J. COHEN, A. VARSHNEY, ET. AL., Simplification envelopes, SIGGRAPH 96 (1996) 119-128.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....and simplified models [15] global or local, and geometry only or geometry with attributes. Local error metric estimates error using local geometric information. Most decimation methods use this metric [17, 14] Global error metric gives error bound that applies globally. Simplification envelope [3] makes two offset surfaces from the given model, and samples triangles that exist between them. Clustering [16] and superface [13] also use global error metric. Many simplification methods use geometric information for their error metric. QEM[8] uses Euclidean distance between a face and a point ....

....with geometric attributes, not any smooth approximation. 2] Discrete curvature error metric is based on discrete curvature so that LOD can be generated precisely, and controlled efficiently. Also it can be used a global error metric, and increase the accuracy of each level s simplified model. [3] We suggest that LOD should be generated by not a simplification ratio but an error metric. Error metric based on discrete curvature can generate the LOD meshes which are recognizable explicitly with each level and preserve overall appearance of its original model. 3 Definitions Surface should ....

J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. Brooks, and W. Wright. Simplification Envelopes. Computer Graphics(SIGGRAPH '96 Proceedings), pages 11912.

....desirable. Even guaranteeing that the common edge contraction operator The different knot classifications of BA are indicated. 3 produces an object homeomorphic to its input requires some care for simplicial complexes [18] Preservation of genus during approximation by a polygonal mesh [16] also requires considerable care. The theorem presented here proves an approximation technique which preserves ambient isotopy over an important sub class of 2 manifolds. 3 Related Work Throughout the article, for any integer CED , the notation F will refer to a function (or manifold) ....

Cohen, J., Varshney, A., Manocha, D., Turk, G., Weber, H., Agarwal, P., Brooks, F., Jr., and Wright, W., Simplification envelopes, Proceedings of ACM SIGGRAPH '96, 119 - 128.

....are narrow in scope. Some of the few are polynomial time algorithms to find approximations to height fields or convex polytopes that are within a factor of optimal [1] For surfaces more general than height fields and convex polytopes, there are simplification algorithms with bounded error (e.g. [4]) but the number of triangles in their approximations are not bounded, so such algorithms are not optimal in a strong sense. The authors are not aware of any polynomial time algorithms that generate approximations to general surfaces that are provably good in both error and number of triangles. ....

J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. Brooks, W. Wright, Simplification envelopes, in: SIGGRAPH '96 Proc., August 1996, pp. 119--128, http://www.cs.unc.edu/geom/envelope.html.

....Thus, LOD management is sometimes referred to as contribution culling. Several level of detail approaches have been used in the various walkthrough systems. Some systems use several static levels of detail, usually 3 10, which are constructed off line using various simplification techniques [25,36,44,70,81]. Then at real time, an appropriate level of detail is selected based on various criteria such as distance from the user s viewpoint and screen space projection. Other systems use a multi resolution hierarchy, which encodes all the levels of detail, and is constructed off line [31, 37,50,51,64, ....

J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. P. Brooks, Jr., and W. V. Wright. Simplification Envelopes. Proceedings of SIGGRAPH '96 (New Orleans, LA, August 4--9, 1996.

....[16] adaptive displays [14] and Hierarchical Occlusion Maps [29] fall into this category. It is also possible to coarsen or refine the model itself as it is being viewed. Progressive and view dependent meshes [19, 20] multiresolution meshes based on subdivisions [17] wavelets [4] and others [8, 13, 15, 26, 12] are examples of this approach. Most of the computation during rendering a mesh is devoted to rasterizing polygons. Consequently, efforts have focused on replacing them with easier primitives such as points that can be rendered as pixels. This has led to intense research on point cloud ....

J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. Brooks and W. Wright. Simplification envelopes. Proc. SIGGRAPH 96, (1996), 119--128.

....static triangulation of models. A one time static tessellation (in sufficient detail) of many real world models, would require hundreds of million of tri supported in part by NSF CAREER award CCR 9733827 and ERC award EEC 9731748 angles [2] Schemes based on view dependent mesh simplification [7, 34, 14, 15, 9] are commonly used to improve the rendering speed on any given graphics system. Typically, these require management of large amounts of data and are still unable to generate more detail than the initial tessellation. Note that these methods first generate a large number of triangles and ....

J. Cohen, A. Varshney, D. Manocha, and G. Turk et al. Simplification envelopes. In Proc. ACM SIGGRAPH, pages 119--128, 1996.

....However, coming up with realistic virtual humans or actors still remains a challenge. Realistic virtual humans (and Avatars) are as important as the virtual environment they reside in. This has been one of the main goals of most Virtual Reality systems. Numerous methods of real time rendering [6,7,8], natural ways for interaction and communication [9] and providing virtual characters with intelligence [10,11] are related techniques for presenting true complexity and realism to all aspects of Virtual Environments. For many years it has been possible to visit virtual worlds using a real time ....

J. Cohen, A. Varshney, D. Manocha, G. Turk and H. Weber, Simplification Envelopes, Proc. SIGGRAPH '96, 1996, pp. 119-128.

....are based on the edge contract operation, which has received attention in the computer graphics community. Hoppe [9, 8] made extensive use of the edge contract operation (unfortunately calling it edge collapse [5] for topology preserving mesh simplification and others followed his approach [2, 6, 20]. But we are not aware of any encoding technique that uses the edge contract op eration for efficient mesh topology compression. For compressing meshes that are not composed of triangles little work has been reported. In the next section we will define what triangle meshes are, as their ....

J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. P. Brooks, and W. V. Wright. Simplification envelopes. In SIGGRAPH'96 Conference Proceedings, pages 119-128, 1996.

....coming up with realistic virtual humans or actors still remains a challenge. Realistic virtual humans are important just as presenting realism is important in Virtual Environments. This has been the main goal of most of the Virtual Reality systems. Numerous methods of real time rendering[6][7] 8] natural way of interaction and communication[9] and providing virtual characters with intelligence[10] 11] are related techniques for presenting true complexity and realism to all aspects of Virtual Environments. We have put considerable efforts to develop and integrate several modules ....

J. Cohen, A. Varshney, D. Manocha, G. Turk and H. Weber, "Simplification Envelopes", Proc. of ACM SIGGRAPH '96, pp.119-128.

....none of which showed this configuration. These operations can be useful in a range of geometric operations of interest to computer graphics and image analysis. Some examples: Dilation could be used to compute the envelope of an object during simplification in algorithms such as that presented in [21]. Dilation and erosion can be used to compute the medial axis of an object, as described in [11] The solvent accessible surface for proteins, an important surface in molecular graphics, is equivalent to the morphological closing of the protein with a sphere of appropriate radius. 6. FUTURE ....

Cohen, J., et al. Simplification Envelopes.inProceedings of SIGGRAPH '96. 1996. New Orleans, LA.

....references are given in [2] 6] Of special interest is Kreylos and Hamann [4] since they use a method closely related to the one presented here. Using a min # approximation approach, one tries to find an approximation with the minimal number of vertices that satisfies a tolerance condition [1]. This approach is relevant for scientific applications. For example, given the size of an object and the view point distance, one can compute the error tolerance related to one pixel on the screen. Approximating the object within this tolerance results in a picture where each data point is no ....

....Our algorithm ensures that no point of the approximating surface deviates more than # from the original surface. This requires us to consider an offset around the original surface, and the approximation surface must stay inside this offset. Such an approach was first proposed by Cohen et al. [1] and was, called simplifiction envelope. A simplification envelope is a linearized and, in some respects, simplified version of the exact offset. 2.2 Simplification Envelopes The simplification envelope of a triangulated surface is constructed in the following way: For each vertex, one computes ....

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J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. Brooks, W. Wright. Simplification Envelopes. Proceedings SIGGRAPH 1996 pp. 119-128.

....caused due to surface attributes (colors, texture, normals, Thus, more complete algorithms are needed to manage mesh attributes during the simplification process. Hoppe [9] uses energy functions, which preserve surface geometry, scalar attributes and discontinuity curves. Cohen et al.[10] use no error measure but only a geometric construction, called simplification envelopes, to minimize the surface deviation. Garland et al. 11, 12] use a quadric error metric giving vertex to plane distances; this metric works for meshes with attributes. Hoppe [13] has improved this technique for ....

J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. Books, and W. Wright, "Simplification envelopes," in Proceedings of SIGGRAPH, August 1996, pp. 119--128.

....every triangle Ti of the decimated mesh at any time maintains a list of original vertices belonging to the currently associated patch i. The Hausdorff distance is then evaluated by finding the most distant point in this list. A special technique for exact distance computation is suggested in [9], where two offset surfaces to the original mesh are computed to bound the space where the decimated mesh should remain. Fairness criteria The distance measures can be used to decide which re moval operation among the candidates is legal and which is not (because it violates the global error ....

Cohen, J., Varshney, A., Manocha, D., Turk, G., Weber, H., Agarwal, P., Brooks, F., Wright, W. (1996) Simplification envelopes, Proc. ACM Siggraph'96, 119-128

....modeling techniques, then survey other related research on dynamics simplification. 2. 1 Model Simplification Model simplification algorithms, such as geometric level of detail and multi resolution modeling techniques, have been proposed to accelerate rendering of complex geometric models [6, 7, 16, 10, 23]. A recent survey on polygonal model simplification is available [18] Funkhouser and Sequin described a generic framework for selecting and switching between different geometric levels of detail (LODs) to attain a nearly constant frame rate for real time walkthrough of architectural buildings ....

J. Cohen, A. Varshney, D. Manocha, and G. Turk et al. Simplification envelopes. In Proc. of ACM Siggraph'96, pages 119--128, 1996.

....the resulting mesh is at least as good as the work in [Hoppe et al. 93] or even better. The idea of building a simplification hierarchy was also proposed and used widely later for other work, including its generalization to tetrahedral grid simplification. Simplification Envelope Cohen et al. Cohen et al. 96] proposed to construct a simplification envelope to guarantee the difference between the approximation and the original is always within a user specified e, and the simplification is done within that envelope. View Dependent and Out of Core Simplification In addition to the general ideas about ....

J. Cohen, A. Varshney, D. Manocha, G. Turk, and H. Webber. Simplification Envelopes. In SICGRAPH '96, pages 119 128, August 1996.

....To offset the STL model of the part, one can offset each facet with a given offset distance along their normal direction. However, this could result in intersections or gaps among the offset segments. Finding all the intersections or filling the gaps for these 3D surfaces is not an easy job [4]. Also using the facet normals for offsetting may not capture original CAD model representation. In our earlier work presented in [6] the averaged normal vector method is used to offset each vertex with the corrected normal direction. An offset normal vector at a vertex is calculated by ....

Cohen, J., Varshney, A., Manocha., D., Turk, G., Weber, H., Agarwal, P., Brooks, F., Wright, W., 1996, "Simplification Envelopes," Computer Graphics Proc., ACM ACM SIGGRAP 119-128.

....can be exploited to efficiently measure a 3D distance in a subsequent simplification algorithm. A large number of simplification algorithms for triangle meshes have been developed, but only a part of them can guarantee a certain geometric approximation error between simplified and original mesh [19, 5]. However, this error must be known to guarantee a certain quality of the rendered images of the simplified model. Unfortunately, the simplification algorithms with this feature are very slow (see [4] for a comparison) or produce over estimations of the error [29, 9] that make the results not ....

....we can interpolate between them using the fractional part of the z value. In this way the distance from the zero set of the distance field (the original surface) is determined with higher accuracy. Using this way of distance calculation the drawback of the simplification envelopes algorithm [5] of having a fixed envelop and therefore not being able to build up a reasonable multiresolution model is avoided. 6.3 Acceleration of distance computation For errors larger than one pixel in the plane defined by the principal direction of the triangle the read out of the distance values can be ....

J. Cohen, A. Varshney, D. Manocha, and G. Turk. Simplification envelopes. Computer Graphics, 30(Annual Conference Series):119--128, 1996.

....is therefore still necessary. 1. 2 Simplification algorithms and multiresolution models A large number of simplification algorithms for triangle meshes have been developed, but only a part of them can guarantee a certain geometric approximation error between simplified and original mesh [16, 6]. However, this error must be known to guarantee a certain quality of the rendered images of the simplified model. Unfortunately, the simplification algorithms with this feature are very slow (see [5] for a comparison) or produce over estimations of the error [25, 9] that make the results useless ....

....by drawing l i using a Bresenham algorithm, see Figure 8. To obtain the error we searched for, the maximum of the read values is multiplied with sin###; where # is the angle between the normal of # and the z direction, see Fig. 9. Note, that like in the simplification envelopes algorithm [6] also in our approach a one sided Hausdorff distance between original and simplified triangulation is measured. Therefore, if this distance is less a certain #, we guarantee that for every point p of the simplified triangulation we can find a point q on the original triangulation with d#p; q# # ....

[Article contains additional citation context not shown here]

J. Cohen, A. Varshney, D. Manocha, and G. Turk. Simplification envelopes. Computer Graphics, 30(Annual Conference Series):119--128, 1996.

....can be exploited to efficiently measure a 3D distance in a subsequent simplification algorithm. A large number of simplification algorithms for triangle meshes have been developed, but only a part of them can guarantee a certain geometric approximation error between simplified and original mesh [16, 5]. However, this error must be known to guarantee a certain quality of the rendered images of the simplified model. Unfortunately, the simplification algorithms with this feature are very slow (see [4] for a comparison) or produce over estimations of the error [24, 8] that make the results useless ....

....interpolate between them using the fractional part of the z value. In this way the distance from the zero set of the distance field (the original surface) is determined with much higher than pixel accuracy. Using this way distance calculation the drawback of the simplification envelopes algorithm [5] of having a fixed envelop and therefore not being able to build up a reasonable multiresolution model is avoided. 7.3 Acceleration of distance computation For errors larger than one pixel in the plane defined by the principal direction of the triangle the read out of the distance values can be ....

J. Cohen, A. Varshney, D. Manocha, and G. Turk. Simplification envelopes. Computer Graphics, 30(Annual Conference Series):119--128, 1996.

....and previous work Recently multiresolution modeling (MRM) for simplicial geometric models (any dimension, non orientable, nonmanifold, non regular) gain massive interest. Multiresolution models provide the basis to handle, visualize and transmit over the network and edit very large datasets [14, 2, 9, 1, 4, 5, 12, 13, 15]. The generation of a MRM of an object generally involves a sequence of local simplification operations like vertex removal, edge collapse, triangle collapse and vertex clustering. The sequence of local simplification operations defines a sequence of coarser and coarser approximations of the ....

J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. P. Brooks, Jr., and W. Wright. Simplification envelopes. In H. Rushmeier, editor, SIGGRAPH 96 Conference Proceedings, Annual Conference Series, pages 119-- 128. ACM SIGGRAPH, Addison Wesley, Aug. 1996.

....[Turk 1992] At the point in the planning process where occlusion is computed, accuracy may be sacrificed for speed by reducing the number of occluding polygons by merging nearby coplanar surface elements. In our implementation, we use a variant of Simplification Envelopes (SE) 84 described in [Cohen et al. 1996]. SE is a method that generalizes offset surfaces to determine an interior and exterior boundary between which the resulting decimated model must lie, and so has the desirable property of having an absolute bound e for the distance between the original surface and the simplified one. The distance ....

J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Webber, P. Agarwal, F. Brooks, and W. Wright. Simplification Envelopes, Proceedings of SIGGRAPH, pp. 119-128, 1996.

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COHEN J., VARSHNEY A., MANOCHA D., TURK G., WEBER H., AGARWAL P., BROOKS F., WRIGHT W.: Simplification envelopes. In Siggraph (1996), pp. 119--128. 9, 10

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J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. P. Brooks, Jr., and W. V. Wright. Simplification envelopes. In Proceedings of SIGGRAPH '96 (New Orleans, LA, August 4--9, 1996.

....algorithms, especially those which involve computing the roots of polynomials of degree greater than four, are quite sophisticated and have little practical value. Much work has been done on developing heuristics for clustering [27, 170, 180] shape analysis [117, 137, 164] surface simplification [75, 157, 194], and ray tracing [120, 223, 272] There are several other geometric optimization problems that are not discussed here. We conclude by mentioning two classes of such problems. The first one is the optimal motionplanning problem, where we are given a moving robot B, an environment with obstacles, ....

J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. P. Brooks, Jr., and W. V. Wright, Simplification envelopes, Proceedings of SIGGRAPH '96 (New Orleans, LA, August 4--9,

....generate its levels of detail. These include algorithms based on vertex clustering [RB93] vertex removal [BS96, SZL92, Tur92] and edge collapsing [HDD 93, Hop96, GH97, Gue95, CMO97, COM98, EM98a] They use different local and global error metrics for simplifying polygonal models. Cohen et al. CVMe96] and Eck et al. EDD 95] have presented algorithms that preserve the topology of the original object and give a global error bound on surface deviation. DLW93, EDD 95] have presented algorithms for multi resolution analysis for surfaces of arbitrary topology types. 4 Other simplification ....

J. Cohen, A. Varshney, D. Manocha, and G. Turk et al. Simplification envelopes. In Proc. of ACM Siggraph'96, pages 119--128, 1996.

....at each node [Clar76] The SGI s Performer toolkit [RH94] and IBM s BRUSH system [SBM 94] provided this capability. The BRUSH system used the LODs generated by a vertex clustering algorithm [RB93] that did not provide good error bounds on the quality of resulting approximations. Cohen et al. Cohe96] used LODs generated using the simplification envelopes algorithm and integrated them into the Performer framework. However, the resulting algorithm was unable to compute drastic simplifications of large environments. Erikson et al. EMB01] used a combination of LODs and HLODs computed using ....

Cohen, J., Varshney, A., Manocha, D., Turk, G., Weber, H., Agarwal, P., Brooks, F., and Wright, W. Simplification Envelopes. In Proc. of ACM SIGGRAPH, 119-128, 1996.

....these is the maximum error in the approximation [DeHaemer91] A refinement of this approach is to find the maximum deviation of any point in the new LOD from the original surface. This has been implemented as a quadric measurement in [Garland97 ] a geometric norm in [Schroeder92] Varshney94] and [Cohen96] as well as an energy term incorporating such geometric terms in [Hoppe93] Hoppe96] and [Popovic97] The problem with using a geometric measure to monitor similarities among models is that the actual goal for LODs is to produce simplified models that look similar to higherdetailed models. ....

....these new points are tessellated to create a new polygon mesh. Some algorithms select the new vertices all at the same time, as in [Turk92] and [Hoppe93] Others select new vertices iteratively, as in [Rossignac93] where several old vertices are replace by a single new one. The second method of [Cohen96] also adds new vertices by iteratively adding new triangles. One of the original methods of object simplification employed image based resampling to create texture LODs [Schachter81] In recent work, He et al. perform image based sampling to create new geometric LODs [He95] In their work, they ....

[Article contains additional citation context not shown here]

Cohen, Jonathan, Amitabh Varshney, Dinesh Manocha, Greg Turk, Hans Weber, Pankaj Agarwal, Frederick Brooks, William Wright, Simplification Envelopes, Proceedings SIGGRAPH 96,

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J. COHEN, A. VARSHNEY, ET. AL., Simplification envelopes, SIGGRAPH 96 (1996) 119-128.

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J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agrawal, F. Brooks, and W. Wright, "Simplification envelopes," in Proc. SIGGRAPH 96, August 1996, pp. 119--128.

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J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agrawal, F. Brooks, W. Wright, Simplification Envelopes, Proc .ACM Siggraph'96, pp. 119-128, August 1996.

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COHEN J., VARSHNEY A., MANOCHA D., TURK G., WEBER H., AGARWAL P., BROOKS F., WRIGHT W.: Simplification envelopes. In SIGGRAPH 1996 (1996), pp. 119--128. 2, 5

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Cohen,J. Varshney,A., Manocha,D., Turk,G. and Weber,H., "Simplification Envelopes", In Computer Graphics(Proc. SIGGRAPH '96), pp.119-128, ACM Press, 1996.

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Cohen, J., Varshney, A., Manocha, D., Turk, G., Weber, H., Agarwal, P., Brooks, F., Jr., and Wright, W., Simplification envelopes, Proceedings of ACM SIGGRAPH '96, 119 - 128.

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Cohen, J., Varshney, A., Manocha, D., Turk, G., Weber, H., Agarwal, P., Brooks, F., and Wright, W. (1996). Simplification Envelopes. In ACM Computer Graphics Proc., SIGGRAPH, NewOrleans, USA, pages 119---128.

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J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. Brooks, and W. Wright. Simplification envelopes. In SIGGRAPH, pages 119---128, 1996.

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J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. P. Brooks, Jr., and W. Wright. Simplification envelopes. In Proceedings of ACM SIGGRAPH 96, pages 119--128, 1996.

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J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwat, F. Brooks, and W. Wright, "Simplification envelopes," in Computer Graphics Proc.---Annu. Conf. Series, Aug. 1996, pp. 119--128.

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Cohen, J., Varshney, A., Manocha, D., Turk, G., Weber, H., Agarwal, P., Brooks, F., and Wright, W. Simplification envelopes. Computer Graphics (SIGGRAPH '96 Proceedings) (1996), 119--128.

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Cohen, J., Varshney, A., Manocha, D., Turk, G., Weber, H., Agarwal, P., Brooks, F. and Wright, W., Simplification envelopes. In Computer Graphics Proc., Annual Conf. Series (Siggraph '96). ACM Press.

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J. Cohen, A. Varshney, D. Manocha, and G. T. et al. Simplification envelopes. In Proc. of ACM Siggraph'96, pages 119--128, 1996.

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Cohen J., Varshney A., Manocha D., Turk G., Weber H., Agarwal P., Brooks F., Wright W, "Simplification Envelopes",., SIGGRAPH 1996, pp 119-128

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Cohen, J., Varshney, A., Manocha, D., Turk, G., Weber, H., Agarwal, P., Brooks, F., and Wright, W. Simplification envelopes. Computer Graphics (SIGGRAPH '96 Proceedings) (1996), 119--128.

No context found.

Cohen, J., Varshney, A., Manocha, D., Turk, G., Weber, H., Agarwal, P., Brooks, F. and Wright, W. Simplification envelopes. In Computer Graphics Proc., Annual Conf. Series (Siggraph '96). ACM Press,

No context found.

J. Cohen, A. Varshney, D. Manocha, G. Turk, etc. Simplification Envelopes. Proceedings of ACM SIGGRAPH 1996.

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J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. Brooks and W. Wright. Simplification envelopes. SIGGRAPH 96, (1996), 119--128.

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Cohen, J., Varshney, A., Manocha, D., Turk, G., Weber, H., Agarwal, P., Brooks, F., Jr., and Wright, W., Simplification envelopes, Proceedings of ACM SIGGRAPH '96, 119 - 128.

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J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. P. Brooks, Jr., and W. V. Wright. Simplification Envelopes. Proceedings of SIGGRAPH '96 (New Orleans, LA, August 4--9, 1996.

No context found.

J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. Brooks, and W. Wright. Simplification Envelopes. Proceedings of SIGGRAPH 96, 1996, 119-128.

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J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. Brooks and W. Wright . Simplification Envelopes . In ACM SIGGRAPH 96 Conference Proceedings, pages 11912.

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J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. P. Brooks Jr., and W. Wright. Simplification envelopes. In Proceedings of SIGGRAPH 96, ACM Computer Graphics Proceedings, Annual Conference Series, pages 119-- 128, August 1996.

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