Visualization of Volume Data with Quadratic Super Splines

Proceedings of the IEEE Visualization Conference

Volumn , Issue , 2003, Pages 393-400

  Rössl, Christian ^a   Zeilfelder, Frank ^b   Nürnberger, Günther ^b   Seidel, Hans Peter ^a  

^a MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

^b UNIVERSITY OF MANNHEIM   (Germany)

Author keywords

Bernstein B zier techniques; Isosurface rendering; Quadratic super splines; Ray casting; Reconstruction; Tetrahedral partition; Volume rendering

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; DATA PROCESSING; INTERPOLATION; JOINTS (ANATOMY); POLYNOMIALS; RAY TRACING;

QUADRATIC SUPERSPLINES; VOLUME RENDERING;

IMAGE PROCESSING;

EID: 0242507600     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (44)

1. BAJAJ, C., BERNARDINI, F., AND XU, G. 1995. Automatic reconstruction of surfaces and scalar fields from 3D scans. In SIGGRAPH'95, 109-118.
2. BAJAJ, C. 1997. Implicit Surface Patches. In Introduction to Implicit Surfaces, Morgan Kaufmann, J. Bloomenthal, Ed., 99-125.
3. BAJAJ, C. 1999. Data Visualization Techniques. John Wiley & Sons.
4. BARTHE, L., MORA, B., DODGSON, N., AND SABIN, M. 2002. Triquadratic reconstruction for interactive modelling of potential fields. In Shape Modeling International 2002, 145-153.
5. BONNEAU, G.-P., HAHMANN, S., AND NIELSON, G. 1996. BLaC-Wavelets: A multiresolution analysis with non-nested spaces. In IEEE Visualization 1996, 43-48.
6. BRODLIE, K., AND WOOD, J. 2001. Recent Advances in Volume Visualization. Computer Graphics Forum 20, 2, 125-148.
7. CARR, H., MÖLLER, T., AND SNOEYINK, J. 2001. Simplicial subdivisions and sampling artifacts. In IEEE Visualization 2001, 99-106.
8. CHEN, M., KAUFMAN, A., AND YAGEL, R. 2000. Volume Graphics. Springer.
9. CHUI, C. 1988. Multivariate Splines. CBMS 54, SIAM.
10. DAHMEN, W., AND THAMM-SCHAAR, T.-M. 1993. Cubicoids: modeling and visualization. Computer Aided Geometric Design 10, 2, 89-108.
11. DAHMEN, W. 1989. Smooth piecewise quadric surfaces. In Math. Methods in CAGD, Academic Press, T. Lyche and L. Schumaker, Eds., 181-194.
12. DAVYDOV, O., AND ZEILFELDER, F. 2003. Scattered data fitting by direct extension of local polynomials with bivariate splines. Adv. Comp. Math. to appear.
13. DE BOOR, C. 1987. B-form basics. In Geometric Modelling, SIAM, G. Farin, Ed., 131-148.
14. DE CASTELJAU, P. 1963. Courbes et surfaces à poles. André Citroën, Automobiles SA, Paris.
15. FARIN, G. 1986. Triangular Bernstein-Bézier patches. CAGD 3, 2, 83-127.
16. GERSTNER, T., AND RUMPF, M. 2000. Multiresolutional Parallel Isosurface Extraction based on Tetrahedral Bisection. In Volume Graphics, Springer, M. Chen, A. Kaufman, and R. Yagel, Eds., 267-278.
17. GROSSO, R., LÜRIG, C., AND ERTL, T. 1997. The multilevel finite element method for adaptive mesh optimization and visualization of volume data. In IEEE Visualization 1997, 387-394.
18. HABER, J., ZEILFELDER, F., DAVYDOV, O., AND SEIDEL, H.-P. 2001. Smooth approximation and rendering of large scattered data sets. In IEEE Visualization 2001, 341-347.
19. 1 splines of arbitrary degree on a tetrahedral partition. (preprint).
20. HOLLIDAY, D., AND NIELSON, G. 2000. Progressive volume models for rectilinear data using tetrahedral Coons volumes. In Data Visualization 2000, Springer, 83-92.
21. HOSCHEK, J., AND LASSER, D. 1993. Fundamentals of Computer Aided Geometric Design. A.K. Peters.
22. KAUFMAN, A. 2000. State-of-the-art in volume graphics. In Volume Graphics, Springer, M. Chen, A. Kaufman, and R.Yagel, Eds., 3-28.
23. KOHLMÜLLER, N., G. NÜRNBERGER, AND ZEILFELDER, F. 2003. Construction of cubic 3D spline surfaces by Lagrange interpolation at selected points. In Curve and Surface Fitting, Saint-Malo 2002, 245-254.
24. 1 spline. Adv. Comp. Math. to appear.
25. LAMAR, E., HAMANN, B., AND JOY, K. 1999. High-quality rendering of smooth isosurfaces. Journal of Visualization and Computer Animation 10(2), 79-90.
26. LORENSEN, W., AND CLINE, H. 1987. Marching cubes: A high resolution 3D surface construction algorithm. SIGGRAPH'87 21, 5, 79-86.
27. MARSCHNER, S., AND LOBB, R. 1994. An evaluation of reconstruction filters for volume rendering. In IEEE Visualization 1994, 100-107.
28. MARTIN, W., AND COHEN, E. 2001. Representation and extraction of volumetric attributes using trivariate splines: a mathematical framework. In Solid Modelling and Applications 2001, 234-240.
29. MEISSNER, M., HUANG, J., BARTZ, D., MUELLER, K., AND CRAWFIS, R. 2000. A practical comparison of popular volume rendering algorithms. In Symposium on Volume Visualization and Graphics 2000, 81-90.
30. MITCHELL, D., AND NETRAVALI, A. 1988. Reconstruction filters in computer graphics. SIGGRAPH'88, 221-228.
31. MÖLLER, T., MUELLER, K., KURZION, Y., MACHIRAJU, R., AND YAGEL, R. 1998. Design of accurate and smooth filters for function and derivative reconstruction. In Symposium on Volume Visualization 1998, 143-151.
32. MORA, B., JESSEL, J.-P., AND CAUBET, R. 2001. Visualization of isosurfaces with parametric cubes. In Eurographics 2001, 377-384.
33. NIELSON, G. 2000. Volume modelling. In Volume Graphics, Springer, M. Chen, A. Kaufman, and R.Yagel, Eds., 29-50.
34. NÜRNBERGER, G., AND ZEILFELDER, F. 2000. Developments inbivariate spline interpolation. J. Comput. Appl. Math. 121, 125-152.
35. 1-splines with optimal approximation order. Adv. Comp. Math. to appear.
36. NÜRNBERGER, G., RÖSSL, C., SEIDEL, H.-P., AND ZEILFELDER, F. 2003. The smoothness and approximation properties of piecewise quadratic quasi-interpolants in three variables. (preprint).
37. 1 cubic splines on triangulated quadrangulations. Adv. Comp. Math. to appear.
38. PARKER, S., SHIRLEY, P., LIVNAT, Y., HANSEN, C., AND SLOAN, P.-P. 1998. Interactive ray tracing for isosurface rendering. In IEEE Visualization 1998, 233-238.
39. PRAUTZSCH, H., BOEHM, W., AND PALUSZNY, M. 2002. Bézier and B-Spline Techniques. Springer.
40. SCHUMAKER, L., AND SOROKINA, T. 2003. Quintic spline interpolation on type-4 tetrahedral partitions. Adv. Comput. Math. to appear.
41. SCHWARZE, J. 1990. Cubic and quartic roots. In Graphics Gems, A. Glassner, Ed. Academic Press, 404-407.
42. THEUSSL, T., MÖLLER, T., HLADUVKA, J., AND GRÖLLER, M. 2003. Reconstruction issues in volume visualization. In Data Visualization: The State of the Art, F. Post, H. B., and G.-P. Bonneau, Eds., 109-126.
43. THÉVENAZ, P., AND UNSER, M. 2001. High-quality isosurface rendering with exact gradients. In ICIP'01, 854-857.
44. WALD, I., AND SLUSALLEK, P. 2001. State of the art in interactive ray tracing. In STAR, EUROGRAPHICS 2001. 21-42.