G Greiner and J Loos. Data Dependent Thin Plate Energy and its use in Interactive Surface Modelling. Computer Graphics Forum, 15(3):175--185, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....by surface primitive (e.g. spline patches, piecewise linear meshes, etc. fairness functional (e.g. membrane, bending, variation of curvature, etc. and numerical approach, i.e. the use of possibly simplified energies and the particular minimization scheme employed. A popular approach [6, 10, 11] for the fairing of spline surfaces is based on computing the fairness integral using numerical quadrature. Splines such as bicubic patches are very smooth (C ; in fact C # in the interior of each integration domain) and the curvatures are well behaved. Hence high order integration rules such ....

....fairing of spline surfaces is based on computing the fairness integral using numerical quadrature. Splines such as bicubic patches are very smooth (C ; in fact C # in the interior of each integration domain) and the curvatures are well behaved. Hence high order integration rules such as Gauss [6, 10] and Lobatto [11] are well suited to compute good approximations of the integrals. The resulting energy minimization problem is solved in different manners. Moreton and Sequin [11] compute a good initial approximation and improve it with an energy gradient descent scheme. The gradients of the ....

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GREINER, G., LOOS, J., AND WESSELINK, W. Data dependent thin plate energy and its use in interactive surface modeling. In Computer Graphics Forum (Proc. EUROGRAPHICS '96), 15(3) (1996), pp. 175--186.

....by the smooth curve minimizing 0 (#(t) dt. 1.1) This functional involves second derivatives and is parametrization independent. Most of the previous work based on smooth surfaces used tensor product B splines of degrees 3 to 5 to represent the surface (see for instance [MS92] and [GLW96]) The high degree of smoothness of these surfaces and consequently of the involved integrands allowed the relatively e#cient numerical evaluation of the energy integrals using high order two dimensional quadrature rules. In [MS92] central di#erences where used to approximate the partial ....

....of the subdivision surface and are positioned as a compromise between the extremes of the previously used simplified and exact functionals. Chapter 2 Setting In this chapter we recall general properties, which are referenced in the following chapters. The notation is to similar the one used in [GLW96]. Einstein summation notation is used in several formulas. 2.1 The Local Surface The surfaces considered here are parametrized over their control mesh. The control mesh is a polyhedral manifold of two dimensional faces embedded in R . We assume that each of these faces can be parametrized ....

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G. Greiner, J. Loos, and W. Wesselink. Data dependent thin plate energy and its use in interactive surface modeling. In Computer Graphics Forum (Proc. EUROGRAPHICS '96), 15(3), pages 175--186, 1996.

....offers direct manipulation of geometric properties to shape the surface. These geometric properties serve as the editable surface constraints and include properties that depend only on first order derivatives, such as interpolating surface points and surface tangents. Similarly, Greiner and Loos [17] present point interpolation constraints and curve interpolation constraints using tensor product B splines. Their work allows the user to constrain any isoparametric curve; that is, a curve for which either u or v is constant. Fortunately, constraining a curve to remain fixed is an exact ....

....fair shapes. Fair, graceful shapes are achieved by minimizing how much a surface can stretch and bend, as in Welch and Witkin [33] This process is described as minimizing the amount of energy stored in the surface. Similar methods for minimizing surface energy are also employed in other research [4, 5, 16, 17, 25, 30]. The deformation energy, or the energy functional in Celniker [4] Celniker and Gossard [5] Celniker and Welch [6] and similarly in Welch and Witkin [33] has the form: E deformation = Z oe (ff stretch fi bend) doe; 2.1) where ff and fi are the stretching and bending weights, and the ....

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Greiner, G., and Loos, J. Data dependent thin plate energy and its use in interactive surface modeling. In Eurographics '96 (1996), vol. 15, pp. C--176-- C--185.

.... surface modeling tasks, it is usually assumed, e.g. in [CG91] HKD93] and the parametric situation is treated exactly like Mathematics of Surfaces VII 1 the (piecewise) functional case [Duc79] Pow94] More sophisticated linearizations of the fairness functional are used in [Gre94] [GLW96] where a non flat reference surface provides the parameter domain instead of the plane. A completely different approach to surface generation are subdivision techniques. Interpolatory refinement schemes like [DGL90] ZSS96] Kob96b] map a given triangular or quadrilateral net to a refined net by ....

....depends on the fairness of the net e N generated by the underlying subdivision scheme e S r . Notice that the vertex locations of e N can also be used as starting values for the iterative solution of (3. 8) This approach is similar to a discrete version of the data dependent functionals of [GLW96] where a reference surface is used to estimate the metric of the solution. However, applying a stationary refinement scheme makes it impossible to guarantee the regularity, e.g. the absence of self intersections, in the refined mesh. This is a simple consequence of the affine invariance of the ....

G. Greiner / J. Loos / W. Wesselink, Data Dependent Thin Plate Energy and its Use in Interactive Surface Modeling , Computer Graphics Forum, 1996

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G. Greiner, J. Loos, and W. Wesselink. Data dependent thin plate energy and its use in interactive surface modeling. In Computer Graphics Forum (EUROGRAPHICS '96 Proceedings), volume 15, pages 175--185, 1996.

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G Greiner and J Loos. Data Dependent Thin Plate Energy and its use in Interactive Surface Modelling. Computer Graphics Forum, 15(3):175--185, 1996.

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GREINER, G., LOOS, J., AND WESSELINK, W. Data dependent thin plate energy and its use in interactive surface modeling. In Computer Graphics Forum (Proc. EUROGRAPHICS '96), 15(3) (1996), pp. 175--186.

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Greiner G., Loos J.: Data dependent thin plate energy and its use in interactive surface modeling. In Eurographics Conference Proceedings, 176--185 (1996).

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G. Greiner, J. Loos, and W. Wesselink. Data dependent thin plate energy and its use in interactive surface modeling. Computer Graphics Forum (Proc. Eurographics '96), 15(3):175--186, 1996.

No context found.

G. Greiner, J. Loos, and W. Wesselink. Data dependent thin plate energy and its use in interactive surface modeling. In Computer Graphics Forum (EUROGRAPHICS '96 Proceedings), volume 15, pages 175--185, 1996.

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