“Dual contouring of hermite data” by Ju, Losasso, Schaefer and Warren

This paper describes a new method for contouring a signed grid whose edges are tagged by Hermite data (i.e; exact intersection points and normals). This method avoids the need to explicitly identify and process “features” as required in previous Hermite contouring methods. Using a new, numerically stable representation for quadratic error functions, we develop an octree-based method for simplifying contours produced by this method. We next extend our contouring method to these simpli£ed octrees. This new method imposes no constraints on the octree (such as being a restricted octree) and requires no “crack patching”. We conclude with a simple test for preserving the topology of the contour during simplification.

1. BLOOMENTHAL, J., AND FERGUSON, K. 1995. Polygonization of non-manifold implicit surfaces. In Proceedings of SIGGRAPH 95, ACM SIGGRAPH / Addison Wesley, Los Angeles, California, Computer Graphics Proceedings, Annual Conference Series, 309-316. ISBN 0-201-84776-0. Google Scholar
2. BLOOMENTHAL, J. 1988. Polygonization of implicit surfaces. Computer Aided Geometric Design 5, 4, 341-356. Google Scholar
3. BONNELL, K. S., SCHIKORE, D. R., JOY, K. I., DUCHAINEAU, M., AND HAMANN, B. 2000. Constructing material interfaces from data sets with volume-fraction information. In IEEE Visualization 2000, 367-372. ISBN 0-7803-6478-3. Google Scholar
4. CIGNONI, P., GANOVELLI, F., MONTANI, C., AND SCOPIGNO, R. 2000. Reconstruction of topologically correct and adaptive trilinear isosurfaces. 399-418.Google Scholar
5. FOLEY, J., VAN DAM, A., FEINER, S., AND HUGHES, J. 1995. Computer Graphics: Principles and Practice. Addison Wesley. Google Scholar
6. FRISKEN, S. F., PERRY, R. N., ROCKWOOD, A. P., AND JONES, T. R. 2000. Adaptively sampled distance fields: A general representation of shape for computer graphics. In Proceedings of SIGGRAPH 2000, ACM Press / ACM SIGGRAPH / Addison Wesley Longman, Computer Graphics Proceedings, Annual Conference Series, 249-254. Google Scholar
7. GARLAND, M., AND HECKBERT, P. S. 1998. Simplifying surfaces with color and texture using quadric error metrics. In IEEE Visualization ’98, IEEE, 263-270. Google Scholar
8. GERSTNER, T., AND PAJAROLA, R. 2000. Topology preserving and controlled topology simplifying multiresolution isosurface extraction. In IEEE Visualization 2000, 259-266. Google Scholar
9. GIBSON, S. F. F. 1998. Using distance maps for accurate surface reconstruction in sampled volumes. In 1998 Volume Visualization Symposium, IEEE, 23-30. Google Scholar
10. GOLUB, G. A., AND VAN LOAN, C. F. 1989. Matrix Computations, second ed. The Johns Hopkins University Press.Google Scholar
11. GUSKOV, I., AND WOOD, Z. 2001. Topological noise removal. In Graphics Interface 2001, 19-26. Google Scholar
12. KOBBELT, L. P., BOTSCH, M., SCHWANECKE, U., AND SEIDEL, H.-P. 2001. Feature-sensitive surface extraction from volume data. In Proceedings of SIGGRAPH 2001, ACM Press / ACM SIGGRAPH, Computer Graphics Proceedings, Annual Conference Series, 57-66. Google Scholar
13. LINDSTROM, P. 2000. Out-of-core simplification of large polygonal models. In Proceedings of SIGGRAPH 2000, ACM Press / ACM SIGGRAPH / Addison Wesley Longman, Computer Graphics Proceedings, Annual Conference Series, 259-262. Google Scholar
14. LIVNAT, Y., SHEN, H.-W., AND JOHNSON, C. R. 1996. A near optimal isosurface extraction algorithm using the span space. 73-84. Google Scholar
15. PERRY, R. N., AND FRISKEN, S. F. 2001. Kizamu: A system for sculpting digital characters. In Proceedings of SIGGRAPH 2001, ACM Press / ACM SIGGRAPH, Computer Graphics Proceedings, Annual Conference Series, 47-56. Google Scholar
16. ROSSIGNAC, J., AND BORRELL, P. 1993. Multi-resolution 3d approximation for rendering complex scenes. In Modeling in Computer Graphics, 455-465.Google Scholar
17. SHEKHAR, R., FAYYAD, E., YAGEL, R., AND CORNHILL, J. F. 1996. Octree-based decimation of marching cubes surfaces. In IEEE Visualization ’96, IEEE, 335-344. Google Scholar
18. STANDER, B. T., AND HART, J. C. 1997. Guaranteeing the topology of an implicit surface polygonization for interactive modeling. In Proceedings of SIGGRAPH 97, ACM SIGGRAPH / Addison Wesley, Los Angeles, California, Computer Graphics Proceedings, Annual Conference Series, 279-286. Google Scholar
19. WESTERMANN, R., KOBBELT, L., AND ERTL, T. 1999. Real-time exploration of regular volume data by adaptive reconstruction of isosurfaces. 100-111.Google Scholar
20. WILHELMS, J., AND GELDER, A. V. 1992. Octrees for faster isosurface generation. 201-227. Google Scholar
21. WOOD, Z. J., DESBRUN, M., SCHRÖDER, P., AND BREEN, D. 2000. Semi-regular mesh extraction from volumes. In IEEE Visualization 2000, 275-282. Google Scholar