Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Anisotropic geometric diffusion in surface processing
Proceedings of the conference on Visualization '00
Feature sensitive surface extraction from volume data
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Anisotropic Diffusion in Vector Field Visualization on Euclidean Domains and Surfaces
IEEE Transactions on Visualization and Computer Graphics
Shrouds: optimal separating surfaces for enumerated volumes
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
Detecting critical regions in scalar fields
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
Adaptive smooth scattered-data approximation for large-scale terrain visualization
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
IEEE Transactions on Visualization and Computer Graphics
Fast multiresolution extraction of multiple transparent isosurfaces
EGVISSYM'01 Proceedings of the 3rd Joint Eurographics - IEEE TCVG conference on Visualization
VIS '04 Proceedings of the conference on Visualization '04
Volume Refinement Fairing Isosurfaces
VIS '04 Proceedings of the conference on Visualization '04
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Volume rendering and isosurface extraction from three-dimensional scalar fields are mostly based on piecewise trilinear representations. In regions of high geometric complexity such visualization methods often exhibit artefacts, due to trilinear interpolation. In this work, we present an iterative fairing method for scalar fields interpolating function values associated with grid points while smoothing the contours inside the grid cells based on variational principles. We present a local fairing method providing a piecewise bicubic representation of two-dimensional scalar fields. Our algorithm generalizes to the trivariate case and can be used to increase the resolution of data sets either locally or globally, reducing interpolation artefacts. In contrast to filtering methods, our algorithm does not reduce geometric detail supported by the data.