A novel cubic-order algorithm for approximating principal direction vectors

ACM Transactions on Graphics

Volumn 23, Issue 1, 2004, Pages 45-63

  Goldfeather, Jack ^a   Interrante, Victoria ^b,c  

^a CARLETON COLLEGE   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

^c University of Minnesota   (United States)

Author keywords

3D shape; Principal directions

Indexed keywords

EXPERIMENTAL INVESTIGATIONS; PRINCIPAL DIRECTION VECTORS; PRINCIPAL DIRECTIONS;

ALGORITHMS; APPROXIMATION THEORY; ERROR ANALYSIS; MATHEMATICAL MODELS;

THREE DIMENSIONAL COMPUTER GRAPHICS;

EID: 12444259267     PISSN: 07300301     EISSN: 07300301     Source Type: Journal    
DOI: 10.1145/966131.966134     Document Type: Article

References (14)

1. CHEN, X. AND SCHMITT, F. 1992. Intrinsic surface properties from surface triangulation. In Proceedings, European Conference on Computer Vision. 739-743.
2. DIEWALD, U., PREUßER, T., AND RUMPF, M. 2000. Anisotropic diffusion in vector field visualization on euclidean domains and surfaces. IEEE Trans. Visual. Comput. Graph. 6, 1 (Apr/June), 139-149.
3. DUNCAN, B. AND OLSON, A. 1992. Shape analysis of protein surfaces. J. Mol. Graph. 10, 1 (Mar.), 50.
4. FLYNN, P. J. AND JAIN, A. K. 1989. On reliable curvature estimation. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 110-116.
5. GIRSHICK, A., INTERRANTE, V., HAKER, S., AND LEMOINE, T. 2000. Line direction matters: an argument for the use of principal directions in line drawings. In Proceedings of the 1st International Symposium on Non Photorealistic Animation and Rendering (Annecy), 43-52.
6. GORLA, G., INTERRANTE, V., AND SAPIRO, G. 2003. Texture synthesis for 3d shape representation. IEEE Trans. Visual. Comput. Graph. 9, 4 (Oct./Dec.), 512-524.
7. HAHMANN, S. 1999. Visualization techniques for surface analysis. In Advanced Visualization Techniques, C. Bajaj, Ed. Wiley, New York.
8. HAMANN, B. 1994. Curvature approximation of 3d manifolds in 4d space. Comput. Aid. Geomet. Des. 11, 6, 621-632.
9. HERTZMANN, A. AND ZORIN, D. 2000. Illustrating smooth surfaces. In Siggraph 2000, Computer Graphics Proceedings, K. Akeley, Ed. ACM Press/ACM SIGGRAPH/Addison Wesley Longman, 517-526.
10. INTERRANTE, V. L. 1997. Illustrating surface shape in volume data via principal direction-driven 3D line integral convolution. Comput. Graph. 31, Annual Conference Series, 109-116.
11. MEYER, M., DESBRUN, M., SCHRÖDER, P., AND BARR, A. H. 2003. Discrete differential-geometry operators for triangulated 2-manifolds. In Visualization and Mathematics III, H.-C. Hege and K. Polthier, Eds. Springer-Verlag, Heidelberg, Germany, 35-57.
12. SAMSON, P. AND MALLET, J.-L. 1997. Curvature analysis of triangulated surfaces in structural geology. Math. Geol. 29, 3 (Apr.), 391-412.
13. TAKASHI MAEKAWA, F.-E. W., AND PATRIKALAKIS, N. M. 1996. Umbilics and lines of curvature for shape interrogation. Comput. Aid. Geomet. Des. 13, 2 (Mar.), 133-161.
14. TAUBIN, G. 1995. Estimating the tensor of curvature of a surface from a polyhedral approximation. In Proceedings of the 5th International Conference on Computer Vision. 902-907.