Geometric Modeling and Processing, 2004. Proceedings

2004

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Displaying Results 1 - 25 of 54
  • Generalized NURBS curves and surfaces

    Publication Year: 2004, Page(s):365 - 368
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2125 KB) | HTML iconHTML

    A representation, the generalized NURBS (G-NURBS), is proposed for modeling parametric curves and surfaces. G-NURBS provides a unified framework for traditional parametric curve and surface. G-NURBS surface based on arbitrary irregular mesh can represent closed surface or trimmed surface with only one surface patch. 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • Least squares ellipsoid specific fitting

    Publication Year: 2004, Page(s):335 - 340
    Cited by:  Papers (9)
    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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  • 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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  • 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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  • 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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  • 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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  • Shrinking: another method for surface reconstruction

    Publication Year: 2004, Page(s):259 - 266
    Cited by:  Papers (5)
    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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  • 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 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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