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Computer Aided Design and Computer Graphics, 2005. Ninth International Conference on

Date 7-10 Dec. 2005

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  • Ninth International Conference on Computer Aided Design and Computer Graphics - Cover

    Publication Year: 2005 , Page(s): c1
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  • Proceedings. Ninth International Conference on Computer Aided Design and Computer Graphics

    Publication Year: 2005
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  • Ninth International Conference on Computer Aided Design and Computer Graphics - Copyright

    Publication Year: 2005 , Page(s): iv
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  • Ninth International Conference on Computer Aided Design and Computer Graphics - Table of contents

    Publication Year: 2005 , Page(s): v - x
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  • Preface

    Publication Year: 2005 , Page(s): xi
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  • Committees

    Publication Year: 2005 , Page(s): xii
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  • The tangency problem of variable radius circle to lines, circles and ellipses

    Publication Year: 2005
    Request Permissions | Click to expandAbstract | PDF file iconPDF (168 KB) |  | HTML iconHTML  

    Variable-radius circles are common constructs in planar constraint solving and are usually not handled completely by algebraic constraint solvers, especially when the ellipse is the geometric entities. Consider the cluster merge problems, there are two constraints between the variable radius circle and each of the rigid geometric objects. It can be handled when the rigid geometric objects concerni... View full abstract»

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  • What order Taylor model is sufficient for subdivision based implicit curve plotting

    Publication Year: 2005
    Request Permissions | Click to expandAbstract | PDF file iconPDF (280 KB) |  | HTML iconHTML  

    In this paper, we conducted some well chosen experimental tests to determine what order is sufficient for Taylor model applied in subdivision based implicit curve plotting algorithm. Test results show that order 1 is sufficient for most test examples with simple expressions, and some more complicated test examples need order 2 or 3. Order 3 is sufficient for all test examples we tested. View full abstract»

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  • C1 continuous rational re-parameterization using monotonic parametric speed partition

    Publication Year: 2005
    Request Permissions | Click to expandAbstract | PDF file iconPDF (168 KB) |  | HTML iconHTML  

    A new method to obtain explicit re-parameterization using piecewise rational linear functions is presented in this paper. Based on the outstanding performance of Mobius transformation on modifying pieces with monotonic parametric speed, we create a partition of the original curve, in which the parametric speed of each segment is of monotonic variation. The values of new parameters corresponding to... View full abstract»

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  • A robust iterative method devoted to pole curve fitting

    Publication Year: 2005
    Request Permissions | Click to expandAbstract | PDF file iconPDF (168 KB) |  | HTML iconHTML  

    Applied to the general formulation of pole curves, least-square fining basically corresponds to minimize a quadratic error function d(P, t) (a sum of squared Euclidean norms) which depends on the set of control points P and nodes t linked to data points. We propose an iterative algorithm alternating between optimizing d(P, t) over t and P. Node corrections are achieved through the projection of da... View full abstract»

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  • Recent advances in shape preserving representations

    Publication Year: 2005
    Request Permissions | Click to expandAbstract | PDF file iconPDF (144 KB) |  | HTML iconHTML  

    Recent results on representations of polynomial curves with evaluation algorithms more efficient than the de Casteljau algorithm and representations alternative to the rational Bezier model are presented and discussed. Special emphasis is given to the shape preserving properties. View full abstract»

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  • A method for constructing G1 continuous splines via matrix decomposition

    Publication Year: 2005
    Request Permissions | Click to expandAbstract | PDF file iconPDF (136 KB) |  | HTML iconHTML  

    Analysis of transforming matrices between Bezier basis functions and geometrically continuous basis functions is presented. It is shown that G2 transforming matrix has some relationship with G1 transforming matrix. Based on this relationship a method of calculating G1 basis functions is introduced, the degree of which is higher than quadratic. These basis functions... View full abstract»

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  • Evolution of 3D curves under strict spatial constraints

    Publication Year: 2005
    Request Permissions | Click to expandAbstract | PDF file iconPDF (216 KB) |  | HTML iconHTML  

    We present a new algorithm for fairing of space curves with respect spatial constraints based on a vector valued curvature function. Smoothing with the vector valued curvature function is superior to standard Frenet techniques since the individual scalar components can be modeled similar to curvature-based curve smoothing techniques in 2D. This paper describes a curve smoothing flow that satisfies... View full abstract»

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  • A fitting approach with dynamic algebraic spline curves

    Publication Year: 2005
    Request Permissions | Click to expandAbstract | PDF file iconPDF (297 KB) |  | HTML iconHTML  

    In computer aided geometric design and computer graphics, fitting point clouds with smooth curves (known as curve reconstruction) is a widely investigated problem. Dynamic implicit curve reconstruction is a new approach appearing in the curve reconstruction. In the paper, we introduce algebraic triangular B-splines into the dynamic implicit curve reconstruction, such that the results of the curves... View full abstract»

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  • Regular Bezier curve: some geometric conditions and a necessary and sufficient condition

    Publication Year: 2005
    Cited by:  Papers (1)
    Request Permissions | Click to expandAbstract | PDF file iconPDF (144 KB) |  | HTML iconHTML  

    The regularity is an important algebraic property for the parametric curve and surface, which depends on their parameterizations. Therefore, determining the regularity of parametric curves or surfaces is a basic problem in evaluating the quality of their parameterizations. In this paper, we present the necessary and sufficient condition for the regular Bezier curve using the Sturm's theorem. Moreo... View full abstract»

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  • Constructing geometric Hermite curve with minimum curvature variation

    Publication Year: 2005
    Cited by:  Papers (1)
    Request Permissions | Click to expandAbstract | PDF file iconPDF (208 KB) |  | HTML iconHTML  

    Based on the smoothness criterion of minimum curvature variation of the curve, tangent angle constraints guaranteeing an optimized geometric Hermite (OGH) curve both mathematically and geometrically smooths is given, and new methods for constructing composite optimized geometric Hermite (COH) curves are presented in this paper. The comparison of the new methods with Yong and Cheng's methods based ... View full abstract»

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  • A method of generating smooth surface using C-curves

    Publication Year: 2005
    Request Permissions | Click to expandAbstract | PDF file iconPDF (392 KB) |  | HTML iconHTML  

    A method of constructing piecewise G1 continuous spline surface using boundary C-curves is presented. C-curves are developed by the basis (sin t, cos t, t, 1), and it overcomes some shortcomings of the nonuniform rational B-splines (NURBS) model. How to develop C-curve into surface becomes a very important problem. Using the convex combination method proposed by Nielson, a piecewise G... View full abstract»

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  • Construction of cubic triangular patches with C1 continuity around a corner

    Publication Year: 2005
    Request Permissions | Click to expandAbstract | PDF file iconPDF (200 KB) |  | HTML iconHTML  

    This paper presents a novel approach for constructing a piecewise triangular cubic polynomial surface with C1 continuity around a common corner vertex. A C1 continuity condition between two cubic triangular patches is first derived using mixed directional derivatives. An approach for constructing a surface with C1 continuity around a corner is then developed. Our a... View full abstract»

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  • Determination of free parameters in algebraic surface blending

    Publication Year: 2005
    Request Permissions | Click to expandAbstract | PDF file iconPDF (320 KB) |  | HTML iconHTML  

    In the paper we propose a method to determine parameters that appear in algebraic surface blending. By minimizing the surface energy and adding some point restrictions, we can select the free parameters such that a blending surface with reasonable shape is constructed. The method seems to be extensible for other surface blending problems, although we concentrate on algebraic surface blending. View full abstract»

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  • Surface blending with curvature continuity

    Publication Year: 2005
    Cited by:  Papers (1)
    Request Permissions | Click to expandAbstract | PDF file iconPDF (296 KB) |  | HTML iconHTML  

    In this paper, a simple, accurate and efficient method is presented for free-form surface blending with curvature continuity. The method is based on an approximate analytical solution to a sixth order partial differential equation (PDE) subjected to blending boundary constraints. The most accurate and fast solution to a PDE is the closed form solution, which however is either very difficult to com... View full abstract»

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  • The constraint elevation for parametric continuity order of NURBS curve and surface

    Publication Year: 2005
    Request Permissions | Click to expandAbstract | PDF file iconPDF (256 KB) |  | HTML iconHTML  

    For the NURBS curve that hold the arbitrary degrees and generally structured knots, under the assumption of unchanging the knot vector and the degree of NURBS curve, we present the constraint conditions for elevating the parametric continuity order of NURBS curve at the interior knots by modifying their control points and weights. Meanwhile, we obtain the freedom degree of the control points and t... View full abstract»

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  • G1-connection between rectangular Bezier patches and multisided Bezier patch

    Publication Year: 2005
    Request Permissions | Click to expandAbstract | PDF file iconPDF (144 KB) |  | HTML iconHTML  

    This paper presents conditions such that multisided Bezier patches G1-continuously fill any n-sided holes, formed by rectangular Bezier patches of any degrees. View full abstract»

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  • Interpolating meshes of curves by Catmull-Clark subdivision surfaces with a shape parameter

    Publication Year: 2005
    Request Permissions | Click to expandAbstract | PDF file iconPDF (136 KB) |  | HTML iconHTML  

    This paper presents a solution to the problem of constructing Catmull-Clark subdivision surfaces interpolating given meshes of cubic B-spline curves. The solution is supplemented by an account of the continuity of the constructed surfaces at and around the extraordinary points of the corresponding meshes. This is conducted through an analysis of the corresponding subdivision matrix, which comes in... View full abstract»

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  • Subdivision surfaces based on point-based splines

    Publication Year: 2005
    Request Permissions | Click to expandAbstract | PDF file iconPDF (1016 KB) |  | HTML iconHTML  

    We present a new interpolatory subdivision scheme based on PB-splines (point-based B-splines), over triangular meshes. Using the stencil of the interpolatory √3-subdivision scheme, we propose a different refinement strategy by introducing a variable a to each regular vertex (valence = 6). By applying different a (locally or globally), the scheme is suitable for adaptive refinement and can pe... View full abstract»

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  • Adaptive refinement scheme for subdivision surfaces based on triangular meshes

    Publication Year: 2005
    Request Permissions | Click to expandAbstract | PDF file iconPDF (224 KB) |  | HTML iconHTML  

    One problem in subdivision surfaces is the number of facets grows exponentially with the level of subdivision. Subdivision schemes are cost intensive at higher levels of subdivision. In this paper, we propose an adaptive subdivision scheme for subdivision surfaces based on triangular meshes and exploit the local smoothness information of a surface for adaptive refinement of a model. With this appr... View full abstract»

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