Geometric Modeling and Processing, 2004. Proceedings

2004

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Displaying Results 1 - 25 of 54
  • 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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  • 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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  • 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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  • 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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  • 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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  • The fractal nature of Bezier curves

    Publication Year: 2004, Page(s):3 - 11
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1392 KB) | HTML iconHTML

    Fractals are attractors - fixed points of iterated function systems. Bezier curves are polynomials - linear combinations of Bernstein basis functions. The de Casteljau subdivision algorithm is used here to show that Bezier curves are also attractors. Thus, somewhat surprisingly, Bezier curves are fractals. This fractal nature of Bezier curves is exploited to derive a new rendering algorithm for Be... 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • G2 continuity conditions for two adjacent B-spline surfaces

    Publication Year: 2004, Page(s):341 - 344
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2974 KB) | HTML iconHTML

    According to the results on the G1 continuity conditions for two arbitrary degree B-spline surfaces with generally structured knots, this paper analyzes the property of the connecting functions of G1 continuity first, then obtains the necessary and sufficient condition of G2 continuity for two arbitrary degree B-spline surfaces with generally structured knots, mean... 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 S32,1 (Δmn(2)) and construct a kind of bivariate cubic NURBS surfaces by using the bivariate B-spline bases in S32,1 (Δmn(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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  • Efficient topology construction from triangle soup

    Publication Year: 2004, Page(s):359 - 364
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1455 KB) | HTML iconHTML

    Triangular mesh is one of the most popular shape representations in computer graphics and the CAD/CAM/ CAE area. In this paper we present a memory and time efficient topology construction algorithm from triangle soup, which is a set of triangles without connectivity information. The proposed algorithm consists of the following steps: (1) vertex merging, (2) internal edge linking, (3) multi-disk ve... View full abstract»

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