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Geometric Modeling and Processing, 2004. Proceedings

2004

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Displaying Results 1 - 25 of 54
  • 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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  • 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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  • 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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  • Intersecting a freeform surface with a ruled or a ringed surface

    Publication Year: 2004, Page(s):38 - 45
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2740 KB) | HTML iconHTML

    We present efficient and robust algorithms for intersecting a freeform surface with a ringed surface or a ruled surface. A ringed surface is given as a one-parameter family of circles. By computing the intersection between a freeform surface and each circle in the family, we can solve the intersection problem. We propose two approaches which are closely related to each other. The first approach de... View full abstract»

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  • An engineering rules based parameterization approach for turbine blade reverse engineering

    Publication Year: 2004, Page(s):311 - 318
    Cited by:  Papers (1)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1463 KB) | HTML iconHTML

    A parameterization approach is presented for turbine blade reverse engineering in this paper. The solution starts with some key features extracted from the point cloud and then the imported sketch templates are optimized to best fit the cross sectional points while satisfying the geometric constraints among the geometry elements of the sketch. In addition, a typical aerodynamic rule (equal circula... 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • A hybrid method for fast computing the curvature scale space image

    Publication Year: 2004, Page(s):124 - 130
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1987 KB) | HTML iconHTML

    The curvature scale space (CSS) technique is one of the key techniques of the MPEG-7 international standard in computer vision and image processing. It was selected as a contour shape descriptor for MPEG-7 after substantial and comprehensive testing. However, to compute a CSS image in general needs to wait a long time. This is very disadvantageous when the CSS technique is applied to an object rec... 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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  • M-band subdivision of bivariate B-splines of uniform partition in three directions

    Publication Year: 2004, Page(s):355 - 358
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1361 KB) | HTML iconHTML

    In this paper, we mainly discuss the refinability of the bivariate B-splines of uniform partition in three directions. We construct the M- band refinement equations of bivariate B-splines of uniform partition in three directions in four spaces (S0-1 (Δ), S10 (Δ), S31 (Δ) and S42 (Δ), res... 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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  • 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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  • 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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  • 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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  • Shrinking: another method for surface reconstruction

    Publication Year: 2004, Page(s):259 - 266
    Cited by:  Papers (2)
    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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  • Optimal mesh signal transforms

    Publication Year: 2004, Page(s):373 - 378
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1433 KB) | HTML iconHTML

    We describe a simple autoregressive model for 3D mesh geometry based on linear prediction. Assuming a Gaussian error term, we show that the resulting probabilistic distribution is a multivariate Gaussian, which may be singular. Furthermore, if the prediction operator is symmetric positive semi-definite, then its eigenvectors coincide with that of the covariance matrix for the distribution. This im... 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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