By William Martin Baker
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In algebraic topology a few classical invariants - comparable to Betti numbers and Reidemeister torsion - are outlined for compact areas and finite staff activities. they are often generalized utilizing von Neumann algebras and their strains, and utilized additionally to non-compact areas and limitless teams. those new L2-invariants comprise very fascinating and novel info and will be utilized to difficulties coming up in topology, K-Theory, differential geometry, non-commutative geometry and spectral concept.
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Additional info for Algebraic Geometry: A New Treatise On Analytical Conic Sections
In this paper, we detail two wavelet-based approaches for shape compression using spherical geometry images, and provide comparisons with previous compression schemes. 1 Introduction In previous work , we introduce a robust algorithm for spherical parametrisation, which smoothly maps a genus-zero surface to a sphere domain. This sphere domain can in turn be unfolded onto a square, to allow remeshing of surface geometry onto a regular 2D grid – a geometry image. One important use for such a representation is shape compression, the concise encoding of surface geometry.
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Geometry compression. Proc. ACM SIGGRAPH 1995, 13–20. 9. : Multiresolution analysis of arbitrary meshes. Proc. ACM SIGGRAPH 1995, 173–182. 10. : Simpliﬁcation and compression of 3D meshes. In Tutorials on Multiresolution in Geometric Modelling, A. Iske, E. Quak, M. S. ), Springer, 2002, pp. 319–361. 11. : Geometry images. Proc. ACM SIGGRAPH 2002, 355–361. 12. : Real time compression of triangle mesh connectivity. Proc. ACM SIGGRAPH 1998, 133–140. 13. : Normal meshes. Proc. ACM SIGGRAPH 2000, 95–102.