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...s functions is not optimized for the representation of smooth contours. Isosurfaces can be emphasized in volume renderings by a proper transfer function [8] or they can be extracted by Marching Cubes =-=[10]-=-. Figures 1a) and b) illustrate the lacking smoothness of isolines based on bilinear and bicubic interpolation, despite of the fact that bicubic spline surfaces minimize thin-plate energy. All linear ...

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..., but they often modify the data. Diffusion and filtering methods are mostly useful for smoothing noisy data. Diffusion-based fairing techniques are also applicable to the fairing of geometric shapes =-=[3, 2]-=-. Variational modeling [16, 7] is often used for fairing parametric surfaces. Using smooth basis functions, like B-splines or quadratic splines on tetrahedra [13], interpolation and fairness constrain...

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...kl.de significant interpolation artifacts to finer scales where they can be eliminated by recursion. Our method can be globally applied, for example in combination with texture-based volume rendering =-=[9, 5]-=-, or it can be used for local refinement. These are the contents of our work: In section 2, we review related work. Our algorithm for the bivariate case (linear and bilinear scalar fields) is describe...

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...ata. Diffusion and filtering methods are mostly useful for smoothing noisy data. Diffusion-based fairing techniques are also applicable to the fairing of geometric shapes [3, 2]. Variational modeling =-=[16, 7]-=- is often used for fairing parametric surfaces. Using smooth basis functions, like B-splines or quadratic splines on tetrahedra [13], interpolation and fairness constraints can be specified for the sc...

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...rlying scalar field with locally supported basis functions is not optimized for the representation of smooth contours. Isosurfaces can be emphasized in volume renderings by a proper transfer function =-=[8]-=- or they can be extracted by Marching Cubes [10]. Figures 1a) and b) illustrate the lacking smoothness of isolines based on bilinear and bicubic interpolation, despite of the fact that bicubic spline ...

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...kl.de significant interpolation artifacts to finer scales where they can be eliminated by recursion. Our method can be globally applied, for example in combination with texture-based volume rendering =-=[9, 5]-=-, or it can be used for local refinement. These are the contents of our work: In section 2, we review related work. Our algorithm for the bivariate case (linear and bilinear scalar fields) is describe...

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...d in section 4. In section 5, we conclude our work. 2 RELATED WORK Visualization of three-dimensional scalar fields is either done by extraction of isosurfaces or by volume rendering, see for example =-=[17, 6, 8]-=-. In both cases, isosurface quality has a significant impact. Not only geometric smoothness, but also isosurface topology depends on the representation of the underlying scalar fields. In the case of ...

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...ng scalar fields. In the case of trilinear scalar fields, isosurface topology is quite complicated. A variant of Marching Cubes [10], extracting topologically correct isosurfaces was recently devised =-=[11]-=-. For trilinear fields, critical points where isosurface topology changes are efficiently detected [14]. Unfortunately, the topology of a trilinear interpolant is often different from the topology of ...

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...ginal scalar field prior to discretization. The task is to find the best reconstruction of the original shape consistent with the discrete data. Image processing techniques like anisotropic diffusion =-=[15, 4]-=- are capable of recognizing local features, but they often modify the data. Diffusion and filtering methods are mostly useful for smoothing noisy data. Diffusion-based fairing techniques are also appl...

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..., but they often modify the data. Diffusion and filtering methods are mostly useful for smoothing noisy data. Diffusion-based fairing techniques are also applicable to the fairing of geometric shapes =-=[3, 2]-=-. Variational modeling [16, 7] is often used for fairing parametric surfaces. Using smooth basis functions, like B-splines or quadratic splines on tetrahedra [13], interpolation and fairness constrain...

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... to the fairing of geometric shapes [3, 2]. Variational modeling [16, 7] is often used for fairing parametric surfaces. Using smooth basis functions, like B-splines or quadratic splines on tetrahedra =-=[13]-=-, interpolation and fairness constraints can be specified for the scalar field. Only few approaches are capable of fairing implicit surfaces. Nielson et al. [12] propose a fairing method for single is...

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...d in section 4. In section 5, we conclude our work. 2 RELATED WORK Visualization of three-dimensional scalar fields is either done by extraction of isosurfaces or by volume rendering, see for example =-=[17, 6, 8]-=-. In both cases, isosurface quality has a significant impact. Not only geometric smoothness, but also isosurface topology depends on the representation of the underlying scalar fields. In the case of ...

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...ariant of Marching Cubes [10], extracting topologically correct isosurfaces was recently devised [11]. For trilinear fields, critical points where isosurface topology changes are efficiently detected =-=[14]-=-. Unfortunately, the topology of a trilinear interpolant is often different from the topology of an original scalar field prior to discretization. The task is to find the best reconstruction of the or...

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...nes or quadratic splines on tetrahedra [13], interpolation and fairness constraints can be specified for the scalar field. Only few approaches are capable of fairing implicit surfaces. Nielson et al. =-=[12]-=- propose a fairing method for single isosurfaces by constrained fairing of curves. The problem of fairing all isolines in a two-dimensional scalar field has been solved at the expense of high computat...

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... exhibit more or less the same problem. Hence, the interpolation artifacts of contours (isolines and -surfaces) may only be reduced effectively by a non-linear optimization method. In a previous work =-=[1]-=-, we have presented an iterative variational fairing approach for 2D scalar fields based on bicubic splines, see figure 1c). The method increases the resolution by knot insertion and iteratively smoot...