J. El-Sana and A. Varshney. Topology simplification for polygonal virtual environments. IEEE Trans. Visualization Comput. Graphics, 4:133--144, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... persistence of non bounding cycles is based on the incremental Betti number algorithm of Delfinado and Edelsbrunner [2] Three dimensional alpha shapes and complexes may be found in Edelsbrunner and Mucke [3] The problem of topological simplification was also ap1 proached by El Sana and Varshney [4] using alpha shape inspired ideas of geometric growth. There is a large body of parallel work on iso surfaces or level sets of 3 dimensional density functions. We refer to Milnor [7] for the mathematics and to Sethian [9] for a numerical view. A density function is a map F : R 3 R and an ....

....of probing an occupied slot of T. It triggers the addition of and i , which means we take the symmetric difference of the two collections. For example, the first collision for the filter of Figure 3 occurs for the negative edge sv. Initially, we have = fs; vg and i equal to 4, the index of v. T[4] is occupied and stores 4 = fu; vg. The sum of the two 0 cycles is 4 = fs; ug, which is the new set . We now have i = 2, the index of u. This time, T[2] is unoccupied and we store the index of sv and the new set in that slot. Correctness. We first show that cycle search halts. Consider a ....

J. El-Sana and A. Varshney. Topology simplification for polygonal virtual environments. IEEE Trans. Visualization Comput. Graphics, 4:133--144, 1998.

.... the simple Cubes dataset (first image) the MI output (second image) and the resulting model simplified by means of QSlim (third image) the results obtained by running QSlim directly on the Cubes dataset (fourth image) creation of non manifold parts) The algorithm by El Sana and Varshney [9] identifies and removes holes, protuberances or cavities by means of hulls, a concept very similar to the concept of shapes [8] in the reconstruction of surfaces from unorganized points. The algorithm is used together with a method (Simplification Envelopes [6] for the reduction of the ....

Jihad El-Sana and Amitabh Varshney. Topology simplification for polygonal virtual environments. IEEE Transactions on Visualization and Computer Graphics, 4(2):133--144, April 1998.

....The recent paper by Edelsbrunner et al. 11] considers topological simplification in the context of alpha complexes. It is worth noting that topological simplification of simplicial complexes in R 3 is a much harder and less intuitive problem than the one we consider. El Sana and Varshney [12][13] address a similar problem of controlled topology simplification for polygonal models. Their approach identifies removable tunnels by rolling a sphere of small radius over the object and filling the tunnels that are not accessible. The method performs well for mechanical CAD models. The ....

J. El-Sana and A. Varshney. Topology simplification for polygonal virtual environments. IEEE Transactions on Visualization and Computer Graphics, 4(2):133--144, June 1998.

.... persistence of nonbounding cycles is based on the incremental Betti number algorithm of Delfinado and Edelsbrunner [3] Threedimensional alpha shapes and complexes may be found in Edelsbrunner and Mucke [4] The problem of topological simplification was also approached by El Sana and Varshney [5] using alpha shape inspired ideas of geometric growth. There is a large body of parallel work on iso surfaces or level sets of 3 dimensional density functions. We refer to Milnor [7] for the mathematics and to Sethian [9] for the numerical computation background. A density function is a map F : ....

J. El-Sana and A. Varshney. Topology simplification for polygonal virtual environments. IEEE Trans. Visualization Comput. Graphics 4 (1998), 133--144.

.... persistence of non bounding cycles is based on the incremental Betti number algorithm of Delfinado and Edelsbrunner [2] Three dimensional alpha shapes and complexes may be found in Edelsbrunner and Mucke [3] The problem of topological simplification was also approached by El Sana and Varshney [4] using alpha shape inspired ideas of geometric growth. There is a large body of parallel work on iso surfaces or level sets of 3 dimensional density functions. We refer to Milnor [6] for the mathematics and to Sethian [8] for the numerical computation background. A density function is a map F : ....

....of probing an occupied slot of T. It triggers the addition of and i , which means we take the symmetric difference of the two collections. For example, the first collision for the filter of Figure 3 occurs for the negative edge sv. Initially, we have = fs; vg and i equal to 4, the index of v. T[4] is occupied and stores 4 = fu; vg. The sum of the two 0 cycles is 4 = fs; ug, which is the new set . We now have i = 2, the index of u. This time, T[2] is unoccupied and we store the index of sv and the new set in that slot. Symmetry can be used to check the results of our ....

J. El-Sana and A. Varshney. Topology simplification for polygonal virtual environments. IEEE Trans. Visualization Comput. Graphics, 4:133--144, 1998.

....but the control over such changes is relatively limited and the hierarchies created by these methods are unsuitable for many purposes, for example, it may be difficult or impossible to parameterize finer levels of hierarchies over the coarse levels. The recent work of El Sana and Varshney [ESV98] based on alpha shapes [EM94] aims to perform topological simplification in a more controlled manner. Qualitative Geometry and Multiscale Topology. For the final highlighted problem, we move from shape representation to shape analysis. Topological invariants (see Section 3.5) such as Betti ....

Jihad El-Sana and Amitabh Varshney. Topology simplification for polygonal virtual environments. IEEE Trans. Visualization and Computer Graphics, 4(2):133--144, April--June 1998.

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