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Geometric Modeling and Processing, 2004. Proceedings

Date 2004

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Displaying Results 1 - 25 of 54
  • Triangular/quadrilateral remeshing of an arbitrary polygonal surface via packing bubbles

    Publication Year: 2004, Page(s):153 - 162
    Cited by:  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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  • Feature based retargeting of parameterized geometry

    Publication Year: 2004, Page(s):163 - 172
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (3639 KB) | HTML iconHTML

    This paper presents an approach for mapping layouts of parametric surface patches to a target 3D geometry. Its main contribution is to facilitate the feature based placement of an arbitrary network of patches, assuring that both boundaries and parametric flow conform to features of the target shape. The technique, referred to as dynamic templates, describes the algorithms and interface of a revers... 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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  • 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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  • 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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  • Fast evaluation of the improved Loop's subdivision surfaces

    Publication Year: 2004, Page(s):205 - 214
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1757 KB) | HTML iconHTML

    For obtaining better curvature distributions of subdivision surfaces, various improvements for Loop's subdivision scheme (C. Loop, 1987) on triangular surface meshes have been made. A careful analysis shows that the fast evaluation technique of the subdivision surface proposed by Stam is no longer usable to these improved schemes. This paper describes a fast evaluating algorithm for improved Loop'... View full abstract»

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  • Least squares ellipsoid specific fitting

    Publication Year: 2004, Page(s):335 - 340
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1499 KB) | HTML iconHTML

    In this paper, a sufficient condition for a quadric surface to be an ellipsoid has been developed and a closed-form solution for ellipsoid fitting is developed based on this constraint, which is a best fit to the given data amongst those ellipsoids whose short radii are at least half of their major radii, in the sense of algebraic distance. A simple search procedure is proposed to pursuit the 'bes... View full abstract»

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  • Overview of recent work on geometry images

    Publication Year: 2004
    Cited by:  Papers (2)  |  Patents (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1271 KB) | HTML iconHTML

    Summary form only given. Surfaces in computer graphics are commonly represented using irregular meshes. While such meshes can approximate a given shape using few vertices, their irregularity comes at a price, since most mesh operations require random memory accesses through vertex indices and texture coordinates. Also, filter kernels must handle arbitrary mesh neighborhoods, and techniques like mo... View full abstract»

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  • Bivariate cubic spline space and bivariate cubic NURBS surfaces

    Publication Year: 2004, Page(s):115 - 123
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1556 KB) | HTML iconHTML

    In this paper, we study the bivariate cubic spline space S32,1mn(2)) and construct a kind of bivariate cubic NURBS surfaces by using the bivariate B-spline bases in S32,1mn(2)). Compared with the bicubic NURBS surfaces, this kind of bivariate NURBS surfaces are non-tensor product surfaces on t... 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 (1)
    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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  • 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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  • Recognition and reconstruction of developable surfaces from point

    Publication Year: 2004, Page(s):301 - 310
    Cited by:  Papers (2)
    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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  • Knot choosing by accommodating the first derivative constraint

    Publication Year: 2004, Page(s):31 - 37
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1422 KB) | HTML iconHTML

    The current cubic spline curve interpolation scheme is derived based on the implicit assumption that the magnitude of the first derivative of the curve is close to a constant. However, the assumption is not realized by the interpolation scheme. A knot choosing technique for parametric cubic spline interpolating curve construction that accommodates this assumption is presented. A comparison of the ... 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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  • 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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  • On convergence of the control polygons series of C-Bezier curves

    Publication Year: 2004, Page(s):49 - 55
    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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  • Interpolatory convexity preserving subdivision schemes for curves

    Publication Year: 2004, Page(s):379 - 381
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1375 KB) | HTML iconHTML

    This paper is concerned with the interpolatory convexity preserving subdivision schemes for curves. The schemes are nonlinear in the control points. The convergence analysis is presented. The limit curves are C1. View full abstract»

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  • Adaptive multi-resolution fitting and its application to realistic head modeling

    Publication Year: 2004, Page(s):345 - 348
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1754 KB) | HTML iconHTML

    The general approach for object modeling is to construct the surface from the high-quality range points obtained from laser scanners. In this paper, we face the noise point cloud obtained from image sequences by a common camera and develop a novel algorithm of adaptive multi-resolution fitting (AMRF) for object modeling. This algorithm combines the adaptive subdivision scheme with multi-resolution... 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 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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  • 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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  • Surface processing by partial differential equation

    Publication Year: 2004, Page(s):13 - 15
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1327 KB) | HTML iconHTML

    Based on continuous surface models one can derive variational problems and geometric evolutions problems for various surface processing applications. In a second step these models can then be discretized by finite element techniques. This concept is demonstrated for surface fairing, surface restoration, surface generation via subdivision, and finally surface parametrization. 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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  • 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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  • 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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