Wavelets in the Geosciences pp 158-188 | Cite as
Spherical wavelets: Efficiently representing functions on a sphere
Chapter
First Online:
- 13 Citations
- 869 Downloads
Keywords
Wavelet Coefficient Scaling Function Subdivision Scheme Multiresolution Analysis Haar Wavelet
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Alfeld, P., Neamtu, M., and Schumaker, L. L. Bernstein-Bézier polynomials on circles, sphere, and sphere-like surfaces. Preprint.Google Scholar
- 2.Carnicer, J. M., Dahmen, W., and Peña, J. M. Local decompositions of refinable spaces. Tech. rep., Insitut für Geometrie und angewandete Mathematik, RWTH Aachen, 1994.Google Scholar
- 3.Certain, A., J. Popović, T. DeRose, T. Duchamp D. Salesin and Werner Stuetzle Interactive Multiresolution Surface Viewing Computer Graphics (SIGGRAPH '96 Proceedings) (1996), 91–98Google Scholar
- 4.Christensen, P. H., Stollnitz, E. J., Salesin, D. H., and DeRose, T. D. Wavelet Radiance. In Proceedings of the 5th Eurographics Workshop on Rendering, 287–302, June 1994.Google Scholar
- 5.Cohen, A., Daubechies, I., and Feauveau, J. Bi-orthogonal bases of compactly supported wavelets. Comm. Pure Appl. Math. 45 (1992), 485–560.Google Scholar
- 6.Cohen, A., Daubechies, I., Jawerth, B., and Vial, P. Multiresolution analysis, wavelets and fast algorithms on an interval. C. R. Acad. Sci. Paris Sér. I Math. I, 316 (1993), 417–421.Google Scholar
- 7.Dahlke, S., Dahmen, W., Schmitt, E., and Weinreich, I. Multiresolution analysis and wavelets on S2 and S3. Tech. Rep. 104, Institut für Geometrie und angewandete Mathematik, RWTH Aachen, 1994.Google Scholar
- 8.Dahmen, W. Stability of multiscale transformations. Tech. rep., Institut für Geometrie und angewandete Mathematik, RWTH Aachen, 1994.Google Scholar
- 9.Dahmen, W., Prössdorf, S., and Schneider, R. Multiscale methods for pseudo-differential equations on smooth manifolds. In Conference on Wavelets: Theory, Algorithms, and Applications, C. K. C. et al., Ed. Academic Press, San Diego, CA, 1994, pp. 385–424.Google Scholar
- 10.Daubechies, I. Ten Lectures on Wavelets. CBMS-NSF Regional Conf. Series in Appl. Math., Vol. 61. Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992.Google Scholar
- 11.Dutton, G. Locational Properties of Quaternary Triangular Meshes. In Proceedings of the Fourth International Symposium on Spatial Data Handling, 901–910, July 1990.Google Scholar
- 12.Dyn, N., Levin, D., and Gregory, J. A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control. Transactions on Graphics 9, 2 (April 1990), 160–169.Google Scholar
- 13.Fekete, G. Rendering and Managing Spherical Data with Sphere Quadtrees. In Proceedings of Visualization 90, 1990.Google Scholar
- 14.Freeden, W., and Windheuser, U. Spherical Wavelet Transform and its Discretization. Tech. Rep. 125, Universität Kaiserslautern, Fachbereich Mathematik, 1994.Google Scholar
- 15.Girardi, M., and Sweldens, W. A new class of unbalanced Haar wavelets that form an unconditional basis for Lp on general measure spaces. Tech. Rep. 1995:2, Industrial Mathematics Initiative, Department of Mathematics, University of South Carolina, 1995. (ftp://ftp.math.scarolina.edu/pub/imi_95/imi95_2.ps).Google Scholar
- 16.Gondek, J. S., Meyer, G. W., and Newman, J. G. Wavelength Dependent Reflectance Functions. In Computer Graphics Proceedings, Annual Conference Series, 213–220, 1994.Google Scholar
- 17.Gortler, S., Schröder, P., Cohen, M., and Hanrahan, P. Wavelet Radiosity. In Computer Graphics Proceedings, Annual Conference Series, 221–230, August 1993.Google Scholar
- 18.Gortler, S. J., and Cohen, M. F. Hierarchical and Variational Geometric Modeling with Wavelets. In Proceedings Symposium on Interactive 3D Graphics, 35–42, April 1995.Google Scholar
- 19.Lee A., W. Sweldens, P. Schröder, L. Cowsar and D. Dobkin MAPS: Multiresolution Adaptive Parameterization of Surfaces Computer Graphics (SIGGRAPH '98 Proceedings), 95–104, 1998Google Scholar
- 20.Liu, Z., Gortler, S. J., and Cohen, M. F. Hierarchical Spacetime Control. Computer Graphics Proceedings, Annual Conference Series, 35–42, July 1994.Google Scholar
- 21.Lounsbery, M. Multiresolution Analysis for Surfaces of Arbitrary Topological Type. PhD thesis, University of Washington, 1994.Google Scholar
- 22.Lounsbery, M., DeRose, T. D., and Warren, J. Multiresolution Surfaces of Arbitrary Topological Type. Department of Computer Science and Engineering 93-10-05, University of Washington, October 1993. Updated version available as 93-10-05b, January, 1994.Google Scholar
- 23.Mitrea, M. Singular integrals, Hardy spaces and Clifford wavelets. No. 1575 in Lecture Notes in Math. 1994.Google Scholar
- 24.Nielson, G. M. Scattered Data Modeling. IEEE Computer Graphics and Applications 13, 1 (January 1993), 60–70.Google Scholar
- 25.Schlick, C. A customizable reflectance model for everyday rendering. In Fourth Eurographics Workshop on Rendering, 73–83, June 1993.Google Scholar
- 26.Schröder, P., and Hanrahan, P. Wavelet Methods for Radiance Computations. In Proceedings 5th Eurographics Workshop on Rendering, June 1994.Google Scholar
- 27.Schröder, P., and Sweldens, W. Spherical wavelets: Texture processing. Tech. Rep. 1995:4, Industrial Mathematics Initiative, Department of Mathematics, University of South Carolina, 1995. (ftp://ftp.math.scarolina.edu/pub/imi_95/imi95_4.ps).Google Scholar
- 28.Sillion, F. X., Arvo, J. R., Westin, S. H., and Greenberg, D. P. A global illumination solution for general reflectance distributions. Computer Graphics (SIGGRAPH '91 Proceedings), Vol. 25, No. 4, pp. 187–196, July 1991.Google Scholar
- 29.Sweldens, W. The lifting scheme: A construction of second generation wavelets. Department of Mathematics, University of South Carolina.Google Scholar
- 30.Sweldens, W. The lifting scheme: A custom-design construction of biorthogonal wavelets. Tech. Rep. 1994:7, Industrial Mathematics Initiative, Department of Mathematics, University of South Carolina, 1994. (ftp://ftp.math.scarolina.edu/pub/imi_94/imi94_7.ps).Google Scholar
- 31.Westerman, R. A Multiresolution Framework for Volume Rendering. In Proceedings ACM Workshop on Volume Visualization, 51–58, October 1994.Google Scholar
- 32.Westin, S. H., Arvo, J. R., and Torrance, K. E. Predicting reflectance functions from complex surfaces. Computer Graphics (SIGGRAPH '92 Proceedings), Vol. 26, No. 2, pp. 255–264, July 1992.Google Scholar
Copyright information
© Springer-Verlag 2000