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Geometric Modeling and Processing, 2004. Proceedings

2004

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Displaying Results 1 - 25 of 54
  • Handling sectional views in volume-based approach to construct 3D solid from 2D views

    Publication Year: 2004, Page(s):267 - 278
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1730 KB) | HTML iconHTML

    This paper presents an algorithm for solid model reconstruction from 2D sectional views based on volume-based approach. None of the existing work in automatic reconstruction from 2D orthographic views have addressed sectional views in detail. It is believed that the volume-based approach is better suited to handle different types of sectional views. The volume-based approach constructs the 3D soli... View full abstract»

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  • Shrinking: another method for surface reconstruction

    Publication Year: 2004, Page(s):259 - 266
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2706 KB) | HTML iconHTML

    We present a method to reconstruct a pipe or a canal surface from a point cloud (a set of unorganized points). A pipe surface is defined by a spine curve and a constant radius of a swept sphere, while a variable radius may be used to define a canal surface. In this paper, by using the shrinking and moving least-squares methods, we reduce a point cloud to a thin curve-like point set which will be a... View full abstract»

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  • Interpreting line drawings of objects with k-vertices

    Publication Year: 2004, Page(s):249 - 258
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1392 KB) | HTML iconHTML

    As part of the goal of automatic creation of B-rep models of engineering objects from freehand sketches, we seek 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 drawn object. Junction and line labels, and provisional depth coordinates, are key parts of this frontal geometry. Many methods for producing fron... View full abstract»

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  • Improved geometric constraints on deformable surface model for volumetric segmentation

    Publication Year: 2004, Page(s):237 - 245
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1891 KB) | HTML iconHTML

    In this paper, we present a deformable surface geometric model for segmenting targets from volumetric data. This model deforms under external forces only, and changes its geometry and topology by using improved geometric constraints. External forces are calculated by using the sum of inflation forces, whose contributions take place on internal regions of objects, and the gradient forces, which pla... View full abstract»

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  • Existence of the normalized B-basis and a practical construction method of the B-algorithm

    Publication Year: 2004, Page(s):66 - 75
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1412 KB) | HTML iconHTML

    Necessary and sufficient conditions for the existence of a normalized B-basis on an extended Chebyshev space are presented. A method for constructing a normalized B-basis is given and the symmetry of the normalized B-basis is proved. Furthermore, a practical construction method for the B-algorithm on an extended Chebyshev space is discussed. Normalized B-bases and B-algorithms on some function spa... View full abstract»

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  • Topological volume skeletonization using adaptive tetrahedralization

    Publication Year: 2004, Page(s):227 - 236
    Cited by:  Papers (26)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2128 KB) | HTML iconHTML

    Topological volume skeletons represent level-set graphs of 3D scalar fields, and have recently become crucial to visualizing the global isosurface transitions in the volume. However, it is still a time-consuming task to extract them, especially when input volumes are large-scale data and/or prone to small-amplitude noise. The paper presents an efficient method for accelerating the computation of s... View full abstract»

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  • Interpolatory √2-subdivision surfaces

    Publication Year: 2004, Page(s):185 - 194
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1774 KB) | HTML iconHTML

    This paper presents a new interpolatory subdivision for quadrilateral meshes. The proposed scheme employs a √2 split operator to refine a given control mesh such that the face number of the refined mesh is doubled after each refinement. For regular meshes, the smallest mask is chosen to calculate newly inserted vertices and special rules are developed to compute the F-vertices for irregular ... View full abstract»

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  • Segmentation and parametrization of arbitrary polygon meshes

    Publication Year: 2004, Page(s):143 - 152
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2575 KB) | HTML iconHTML

    Polygon meshes are ubiquitous in geometric model representation. Segmentation and parametrization of arbitrary polygon meshes are closely related and crucial in many applications. The primary aim of this paper is to find an efficient and practical way to segment and resample geometric models. We automatically generate a triangular patch network by a simplification algorithm. A simple and cheap alg... View full abstract»

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  • Smooth trimmed NURBS surface connection with tension control

    Publication Year: 2004, Page(s):56 - 65
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (6974 KB) | HTML iconHTML

    An automatic smooth surface connection method that has the capability of tension control is presented. Given two trimmed NURBS surfaces, the new method constructs a smooth connection surface to connect the trimming regions of the trimmed surfaces at the trimming curves. The connection satisfies pseudo-G1 or pseudo-C1 smoothness requirement. The construction process consists o... View full abstract»

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  • Efficient and stable numerical algorithms on equilibrium equations for geometric modeling

    Publication Year: 2004, Page(s):291 - 300
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (3430 KB) | HTML iconHTML

    In this paper the applications of equilibrium equation to geometric modeling is exploited and efficient numerical algorithms are proposed for solving the equilibrium equation. First we show that from diverse geometric modeling applications the equilibrium system can be extracted as the central framework. Second, by exploiting in-depth the special structures inherent in the geometric applications, ... View full abstract»

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  • Shape-preserving MQ-B-splines quasi-interpolation

    Publication Year: 2004, Page(s):85 - 92
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1559 KB) | HTML iconHTML

    Based on the definition of MQ-B-splines, this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in details. Examples are shown to demonstrate the capacity of the quasi-interpolants for curve representation. View full abstract»

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  • Surface interpolation of meshes with shape optimization

    Publication Year: 2004, Page(s):103 - 112
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1676 KB) | HTML iconHTML

    Subdivision surface is an efficient geometric modeling tool that is generated by repeated approximation or interpolation from an initial control mesh. For each time of subdivision the old mesh will be split and the vertexes of the mesh will be refined for a new mesh. Most existing algorithms aim to construct a smooth subdivision surface by smoothing the vertexes of the split mesh. When some featur... View full abstract»

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  • Chord length (motivated) parameterization of marching cubes isosurfaces

    Publication Year: 2004, Page(s):19 - 30
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2501 KB) | HTML iconHTML

    We describe a new technique for the parameterization of isosurfaces which result from the marching cubes (mc) algorithm. The motivation for the methods is based upon the method of chord length parameterization for curves. The method of extending the concept of curve parameterization to isosurface parameterization is based upon a relatively simple but very useful observation about a subset of the e... View full abstract»

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  • Global curvature analysis and segmentation of volumetric data sets using trivariate B-spline functions

    Publication Year: 2004, Page(s):217 - 226
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2818 KB) | HTML iconHTML

    This paper presents a scheme to globally compute, bound, and analyze the Gaussian and mean curvatures of an entire volumetric data set, using a trivariate B-spline volumetric representation. The proposed scheme is not only precise and insensitive to aliasing, but also provides a method to globally segment the images into volumetric regions that contain convex or concave {elliptic) iso-surfaces, pl... View full abstract»

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  • Topology-free cut-and-paste editing over meshes

    Publication Year: 2004, Page(s):173 - 182
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (3008 KB) | HTML iconHTML

    Existing cut-and-paste editing methods over meshes are inapplicable to regions with non-zero genus. To overcome this drawback, we propose a novel method in this paper. Firstly, a base surface passing through the boundary vertices of the selected region is constructed using the boundary triangulation technique. Considering the connectivity between the neighboring vertices, a new detail encoding tec... View full abstract»

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  • Analyzing and enhancing the robustness of implicit representations

    Publication Year: 2004, Page(s):131 - 140
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (3084 KB) | HTML iconHTML

    We introduce a robustness measure which allows to analyze implicitly defined curves and surfaces with respect to their stability. It can be used to bound the maximal position error, which is introduced by small perturbations of the coefficients of a curve or surface. It is shown that the robustness of an implicitly defined curve or surface can be enhanced by multiplying it with auxiliary factors. View full abstract»

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  • On convergence of the control polygons series of C-Bezier curves

    Publication Year: 2004, Page(s):49 - 55
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1366 KB) | HTML iconHTML

    The C-Bezier curve is introduced to CAD/CAM to deal with circular arcs, cylinders, and cones. It can precisely represent these conic curves in a Bezier-like way. A conjecture of Q.Y. Chen and G.Z. Wang (2003) is that the sequence of control polygons associated with the C-Bezier representation of a curve converges to the curve itself as the curve degree n goes to infinity. In this paper we prove th... View full abstract»

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  • Theory of 2D nonseparable optimal m-band wavelets and its applications

    Publication Year: 2004, Page(s):331 - 334
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1351 KB) | HTML iconHTML

    The theory of 1D generalized multiresolution analysis (GMRA) with quasi-real dilation is put forward. In this paper we will focus on the 2D extension of the optimal m-band wavelets and its applications in planar image processing. Given a class of image, we will present optimal m-band wavelets for them only by a part of samples. The efficiency and superiority of the algorithm can been seen from the... View full abstract»

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  • Three-axis NC cutter path generation for subdivision surface

    Publication Year: 2004, Page(s):349 - 354
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1671 KB) | HTML iconHTML

    In this paper we propose methodologies and algorithms of NC cutter path generation for subdivision surfaces. We select Loop surface as the subdivision surface. A path plan including rough cut and finish-cut is developed based on LoD (level of detail) property of the subdivision surface. We generate a coarse mesh that covers the limit surface to implement rough cut. For finish-cut we use ball-end m... View full abstract»

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  • BIUP3: boundary topological invariant of 3D objects through front propagation at a constant speed

    Publication Year: 2004, Page(s):369 - 372
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1386 KB) | HTML iconHTML

    Topological features constitute the highest abstraction in object representation. Euler characteristic is one of the most widely used topological invariants. The computation of the Euler characteristic is mainly based on three well-known mathematical formulae, which calculate either on the boundary of object or on the whole object. However, as digital objects are often non-manifolds, none of the k... View full abstract»

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  • Surface reconstruction with triangular B-splines

    Publication Year: 2004, Page(s):279 - 287
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2143 KB) | HTML iconHTML

    This paper presents a modeling technique for reconstructing a triangular B-spline surface from a set of scanned 3D points. Unlike existing surface reconstruction methods based on tensor-product B-splines which primarily generate a network of patches and then enforce certain continuity (usually, G1 or C1) between adjacent patches, our algorithm can avoid the complicated proced... View full abstract»

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  • Some estimates of the height of rational Bernstein-Bezier triangular surfaces

    Publication Year: 2004, Page(s):79 - 84
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1388 KB) | HTML iconHTML

    Subdivision, intersection and triangulation of a surface are the basic and common operations in computer aided design and computer graphics. A complicated surface can be approximated by some triangular patches. The key technique of this problem is the estimation of approximation error. This work has been done in some papers by estimating second derivatives of the surface, thus very complicated com... View full abstract»

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  • Convergent discrete Laplace-Beltrami operators over triangular surfaces

    Publication Year: 2004, Page(s):195 - 204
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1813 KB) | HTML iconHTML

    The convergence property of the discrete Laplace-Beltrami operators is the foundation of convergence analysis of the numerical simulation process of some geometric partial differential equations which involve the operator. In this paper we propose several simple discretization schemes of Laplace-Beltrami operators over triangulated surfaces. Convergence results for these discrete Laplace-Beltrami ... View full abstract»

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  • Triangular/quadrilateral remeshing of an arbitrary polygonal surface via packing bubbles

    Publication Year: 2004, Page(s):153 - 162
    Cited by:  Papers (1)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (8199 KB) | HTML iconHTML

    This paper describes a new computational method for creating a triangular and quadrilateral mesh of an arbitrary polygonal surface while controlling the anisotropy and directionality of the mesh. The input polygonal surface may include non-manifold edges and holes, and it can be either a closed polyhedron or an open polygonal surface. The method creates a mesh in two steps. In the first step, volu... View full abstract»

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  • Recognition and reconstruction of developable surfaces from point

    Publication Year: 2004, Page(s):301 - 310
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1566 KB) | HTML iconHTML

    Given a cloud P of data points, we present techniques and algorithms to decide whether P could be measurements of a developable surface and to reconstruct the original shape of the surface. We will use the dual approach to developable surfaces, which says that a developable surface can be considered as envelope of a one-parameter family of planes. A classification will be given which detects cones... View full abstract»

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