Article

Free access

Fairing Scalar Fields by Variational Modeling of Contours

Author:

Martin BertramAuthors Info & Claims

VIS '03: Proceedings of the 14th IEEE Visualization 2003 (VIS'03)

Page 51

https://doi.org/10.1109/VISUAL.2003.1250398

Published: 22 October 2003 Publication History

PDF eReader

Abstract

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.

References

[1]

BERTRAM, M., TRICOCHE, X., AND HAGEN, H. 2003. Adaptive smooth scattered-data approximation. In Proceedings of VisSym'03, Joint Eurographics and IEEE TCVG Symposium on Visualization, IEEE, Data Visualisation, 177-184 & 297.

Digital Library

Google Scholar

[2]

CLARENZ, U., DIEWALD, U., AND RUMPF, M. 2000. Nonlinear anisotropic diffusion in surface processing. In Proceedings of Visualization'00 , IEEE, 397-405 & 580.

Digital Library

Google Scholar

[3]

DESBRUN, M., MEYER, M., SCHROEDER, P., AND BARR, A. 1999. Implicit fairing of irregular meshes using diffusion and curvature flow. In Proceedings of Siggraph'99, ACM, Computer Graphics, 317-324.

Digital Library

Google Scholar

[4]

DIEWALD, U., PREUSSER, T., AND RUMPF, M. 2000. Anisotropic diffusion in vector field visualization on euclidean domains and surfaces. In Transactions on Visualization and Computer Graphics, IEEE, vol. 6, 139-149.

Digital Library

Google Scholar

[5]

GERSTNER, T. 2001. Fast multiresolution extraction of multiple transparent isosurfaces. In Proceedings of VisSym'03, Joint Eurographics and IEEE TCVG Symposium on Visualization, IEEE, Data Visualisation, 35-44 & 336.

Digital Library

Google Scholar

[6]

HAGEN, H., BRUNNETT, G., AND SANTARELLI, P. 1993. Variational principles in curve and surface design. In Surveys on Mathematics for Industry, vol. 3, 1-27.

Google Scholar

[7]

KOBBELT, L., BOTSCH, M., SCHWANECKE, U., AND SEIDEL, H.-P. 2001. Feature-sensitive surface extraction from volume data. In Proceedings of Siggraph'01, ACM, Computer Graphics, 57-66.

Digital Library

Google Scholar

[8]

LORENSEN, W., AND CLINE, H. 1987. Marching cubes: a high resolution 3d surface construction algorithm. In Proceedings of Siggraph'87, ACM, Computer Graphics, 163-169.

Digital Library

Google Scholar

[9]

NIELSON, G., GRAF, G., HOLMES, R., HUANG, A., AND PHIELIPP, M. 2003. Shrouds: optimal separating surfaces for enumerated volumes. In Proceedings of VisSym'03, Joint Eurographics and IEEE TCVG Symposium on Visualization, 2003, Data Visualisation, 75-84 & 287.

Digital Library

Google Scholar

[10]

NIELSON, G. 2003. On marching cubes. In Transactions on Visualization and Computer Graphics, IEEE, vol. 9, 283-297.

Digital Library

Google Scholar

[11]

WEBER, G., SCHEUERMANN, G., AND HAMANN, B. 2003. Detecting critical regions in scalar fields. In Proceedings of VisSym'03, Joint Eurographics and IEEE TCVG Symposium on Visualization, IEEE, Data Visualisation, 85-94 & 288.

Digital Library

Google Scholar

[12]

WEICKERT, J. 1998. In Anisotropic diffusion in image processing, Teubner Stuttgart, ECMI Series.

Google Scholar

[13]

WELCH, W., AND WITKIN, A. 1992. Variational surface modeling. In Proceedings of Siggraph'92, ACM, Computer Graphics, 157-166.

Digital Library

Google Scholar

[14]

WESTERMANN, R., KOBBELT, L., AND ERTL, T. 1999. Real-time exploration of regular volume data by adaptive reconstruction of isosurfaces. In The Visual Computer, vol. 15, 100-111.

Crossref

Google Scholar

Cited By

View all

Nielson G(2004)Radial Hermite Operators for Scattered Point Cloud Data with Normal Vectors and Applications to Implicitizing Polygon Mesh Surfaces for Generalized CSG Operations and SmoothingProceedings of the conference on Visualization '0410.1109/VISUAL.2004.87(203-210)Online publication date: 10-Oct-2004
https://dl.acm.org/doi/10.1109/VISUAL.2004.87
Bertram M(2004)Volume Refinement Fairing IsosurfacesProceedings of the conference on Visualization '0410.1109/VISUAL.2004.127(449-456)Online publication date: 10-Oct-2004
https://dl.acm.org/doi/10.1109/VISUAL.2004.127

Fairing Scalar Fields by Variational Modeling of Contours
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis

Recommendations

Fitting and fairing Hermite-type data by matrix weighted NURBS curves
Abstract
This paper proposes techniques to fit and fair sequences of points together with normals or tangents at the points by matrix weighted NURBS curves. Given a set of Hermite-type data, a matrix weighted NURBS curve is constructed by ...
Highlights
- Weight matrices for matrix weighted NURBS curves are robustly computed.
- Matrix ...
Fairing Recursive Subdivision Surfaces with Curve Interpolation Constraints
SMI '01: Proceedings of the International Conference on Shape Modeling & Applications

Given a polygonal mesh with a set of tagged control polygons, a subdivision surface that interpolates the B-spline curves of these control polygons can be obtained by constructing a set of polygonal complexes, each of which converges to one of the given ...
Total curvature variation fairing for medial axis regularization

Display Omitted Method for regularization of a medial axis of a planar domain.Boundary curve of domain is smoothed by a new fairing method.Fairing is based on total variation regularization. We present a new fairing method for planar curves, which is ...

Comments

Information & Contributors

Information

Published In

VIS '03: Proceedings of the 14th IEEE Visualization 2003 (VIS'03)

October 2003

664 pages

ISBN:0769520308

Publisher

IEEE Computer Society

United States

Publication History

Published: 22 October 2003

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

2
Total Citations
View Citations
162
Total Downloads

Downloads (Last 12 months)21
Downloads (Last 6 weeks)6

Reflects downloads up to 25 Dec 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Nielson G(2004)Radial Hermite Operators for Scattered Point Cloud Data with Normal Vectors and Applications to Implicitizing Polygon Mesh Surfaces for Generalized CSG Operations and SmoothingProceedings of the conference on Visualization '0410.1109/VISUAL.2004.87(203-210)Online publication date: 10-Oct-2004
https://dl.acm.org/doi/10.1109/VISUAL.2004.87
Bertram M(2004)Volume Refinement Fairing IsosurfacesProceedings of the conference on Visualization '0410.1109/VISUAL.2004.127(449-456)Online publication date: 10-Oct-2004
https://dl.acm.org/doi/10.1109/VISUAL.2004.127

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Abstract

References

Cited By

Recommendations

Fitting and fairing Hermite-type data by matrix weighted NURBS curves

Fairing Recursive Subdivision Surfaces with Curve Interpolation Constraints

Total curvature variation fairing for medial axis regularization

Comments

Information

Published In

Publisher

Publication History

Author Tags

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations