{"title":"An effective condition for sampling surfaces with guarantees","authors":"J. Boissonnat, S. Oudot","doi":"10.2312/SM.20041381","DOIUrl":"https://doi.org/10.2312/SM.20041381","url":null,"abstract":"The notion of ε-sample, as introduced by Amenta and Bern, has proven to be a key concept in the theory of sampled surfaces. Of particular interest is the fact that, if E is an ε-sample of a smooth surface S for a sufficiently small ε, then the Delaunay triangulation of E restricted to S is a good approximation of S, both in a topological and in a geometric sense. Hence, if one can construct an ε-sample, one also gets a good approximation of the surface. Moreover, correct reconstruction is ensured by various algorithms.In this paper, we introduce the notion of loose ε-sample. We show that the set of loose ε-samples contains and is asymptotically identical to the set of ε-samples. The main advantage of loose ε-samples over ε-samples is that they are easier to check and to construct. We also present a simple algorithm that constructs provably good surface samples and meshes.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130648383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"3D discrete skeleton generation by wave propagation on PR-octree for finite element mesh sizing","authors":"W. R. Quadros, K. Shimada, S. Owen","doi":"10.2312/SM.20041410","DOIUrl":"https://doi.org/10.2312/SM.20041410","url":null,"abstract":"This paper proposes a new algorithm to generate a disconnected, three-dimensional (3D) skeleton and an application of such a skeleton to generate a finite element (FE) mesh sizing function of a solid. The mesh sizing function controls the element size and the gradient, and it is crucial in generating a desired FE mesh. Here, a geometry-based mesh sizing function is generated using a skeleton. A discrete skeleton is generated by propagating a wave from the boundary towards the interior on an octree lattice of an input solid model. As the wave propagates, the distance from the boundary and direction of the wave front are calculated at the lattice-nodes (vertices) of the new front. An approximate Euclidean distance metric is used to calculate the distance traveled by the wave. Skeleton points are generated at the region where the opposing fronts meet. The distance at these skeleton points is used to measure both proximity between geometric entities and feature size, and is utilized to generate the mesh size at the lattice-nodes. The proposed octree-based skeleton is more accurate and efficient than traditional voxel-based skeleton and proves to be great tool for mesh sizing function generation.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"222 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113966866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Christian Rössl, Frank Zeilfelder, G. Nürnberger, H. Seidel
{"title":"Spline approximation of general volumetric data","authors":"Christian Rössl, Frank Zeilfelder, G. Nürnberger, H. Seidel","doi":"10.2312/SM.20041378","DOIUrl":"https://doi.org/10.2312/SM.20041378","url":null,"abstract":"We present an efficient algorithm for approximating huge general volumetric data sets, i.e. the data is given over arbitrarily shaped volumes and consists of up to millions of samples. The method is based on cubic trivariate splines, i.e. piecewise polynomials of total degree three defined w.r.t, uniform type-6 tetrahedral partitions of the volumetric domain. Similar as in the recent bivariate approximation approaches (cf. [10, 15]), the splines in three variables are automatically determined from the discrete data as a result of a two-step method (see [40]), where local discrete least squares polynomial approximations of varying degrees are extended by using natural conditions, i.e. the continuity and smoothness properties which determine the underlying spline space. The main advantages of this approach with linear algorithmic complexity are as follows: no tetrahedral partition of the volume data is needed, only small linear systems have to be solved, the local variation and distribution of the data is automatically adapted, Bernstein-Bézier techniques well-known in Computer Aided Geometric Design (CAGD) can be fully exploited, noisy data are automatically smoothed. Our numerical examples with huge data sets for synthetic data as well as some real-world data confirm the efficiency of the methods, show the high quality of the spline approximation, and illustrate that the rendered iso-surfaces inherit a visual smooth appearance from the volume approximating splines.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132429694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimization techniques for approximation with subdivision surfaces","authors":"Martin Marinov, L. Kobbelt","doi":"10.2312/SM.20041382","DOIUrl":"https://doi.org/10.2312/SM.20041382","url":null,"abstract":"We present a method for scattered data approximation with subdivision surfaces which actually uses the true representation of the limit surface as a linear combination of smooth basis functions associated with the control vertices. This is unlike previous techniques which used only piecewise linear approximations of the limit surface. By this we can assign arbitrary parameterizations to the given sample points, including those generated by parameter correction. We present a robust and fast algorithm for exact closest point search on Loop surfaces by combining Newton iteration and non-linear minimization. Based on this we perform unconditionally convergent parameter correction to optimize the approximation with respect to the L2 metric and thus we make a well-established scattered data fitting technique which has been available before only for B-spline surfaces, applicable to subdivision surfaces. Further we exploit the fact that the control mesh of a subdivision surface can have arbitrary connectivity to reduce the L∞ error up to a certain user-defined tolerance by adaptively restructuring the control mesh. By employing iterative least squares solvers, we achieve acceptable running times even for large amounts of data and we obtain high quality approximations by surfaces with relatively low control mesh complexity compared to the number of sample points. Since we are using plain subdivision surfaces, there is no need for multiresolution detail coefficients and we do not have to deal with the additional overhead in data and computational complexity associated with them.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122356599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Euler operators for stratified objects with incomplete boundaries","authors":"A. Gomes","doi":"10.2312/SM.20041408","DOIUrl":"https://doi.org/10.2312/SM.20041408","url":null,"abstract":"Stratified objects such as those found in geometry-based systems (e.g. CAD systems and animation systems) can be stepwise constructed and manipulated through Euler operators. The operators proposed in this paper extend prior operators (e.g. the Euler-Masuda operators) provided that they can process n-dimensional stratified subanalytic objects with incomplete boundaries. The subanalytic objects form the biggest closed family of geometric objects defined by analytic functions. Basically, such operators are attachment, detachment, subdivision, and coaslescence operations without a prescribed order, providing the user with significant freedom in the design and programming of geometric applications.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128804872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
B. McCormick, B. Busse, Purna Doddapaneni, Z. Melek, J. Keyser
{"title":"Compression, segmentation, and modeling of filamentary volumetric data","authors":"B. McCormick, B. Busse, Purna Doddapaneni, Z. Melek, J. Keyser","doi":"10.2312/SM.20041411","DOIUrl":"https://doi.org/10.2312/SM.20041411","url":null,"abstract":"We present a data structure for the representation of filamentary volumetric data, called the L-block. While the L-block can be used to represent arbitrary volume data sets, it is particularly geared towards representing long, thin, branching structures that prior volumetric representations have difficulty dealing with efficiently. The data structure is designed to allow for easy compression, storage, segmentation, and reconstruction of volumetric data such as scanned neuronal data. By \"polymerizing\" adjacent connected voxels into connected components, L-block construction facilitates real-time data compression and segmentation, as well as subsequent geometric modeling and visualization of embedded objects within the volume data set. We describe its application in the context of reconstruction of brain microstructure at a neuronal level of detail.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124576993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Shortest circuits with given homotopy in a constellation","authors":"D. Michelucci, M. Neveu","doi":"10.2312/SM.20041405","DOIUrl":"https://doi.org/10.2312/SM.20041405","url":null,"abstract":"A polynomial method is described for computing the shortest circuit with a prescribed homotopy on a surface. The surface is not described by a mesh but by a constellation: a set of sampling points. Points close enough (their distance is less than a prescribed threshold) are linked with an edge: the induced graph is not a triangulation but still permits to compute homologic and homotopic properties. Advantages of constellations over meshes are their simplicity and robustness.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131477320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Contour interpolation with bounded dihedral angles","authors":"S. Bereg, Minghui Jiang, B. Zhu","doi":"10.2312/SM.20041406","DOIUrl":"https://doi.org/10.2312/SM.20041406","url":null,"abstract":"In this paper, we present the first nontrivial theoretical bound on the quality of the 3D solids generated by any contour interpolation method. Given two arbitrary parallel contour slices with n vertices in 3D, let α be the smallest angle in the constrained Delaunay triangulation of the corresponding 2D contour overlay, we present a contour interpolation method which reconstructs a 3D solid with the minimum dihedral angle of at least α/8. Our algorithm runs in O(nlogn) time where n is the size of the contour overlay.We also present a heuristic algorithm that optimizes the dihedral angles of a mesh representing a surface in 3D.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124919685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Progressive dimension-independent Boolean operations","authors":"A. Paoluzzi, Valerio Pascucci, G. Scorzelli","doi":"10.2312/SM.20041391","DOIUrl":"https://doi.org/10.2312/SM.20041391","url":null,"abstract":"This paper introduces a new progressive multi-resolution approach for representating and processing polyhedral objects of any dimension. Our representation, a variant of BSP trees [Nay90] combined with the Split scheme introduced in [BP96], allows progressive streaming and rendering of solid models at multiple levels of detail (LOD). Boolean set operations are computed progressively by reading in input a stream of incremental refinements of the operands. Each refinement of the input is mapped immediately to a refinement of the output so that the result is also represented as a stream of progressive refinements. The computation of complex models results in a tree of pipelined processes that make continuous progress concurrently, so that coarse approximations of the final results are obtained nearly instantly, long before the input operands are fully processed. We demonstrate the practical effectiveness of this approach with models constructed with our prototype system.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125354866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Peter Ashley Clifford Varley, R. Martin, H. Suzuki
{"title":"Making the most of using depth reasoning to label line drawings of engineering objects","authors":"Peter Ashley Clifford Varley, R. Martin, H. Suzuki","doi":"10.2312/SM.20041390","DOIUrl":"https://doi.org/10.2312/SM.20041390","url":null,"abstract":"Automatic creation of B-rep models of engineering objects from freehand sketches would benefit designers. A subgoal is to take a single line drawing (with hidden lines removed), and from it deduce an initial 3D geometric realisation of the visible part of the object. Junction and line labels, and provisional depth coordinates, are important components of this frontal geometry. Most methods for producing frontal geometry use line labelling, but this takes little or no account of geometry. As a result, the line labels produced can be unreliable.Previously, we proposed an approach which inflates a drawing to produce provisional depth coordinates, and uses these to make deductions about line labels. Even a naïve implementation can outperform previous line labelling methods in certain cases. In this paper, we further enhance this approach. We extend the algorithm to non-isometric-projection drawings, consider improved ways of realising some of the concepts, and also consider how to combine this approach with other labelling techniques to gain the benefits of each.We test our approach using to be drawings of what we consider representative samples of engineering objects; these exemplify difficulties not considered in many previous papers on line labelling. Our results, based on this test set, show that the enhancements result in significant benefits.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130020912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
