International Journal of Shape Modeling

يمكن بروتوكول المصادقة القابل للإنكار المستقبل من التعرف على المصدر الحقيقي لأي رسالة بعينها، ولكنه لا يمكن الطرف الثالث من إثبات هوية المرسل. تعتبر تلك الخاصية مفيدة جدا في توفير تفاوض آمن عبر شبكة الإنترنت. تصف الورقة العلمية الحالية بروتوكول المصادقة غير التفاعلي والقابل للإنكار باستخدام نظام تواقيع خوارزمية التوقيع الرقمي ذو المنحنى الإهليجي (ECDSA). تعتمد مسألة الأمان في هذا البروتوكول على صعوبة كسر مسألة الخوارزميات المتقطعة ذات المنحى الإهليجي (ECDLP). يمكن تطبيق ذلك البروتوكول في الأجهزة المتنقلة منخفضة الطاقة وذات المعالجات الصغيرة كالبطاقات الذكية، وأجهزة المساعدة الشخصية، ... الخ.

International Journal of Shape ModelingVol. 16, No. 01n02, pp. 1-7 (2010) No AccessEDITORIAL: CONTENT-SENSITIVE METHODS FOR GEOMETRIC MODELINGSONG YU, IMRE HORVÁTH, and FERRUCCIO MANDORLISONG YU Faculty of Industrial Design Engineering, Delft University of Technology, Landbergstraat 15, 2628CE, Delft, The Netherlands, IMRE HORVÁTHFaculty of Industrial Design Engineering, Delft University of Technology, Landbergstraat 15, 2628CE, Delft, The Netherlands, and FERRUCCIO MANDORLIFaculty of Engineering, Università Politecnica delle Marche, Via Brecce Bianche, Ancona, Italyhttps://doi.org/10.1142/S0218654310001250Cited by:1 Next AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail References I. Horváth , Shifting paradigms of computer aided design ( Delft University Press , 1998 ) . Google Scholar M. E. Mortenson , Geometric modeling , 3rd edn. ( Industrial Press , 2006 ) . Google ScholarP. Min, M. Kazhdan and T. Funkhouser, A comparison of text and shape matching for retrieval of online 3D models, European Conference on Digital Libraries pp. 209–220. Google ScholarT. Igarashi, S. Matsuoka and H. Tanaka, Teddy: A sketching interface for 3D freeform design, SIGGRAPH'99 pp. 409–416. Google Scholar J. Lee and T. Funkhouser , Sketch-based search and composition of 3D models , EUROGRAPHICS Workshop on Sketch-Based Interfaces and Modeling . Google ScholarJ. Lee and J. Park, International Journal of CAD/CAM 7(1), (2007). Google ScholarJ. Pu and D. Gur, Computer Aided Design 41(12), 857 (2009), DOI: 10.1016/j.cad.2009.05.005. Crossref, Google Scholar X. Chen, A. Golovinskiy, and T. Funkhouser, A benchmark for 3D mesh segmentation, ACM Transactions on Graphics, SIGGRAPH'09, 28(3) (Aug. 2009) . Google ScholarJ. W. H. Tangelder and R. C. Veltkamp, Multimedia Tools and Applications 39(3), 441 (2008), DOI: 10.1007/s11042-007-0181-0. Crossref, Google ScholarR. Gal and D. Cohen-Or, ACM Transactions on Graphics 25(1), 130 (2006), DOI: 10.1145/1122501.1122507. Crossref, Google ScholarI. E. Berezhnoy, E. O. Postma and H. J. van den Herik, Machine Vision and Applications 20(1), 1 (2009), DOI: 10.1007/s00138-007-0098-7. Crossref, Google ScholarY. Xiang, J. Arora and K. Abdel-Malek, Journal of biomechanics (2010). Google Scholar G. Gerlach , W. Dotzel and D. Müller , Introduction to microsystem technology, A guide for students , Microsystem and Nanotechnology Series ( Wileyl , 2008 ) . Google ScholarB. Tamadazteet al., The International Journal of Robotics Research 29(11), 1416 (2010), DOI: 10.1177/0278364910376033. Crossref, Google ScholarD. Baowan, B. J. Cox and J. M. Hill, Nanotechnology 19(7), (2008), DOI: 10.1088/0957-4484/19/7/075704. Google Scholar FiguresReferencesRelatedDetailsCited By 1D3AdvM: A direct 3D adversarial sample attack inside mesh dataHuangxinxin Xu, Fazhi He, Linkun Fan and Junwei Bai1 Aug 2022 | Computer Aided Geometric Design, Vol. 97 Recommended Vol. 16, No. 01n02 Metrics History PDF download

The tensorial Bernstein basis for multivariate polynomials in n variables has a number 3n of functions for degree 2. Consequently, computing the representation of a multivariate polynomial in the tensorial Bernstein basis is an exponential time algorithm, which makes tensorial Bernstein-based solvers impractical for systems with more than n = 6 or 7 variables. This article describes a polytope (Bernstein polytope) with a number of faces, which allows to bound a sparse, multivariate polynomial expressed in the canonical basis by solving several linear programming problems. We compare the performance of a subdivision solver using domain reductions by linear programming with a solver using a change to the tensorial Bernstein basis for domain reduction. The performance is similar for n = 2 variables but only the solver using linear programming on the Bernstein polytope can cope with a large number of variables. We demonstrate this difference with two formulations of the forward kinematics problem of a Gough-Stewart parallel robot: a direct Cartesian formulation and a coordinate-free formulation using Cayley-Menger determinants, followed by a computation of Cartesian coordinates. Furthermore, we present an optimization of the Bernstein polytope-based solver for systems containing only the monomials xi and . For these, it is possible to obtain even better domain bounds at no cost using the quadratic curve (xi, ) directly.

The paper introduces the concept of functional segmentation for segregating the strokes in a product concept sketch into functionally meaningful groups. Analysis of the distributions of starting points, time and mean pressure associated with the strokes in sketches revealed that shape defining and shape detailing strokes are separable through thresholding of the stroke parameters. The inter-stroke time plot exhibited characteristic spikes which enabled stroke-sets to be conveniently segmented in to temporal groups. The temporal evolution of shape defining elements and the genesis of feature hierarchy showed significant correlation. This algorithmic stroke organization showed significant match with the segmentation done by designers interactively. Spatial grouping algorithms developed using Gestalt principles isolated shapes in a sketch well. A unified multi-parameter grouping and averaging technique is also presented for obtaining single stroke sketches without losing the feature structure. The work thus demonstrates that algorithmic functional segmentation require both geometric and non-geometric data (viz. coordinates, time-stamp and pressure associated with the strokes) and that the role based classification of strokes helps to relate functional composition of the product and temporal evolution of the sketch. The work identifies how the designers emotion, rational thinking and visualization skill influence the product concept sketching process.

Prevalent discretization methods based on Delaunay Triangulations and Advancing Fronts, which sample and mesh simultaneously, can guarantee well shaped triangles but at a fairly high computational cost. In this paper we present a novel and flexible two-part sampling and meshing algorithm, which produces topologically correct meshes on arbitrary boundary representations whose faces are represented parametrically, without requiring an initial coarse mesh. Our method is based on a hybrid spatial partitioning scheme driven by user-designed subdivision rules that combines the power of quadtree decomposition with the flexibility of the binary decompositions to produce meshes that favor prescribed geometric properties. Importantly, the algorithm offers a performance increase of approximately two orders of magnitude over Delaunay based methods and at least one order of magnitude over advancing front methods. At the same time, our algorithm is practically as fast as the computationally optimal algorithm based on a pure quadtree decomposition, but with a markedly better distribution in the regions with parametric distortion. The hierarchical nature of our surface decomposition is well suited to interactive applications and multithreaded implementation.

Behaviour analysis loop is largely performed on virtual product model before its physical manufacturing. The last avoids high expenses in terms of money and time spent on intermediate manufacturing. It is gainful from the reality to the virtuality but the process could be further optimized especially during the product behaviour optimization phase. This process involves repetition of four main processing steps: CAD design and modification, mesh creation, Finite Element (FE) model generation with the association of physical and geometric data, FE Analysis. The product behaviour analysis loop is performed on the first design solution as well as on the numerous successive product optimization loops. Each design solution evaluation necessitates the same time as required for the first product design that is particularly crucial in the context of maintenance. In this paper we propose a new framework for CAD-less product optimisation through FE analysis which reduces the model preparation activities traditionally required for FE model creation. More concretely, the idea is to directly operate on the firstly created FE mesh, enriched with physical/geometric semantics, to perform the product modifications required to achieve its optimised version. In order to accomplish the proposed CAD-less FE analysis framework, modification operators acting on both the mesh geometry and the associated semantics need to be devised. In this paper we discuss the underlying concepts and present possible components for the development of such operators. A high-level operator specification is proposed according to a modular structure that allows an easy realisation of different mesh modification operators. Here, two instances of this high-level operator are described: the planar cracking and the drilling. The realised prototypes validated on industrial FE models show clearly the feasibility of this approach.

In this paper, a platform geometrical sensitivity value for a part has been defined. Calculation and simulation methods have been defined and tested to be used in industrial "real-life" environments. Present calculation and simulation methods for assembly analysis in a single product development have been used as a basis. These methods have been further developed and adapted to suit product family development, or platforms. The assembly geometrical sensitivity value can be used to predict the effect of tolerance stacking without having data of tolerance sizes available. Using sensitivity calculation in each assembly step gives an indication of the risk of functional failure and non-fulfilled specifications due to tolerance stacking. The platform geometrical sensitivity value could be used for optimization of a part or an assembly, by means of geometric variation, not only for one product environment but also for a complete product family simultaneously. This decreases the risk of sub-optimization of part location and assembly concepts. Using the platform geometrical sensitivity value, the effect of tolerance stacking could be predicted for all assemblies conceptually and the result can be used to dimension specific part tolerances. All equations and mathematical connections are described in detail in the paper but, due to the mathematical complexity of 3D modeling, the calculations have been performed in a geometry simulation tool. Further research needs to be done to establish a proper working procedure using platform geometrical sensitivity value.

Style sketches are an essential tool for the expression and the definition of the shape of industrial products. We present a novel wavelet approach for sketch segmentation and editing expressly addressed to the designer needs. Starting from a 2D curve drawn by a user with a graphics tablet, our algorithm converts it in a B-spline representation, detects the style features, allows interactive smoothing and continuous local and global editing. The novelty compared to the existing literature is the combination of: (i) unified wavelet approach to segmentation, smoothing and editing, (ii) support for endpoint C0 and C1 continuity constraints and (iii) implementation with an interactive pen-tablet interface. Our approach requires low memory footprints with time complexity linear in the number of control points. We validated the algorithm with synthetic and practical tests.

We propose a novel approach to automatically fill holes in triangulated models. Each hole is filled using a minimum energy surface that is obtained in three steps. First, we unfold the hole boundary onto a plane using energy minimization. Second, we triangulate the unfolded hole using a constrained Delaunay triangulation. Third, we embed the triangular mesh as a minimum energy surface in ℝ3. When embedding the triangular mesh, any energy function can be used to estimate the missing data. We use a variational multi-view approach to estimate the missing data. The running time of the method depends primarily on the size of the hole boundary and not on the size of the model, thereby making the method applicable to large models. Our experiments demonstrate the applicability of the algorithm to the problem of filling holes bounded by highly curved boundaries in large models.

Shape design is often performed by starting from a basic surface and by refining it afterward by adding details. In order to construct this first approximation surface, we present in this article a method to generate a basic polyhedron from a volumic voxel-based skeleton. This approach preserves the topology described by the discrete skeleton in a 3D grid considering the 26-adjacency: if a cycle is sketched, then there is a hole in the resulting surface, and if a closed hull is designed, then the output has a cavity. We verify the same properties for connected components. This surrounding basic polyhedron is computed with simple geometrical rules, and it is a good starting point for 3D shape design from a discrete voxel skeleton. In order to add multiresolution features to our approach, we use this rough mesh as the control polyhedron of a subdivision surface, according to the Loop scheme dedicated to triangulated surfaces. We show that the resulting set of smooth refined meshes is well suited for further modifications in the frame of a 3D modeling software.

We present a novel approach to morph between two isometric poses of the same non-rigid object given as triangular meshes. We model the morphs as linear interpolations in a suitable shape spaceS. For triangulated 3D polygons, we prove that interpolating linearly in this shape space corresponds to the most isometric morph in R 3 . We extend this shape space to arbitrary triangulations in 3D using a heuristic approach.

Surface registration involving the estimation of a rigid transformation (pose) which aligns a model provided as a triangulated mesh with a set of discrete points (range data) sampled from the actual object is a core task in computer vision. This paper refines and explores the previously introduced notion of Continuum Shape Constraint Analysis (CSCA) which allows the assessment of object shape towards predicting the performance of surface registration algorithms. Conceived for computer-vision assisted spacecraft rendezvous analysis, the approach was developed for blanket or localized scanning by LIDAR or similar range-finding scanner that samples non-specific points from the object across an area. Based on the use of Iterative Closest-Point Algorithm (ICP) for pose estimation, CSCA is applied to a surface-based self-registration cost function which takes into account the direction from which the surface is scanned. The continuum nature of the CSCA formulation generates a registration cost matrix and any derived metrics as pure shape properties of the object. For the context of directional scanning as considered in the paper, these properties also become functions of viewing direction and is directly applicable to the best view problem for LIDAR/ICP pose estimation. This paper introduces the Expectivity Index and uses it to illustrate the ability of the CSCA approach to identify productive views via the expected stability of the global minimum solution. Also demonstrated through the examples, CSCA can be used to produce visual maps of geometric constraint that facilitate human interpretation of the information about the shape. Like the ICP algorithm it supports, the CSCA approach processes shape information without the need for specific feature identification and is applicable to any type of object.

The level set method (LSM) is used in a wide variety of applications. In this paper, the authors propose an approach to detect and eliminate protruding and hollow features in triangular meshes using the technique. First, uniform grid points are generated based on a given mesh model, and these points are then clustered with respect to a user-defined threshold using LSM. Finally, the mesh model is segmented in consideration of the grouped grid points. The results of experiments performed using the proposed method indicate its suitability for the purpose at hand.

Three-dimensional clouds of largely unorganized coordinate data are often used to reconstruct freeform surfaces and shapes for a variety of seemingly diverse reverse engineering applications involving computer-aided design, anatomical reconstruction, cartography, digital archaeology, and infrastructural renewal. The point cloud data acquired by non-contact digitizers is very dense and includes numerous scanning errors. As a consequence, the captured data must be filtered and simplified for accurate surface reconstruction. Many existing data simplification techniques are, however, complex and do not directly support the development of spline-based surface models. In this paper a novel contour-based simplification algorithm is introduced for creating B-spline facial surface models directly from scanned data. The algorithm first extracts a series of equally-spaced sectioned contours from an unorganized 3D point cloud by mapping points onto a set of user-defined parallel planes. Each extracted contour is then regenerated as a cubic B-spline curve with a reduced number of control points using a user-defined reduction ratio. A freeform surface is finally created from these contiguous reconstructed contours by a lofting process. Deviation analysis that compares the final reconstructed surface to the original point cloud data is used to demonstrate the effectiveness of the proposed algorithm. The results show that the proposed algorithm generates a fairly accurate spline-based surface model from unstructured points using less than 20% of the actual scanned data. Surface accuracies are enhanced with increased number of initial contours and a greater second stage data reduction ratio.

We describe a heuristic method for reconstructing a region in the plane from a noisy sample of points. The method uses radial basis functions with Gaussian kernels to compute a fuzzy membership function which provides an implicit approximation for the region. We also evaluate our reconstruction method for several sampling conditions.

In this paper we prove a well known contour evolution technique can result in inconsistent non-simple or self-intersecting polygons. This technique is used as a pre-processing step to a number of shape matching and part-decomposition strategies which are only well-defined for simple polygons. We analyze one such class of shape matching strategies, which use a highly cited method based on turning-functions to determine similarity. We prove that due to the possibility of self-intersecting polygons these methods are not well-defined. A simple alteration to the original contour evolution technique, which ensures the evolution of a consistent simple polygon, is proposed. This technique only alters the result slightly relative to the original evolution technique and therefore maintains the property of suitable shape evolution.

This paper studies triangulations obtained from Poisson disc sampling. The Poisson disc sampling strategy with radius parameter α can be used to obtain a set of points in the interior or on the boundary of a given solid object in the plane. Using this sampling, we study a certain triangulation from its α-complex which results in two contributions. First, if we choose the same parameter α for the Poisson disc sampling and for the solid α-complex, we prove that all the triangles in the complex have aspect ratio less or equal than , which is only three times the aspect ratio of an equilateral triangle. Moreover, we prove that this bound is tight. Second, we establish a condition on the parameter α that allows to recover, with topological guarantees, the original solid object from the α-complex representation.

Every surface in the Euclidean space ℝ3 admits a canonical Riemannian metric that has constant Gaussian curvature and is conformal to the original metric. Similarly, 3-manifolds can be decomposed into pieces that admit canonical metrics. Such metrics not only have theoretical significance in 3-manifold geometry and topology, but also have potential applications to practical problems in engineering fields such as shape classification. In this paper we present an algorithm that is based on a discrete curvature flow to compute constant curvature metrics on 3-manifolds that are hyperbolic and have boundaries of a certain type. We also provide an approach to visualize such a metric by embedding the fundamental domain and universal covering in the hyperbolic space ℍ3. Some experimental results are given for both algorithms. Furthermore, we propose an algorithm to automatically construct truncated tetrahedral meshes for 3-manifolds with boundaries. It can not only generate inputs to the curvature flow algorithm,...