We focus on the bounded uncertainty sensing model where the target is a point in the d-dimensional Euclidean space. Each sensor measurement corresponds to a convex polyhedral subset of the space. The measurements are merged by intersecting corresponding sets. We show that, on the plane, four sensors are sufficient (and sometimes necessary) to obtain an estimate whose area is at most twice the area of the best possible estimate (obtained by intersecting all measurements). We also extend this result to arbitrary dimensions and show that a constant number of sensors suffice for a constant factor approximation in arbitrary dimensions. Both constants depend on the dimensionality of the space but are independent of the total number of sensors in the network.

关键词： Camera networks and sensor selection computational geometry and object modeling geometric algorithms languages and systems minimum enclosing simplex polytope approximation sensor networks

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Scalable Contour Tree Computation by Data Parallel Peak Pruning

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2021年第4期27卷 2437-2454页

作者： Carr, Hamish A. Weber, Gunther H. Sewell, Christopher M. Rubel, Oliver Fasel, Patricia Ahrens, James P. Univ Leeds Leeds LS2 9JT W Yorkshire England Lawrence Berkeley Natl Lab Computat Res Div Berkeley CA 94720 USA Univ Calif Davis Dept Comp Sci Davis CA 95616 USA Los Alamos Natl Lab Los Alamos NM 87545 USA

As data sets grow to exascale, automated data analysis and visualization are increasingly important, to intermediate human understanding and to reduce demands on disk storage via in situ analysis. Trends in architecture of high performance computing systems necessitate analysis algorithms to make effective use of combinations of massively multicore and distributed systems. One of the principal analytic tools is the contour tree, which analyses relationships between contours to identify features of more than local importance. Unfortunately, the predominant algorithms for computing the contour tree are explicitly serial, and founded on serial metaphors, which has limited the scalability of this form of analysis. While there is some work on distributed contour tree computation, and separately on hybrid GPU-CPU computation, there is no efficient algorithm with strong formal guarantees on performance allied with fast practical performance. We report the first shared SMP algorithm for fully parallel contour tree computation, with formal guarantees of O(lg V lgt) parallel steps and O(V lg V) work for data with V samples and t contour tree supernodes, and implementations with more than 30x parallel speed up on both CPU using TBB and GPU using Thrust and up 70x speed up compared to the serial sweep and merge algorithm.

关键词： Topological analysis contour tree merge tree data parallel algorithms computer graphics computational geometry and object modeling curve surface solid and object representations simulation and modeling simulation output analysis

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SEPARATION FOR BOUNDARY TO CSG CONVERSION

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ACM TRANSACTIONS ON GRAPHICS 1993年第1期12卷 35-55页

作者： SHAPIRO, V VOSSLER, DL GM CORP DEPT COMP SCIRES & ENVIRON STAFFWARRENMI 48090 EDS UNIGRAPH CYPRESSCA 90630

important applications of b-rep --> CSG conversion arise in solid modeling, image processing, and elsewhere. In addition, the problem is of considerable theoretical interest. One of the most difficult steps in performing b-rep --> CSG conversion for a curved solid object consists of determining a set of half-spaces that is sufficient for a CSG representation of the solid. This usually requires the construction of additional half-spaces whose boundaries do not contribute to the boundary of the solid. Such half-spaces are called separating half-spaces because their purpose is to separate certain subsets inside the solid from those outside of the solid. Construction of separating half-spaces is specific to a particular geometric domain, but several generic approaches are possible. We use the information present in the boundary of the solid being converted to study the constraints on the degree of separating half-spaces, and show that a sufficient set of linear separating half-spaces exists for any solid whose boundary contains only planar edges. A complete construction is given for solids whose faces lie in convex surfaces. Separation for more general solids, whose b-rep includes other surfaces and nonplanar edges, is also discussed, but this general problem remains poorly understood. We apply the boundary-based separation to solids bounded by general quadric surfaces. Specifically, we prove that a sufficient set of linear separating half-spaces exists for any such solid and consider the required constructions in several common situations. The presented results allowed a successful implementation of an experimental b-rep --> CSG conversion system that converts natural quadric b-reps in Parasolid(TM) to efficient CSG representations in PADL-2.

关键词： ALGEBRAIC geometry BOUNDARY REPRESENTATION (B-REP) computational geometry and object modeling COMPUTER-AIDED DESIGN COMPUTER GRAPHICS CONSTRUCTIVE SOLID geometry (CSG) CONVERSION QUADRICS SEMIALGEBRAIC SETS SEPARATION SOLID modeling SPACE DECOMPOSITION

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Optimal discrete Morse functions for 2-manifolds

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computational geometry-THEORY AND APPLICATIONS 2003年第3期26卷 221-233页

作者： Lewiner, T Lopes, H Tavares, G Pontificia Univ Catolica Rio de Janeiro Dept Matemat Lab MatMidia BR-22453900 Rio De Janeiro Brazil

Morse theory is a powerful tool in its applications to computational topology, computer graphics and geometric modeling. It was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes. It opens up several categories of interesting objects (particularly meshes) to applications of Morse theory. Once a Morse function has been defined on a manifold, then information about its topology can be deduced from its critical elements. The main objective of this paper is to introduce a linear algorithm to define optimal discrete Morse functions on discrete 2-manifolds, where optimality entails having the least number of critical elements. The algorithm presented is also extended to general finite cell complexes of dimension at most 2, with no guarantee of optimality. (C) 2003 Elsevier B.V. All rights reserved.

关键词： Morse theory Forman theory computational topology computational geometry and object modeling

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PICO: Procedural Iterative Constrained Optimizer for Geometric modeling

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2021年第10期27卷 3968-3981页

作者： Krs, Vojtech Mech, Radomir Gaillard, Mathieu Carr, Nathan Benes, Bedrich Purdue Univ Dept Comp Graph Technol W Lafayette IN 47907 USA Adobe Res San Jose CA 95110 USA

Procedural modeling has produced amazing results, yet fundamental issues such as controllability and limited user guidance persist. We introduce a novel procedural model called PICO (Procedural Iterative Constrained Optimizer) and PICO-Graph that is the underlying procedural model designed with optimization in mind. The key novelty of PICO is that it enables the exploration of generative designs by combining both user and environmental constraints into a single framework by using optimization without the need to write procedural rules. The PICO-Graph procedural model consists of a set of geometry generating operations and a set of axioms connected in a directed cyclic graph. The forward generation is initiated by a set of axioms that use the connections to send coordinate systems and geometric objects through the PICO-Graph, which in turn generates more objects. This allows for fast generation of complex and varied geometries. Moreover, we combine PICO-Graph with efficient optimization that allows for quick exploration of the generated models and the generation of variants. The user defines the rules, the axioms, and the set of constraints;for example, whether an existing object should be supported by the generated model, whether symmetries exist, whether the object should spin, etc. PICO then generates a class of geometric models and optimizes them so that they fulfill the constraints. The generation and the optimization in our implementation provides interactive user control during model execution providing continuous feedback. For example, the user can sketch the constraints and guide the geometry to meet these specified goals. We show PICO on a variety of examples such as the generation of procedural chairs with multiple supports, generation of support structures for 3D printing, generation of spinning objects, or generation of procedural terrains matching a given input. Our framework could be used as a component in a larger design workflow;its strongest applica

关键词： Optimization geometry Shape computational modeling Grammar Three-dimensional displays Solid modeling computational geometry and object modeling three-dimensional graphics and realism

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DEPTH-ORDER POINT CLASSIFICATION TECHNIQUES FOR CSG DISPLAY ALGORITHMS

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ACM TRANSACTIONS ON GRAPHICS 1991年第1期10卷 40-70页

作者： JANSEN, FW DELFT UNIV TECHNOL FAC IND DESIGN ENGNDELFTNETHERLANDS

Constructive Solid geometry (CSG) defines objects as Boolean combinations (CSG trees) of primitive solids. To display such objects, one must classify points on the surfaces of the primitive solids with respect to the resulting composite object, to test whether these points lie on the boundary of the composite object or not. Although the point classification is trivial compared to the surface classification (i.e., the computation of the portion of the faces of primitive solids that lie on the boundary of the composite object), for CSG models with a large number of primitive solids (large CSG trees), the point classification may still consume a considerable fraction of the total processing time. This paper presents an overview of existing and new efficiency-improving techniques for classifying points in depth order. The different techniques are compared through experiments.

关键词： computational geometry and object modeling CONSTRUCTIVE SOLID geometry (CSG) CSG ALGORITHMS DISPLAY ALGORITHMS SOLID modeling 3-DIMENSIONAL GRAPHICS AND REALISM

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Cubic Gradient-Based Material Interfaces

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2013年第10期19卷 1687-1699页

作者： Prilepov, Iuri Obermaier, Harald Deines, Eduard Garth, Christoph Joy, Kenneth I. Univ Calif Davis Dept Comp Sci Inst Data Anal & Visualizat Davis CA 95616 USA CD Adapco Austin TX 78750 USA Tech Univ Kaiserslautern D-67653 Kaiserslautern Germany

Multifluid simulations often create volume fraction data, representing fluid volumes per region or cell of a fluid data set. Accurate and visually realistic extraction of fluid boundaries is a challenging and essential task for efficient analysis of multifluid data. In this work, we present a new material interface reconstruction method for such volume fraction data. Within each cell of the data set, our method utilizes a gradient field approximation based on trilinearly blended Coons-patches to generate a volume fraction function, representing the change in volume fractions over the cells. A continuously varying isovalue field is applied to this function to produce a smooth interface that preserves the given volume fractions well. Further, the method allows user-controlled balance between volume accuracy and physical plausibility of the interface. The method works on two-and three-dimensional Cartesian grids, and handles multiple materials. Calculations are performed locally and utilize only the one-ring of cells surrounding a given cell, allowing visualizations of the material interfaces to be easily generated on a GPU or in a large-scale distributed parallel environment. Our results demonstrate the robustness, accuracy, and flexibility of the developed algorithms.

关键词： Visualization boundary representations computational geometry and object modeling

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