N. Dyn, J. Gregory, and D. Levin, A butterfly subdivision scheme for surface interpolation with tension control,ACM Transactions on Graphics, 9 (1990), pp. 160--169. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
First 50 documents Next 50
Multivariate Refinable Hermite Interpolants - Han, Yu, Piper (2003) (Correct)
....#. Let # PS be the triangulation of based on barycentric subdivision of T i,j . Then # 2,#PS is exactly the refinable shift invariant subspace generated by #( #) Our next example is a C Hermite Butterfly Scheme , a vector version of the C Butterfly scheme by Dyn, Levin and Gregory [14]. Example 3.4 With G = D 6 , M = 2I 2 and ( 2, a D 6 symmetric Hermite interpolatory mask of order 1 reproducing # 4 is given by 0 1 2 1 2 25 32 25 64 1 8 11 64 9 64 0 0 7 64 1 32 0 77 256 0 9 64 13 128 0 0 1 16 , a( 1, 2) 1 64 ....
N. Dyn, D. Levin, and J. A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transaction on Graphics, 9(2), April 1990.
Towards a Ternary Interpolating Subdivision Scheme.. - Dodgson, Sabin.. (2002) (Correct)
....but this value of lies outside the range of values for which the scheme is C2. Again, it is not clear whether any useful conclusions can be drawn from the number of times that we can divide through by the box spline mask. 3 Bivariate binary subdivision The butterfly subdivision scheme [3] is an extension of the binary univariate subdivision scheme to the case of the triangular mesh. Figure 2 shows the stencil used to generate a new vertex s value in the regular case. It is necessary # # # # # # # # Figure 2: The non trivial stencil of the butterfly scheme in the regular ....
N. Dyn, D. Levin, and J. A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics, 9(2):160--169, 1990.
A Cascadic Geometric Filtering Approach to Subdivision - Diewald, Morigi, Rumpf (Correct)
....introduced by Hoppe et al. 16] incorporates sharp edges on the final limit surface. Since the ability to control the resulting surface exactly is very important in many applications, a number of interpolating schemes have been proposed to force the limit surface to interpolate particular points [10,11,18,33]. Dyn, Gregory and Levin [10] introduced the butterfly scheme, a simple interpolating subdivision algorithm applicable to arbitrary triangular meshes. Since it only leads to surfaces in the regular setting (all vertices of the mesh have valence 6) an improved butterfly scheme, the so called ....
N. Dyn, D. Levin, and J. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Trans. on Graphics, 9:160--169, 1990.
Polynomial Surfaces Interpolating Arbitrary Triangulations - Hahmann, Bonneau (2003) (Correct)
....why macro patch boundary curves and therefore the surface itself has unwanted undulations (see fig. 19) In comparison to these result let us also show in fig. 21 the result obtained with one of the two triangular interpolatory subdivision surface schemes: the butterfly subdivision scheme [5]. Again the shape of the surface is clearly not acceptable for this input mesh. Figure 15: left: regular mesh, right: deformed mesh. both meshes are shown with fiat shading and wire frame, they are open meshes. Figure 16: interpolation with arline map of tangents. Figure 17: interpolation with ....
Dyn N., Levin D., Gregory J.A., A butterfly subdivision scheme for surface interpolation with tension control, ACM Transactions on Graphics 9 (1990), 160 169.
3D Geometry Coding using Mixture Models and the Estimation . . . - Lavu (2002) (Correct)
....vertices do not change as we introduce new vertices at each new level. The new vertices introduced at each step are usually referred to as the odd vertices and the old vertices are usually referred to as the even vertices. The Loop subdivision scheme [10] and the butterfly subdivision scheme [11] are examples of approximating and interpolating subdivision schemes respectively. The modified butterfly subdivision scheme [12] is an improvement over the original butterfly scheme. Figure 2.5 and figure 2.6 show the rules used for the Loop and the modified butterfly subdivision schemes ....
Nira Dyn, David Levine, and John A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics (TOG), 9(2):160--169, 1990. 59
A Generative Classification of Mesh Refinement Rules.. - Ivrissimtzis.. (2002) (2 citations) (Correct)
....the added fractions in the coordinates of the point P 1 in the cases TD,QD,QM can be omitted as they convey no information. With this abbreviated notation the familiar Doo Sabin [5] scheme follows the refinement pattern QD(2,0) the Catmull Clark [2] is QP(2,0) the Loop [11] and the Butterfly [7] are TP(2,0) and the # 3 scheme is TP(1,1) Some further shortening of the noatation may be achieved with the unification of P and M cases in a more more compact but less instructive notation. 8 Conclusion We have presented a unified framework for the classification of regular mesh refinement ....
Nira Dyn, David Levin, and John A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics, 9(2):160--169, 1990.
Mass: Multiresolutional Adaptive Solid Subdivision - Chang (Correct)
....Scheme Figure 8: The subdivision masks for the Butterfly scheme. a) The regular mask. b) The boundary mask (the 4 point scheme) Dyn et al. 34, 37, 31, 36, 33] developed interpolatory subdivision curves and extended them to surface cases. They introduced an interpolatory subdivision scheme [35, 37] based on their interpolatory curves. The scheme is oftentimes called Butterfly scheme because of the shape of its neighbor mask. It is a face split and triangular based scheme. At level #,we introduce new edge point e by the following rule: e 1 2 1 ) 2w(p 3 ) 7 ) ....
....the convex polytopes as tiles. Archimedean tilings consist of regular polygons, in general. However, they are not isohedral tilings. We refer them as anisohedral tilings. For instance, the Catmull Clark scheme [19] is based on the [4 ] tiling and the Loop scheme [56] and the Butterfly scheme [35] are based on the [6 ] tiling on regular meshes. Kobbelt s # 3 subdivision scheme [51] produce the [3.12 ] tiling when it is applied once, and then it regenerate the finer [6 ] tiling at the second pass. Velho s 4 8 subdivision [93] is based on the regular [4.8 ] tiling. See Figure 12 ....
[Article contains additional citation context not shown here]
N. Dyn, D. Levin, and J. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics, 9(2):160--169, Apr. 1990.
Anisotropic Diffusion of Subdivision Surfaces and Functions on.. - Bajaj, Xu (2002) (2 citations) (Correct)
....mesh of the limit surface. Several subdivision schemes for generating smooth surfaces have been proposed. Some of them are interpolatory, i.e. the vertex positions of the coarse mesh are fixed, and only the newly added vertex positions need to be computed (see e.g. 18] for quadrilateral meshes, [10, 42] for triangular meshes) while others are approximatory (see e.g. 3, 9] for quadrilateral meshes, 19] for triangular meshes, 23] for general polyhedra) These approximatory subdivision schemes compute both the old and new vertex positions at each refinement step. Generally speaking, ....
Nira Dyn, David Levin, and John A. Gregory. A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control. ACM Transactions on Graphics, 9(2):16( 169, April 1990.
Adaptive Subdivision Schemes for Triangular Meshes - Amresh, Farin, Razdan (Correct)
....because it easily addresses the issues raised by multiresolution techniques to address the challenges raised for modeling complex geometry. The subdivision schemes introduced by Catmull and Clark[l] and Doo and Sabin[2] set the tone for other schemes to follow and schemes like Loop[6] Butterfly[3] and Modified Butterfly[14] Kobbelt [4] have become popular. These schemes are chiefly classified as either approximat ing, where the original vertices are not retained at newer levels of subdivision, or interpolating, where subdivision makes sure that the original vertices are carried over to ....
N. Dyn, J. Gregory, and D. Levin. A butterfly subdivision scheme for surface interpolation with tension control. ACM Trans. Graph., 9:160-169, 1990.
Refinement Operators for Triangle Meshes - Alexa (2002) (6 citations) (Correct)
....changed using a refinement operator, i.e. additional vertices and edges are inserted. Then, the mesh is smoothed, i.e. a geometry is attached to the vertices. Since convergence and surface properties mainly depend on the smoothing rules a lot of e#ort has been devoted to their design and analysis [1,7 9]. Refinement operators are also used in the context of remeshing (e.g. 4] Here, a regular connectivity mesh is generated bottom up by refining a coarse control mesh using the geometry given by a fine irregular mesh (or some other geometric structure) Until recently, subdivision and remeshing ....
.... (e.g. 4] Here, a regular connectivity mesh is generated bottom up by refining a coarse control mesh using the geometry given by a fine irregular mesh (or some other geometric structure) Until recently, subdivision and remeshing of triangles has almost exclusively used the 1 to 4 split [5,1]. Kobbelt s # 3 subdivision refines triangles by inserting a new vertex in the centroid of each triangle and then flip edges to generate a regular triangulation [2] Email address: alexa gris.informatik.tu darmstadt.de (Marc Alexa) Preprint submitted to CAGD Short Communication 29 October ....
N. Dyn, J. Gregory, D. Levin. A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control. ACM Trans. Graph. 9, pp. 160--169, 1990
A Layered Approach to Deformable Modeling and Animation - Chua, Neumann (Correct)
....alternatives can represent deformable objects, the rendering pipeline is optimized for triangular meshes. The deficiency of accurate modeling using meshes is compensated by the introduction of mesh refinement primitives such as Catmull Clark surfaces [15] and other surface interpolatory schemes [16, 17, 18, 19, 27]. The idea behind all of these methods is inserting new triangles or quadrilaterals based on a weighting of a local cluster of vertices. These techniques achieve smooth and continuous surfaces when recursively applied to the mesh. New techniques [23, 24] deal with two processes: controlling ....
N. Dyn, D. Levin, J. Gregory. A Butterfly subdivision scheme for surface interpolation with Tension Control. Transaction on Graphics Vol. 9, No. 2, April 1990, pp. 160- 169.
Filling N-sided holes using combined subdivision schemes - Levin Self-citation (Levin) (Correct)
....conditions. Subdivision schemes provide efficient algorithms for the design, representation and processing of smooth surfaces of arbitrary topological type. Their simplicity and their multiresolution structure make them attractive for applications in 3D surface modeling, and in computer graphics [7,9,11,13,19,27,28]. The subdivision scheme presented in this paper falls into the category of combined subdivision schemes [14,15,17,18] where the underlying surface is Saint Malo Proceedings 1 XXX, XXX, and Larry L. Schumaker (eds. pp. 1 8. Copyright o 2000 by Vanderbilt University Press, Nashville, TN. ....
N. Dyn, J. A. Greogory, and D. Levin. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics, 9:160--169, 1990.
Analyzing The Characteristic Map Of Triangular Subdivision.. - Georgum La Uf (Correct)
No context found.
N. Dyn, J. Gregory, and D. Levin, A butterfly subdivision scheme for surface interpolation with tension control,ACM Transactions on Graphics, 9 (1990), pp. 160--169.
Characteristics of Dual - Triangular Subdivision Dodgson (Correct)
No context found.
Dyn, N., D. Levin and J. A. Gregory, A butterfly subdivision scheme for surface interpolation with tension control, ACM Trans. on Graphics 9 (1990) 160--169.
Unknown - Subdivision Algorithm Hartmut (Correct)
No context found.
N. Dyn, J.D. Gregory, and D. Levin (1990). A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control. ACM Transactions on Graphics, 9(2):160--169.
Technical Report - Number Computer Laboratory (1993) (2 citations) (Correct)
No context found.
N. Dyn, D. Levin, and J. A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics, 9(2):160--169, 1990.
Grupo de Tratamiento de Imagenes - Dpto De Senales (Correct)
No context found.
N. Dyn, D. Levin, A Butterfly Subdivision Scheme for Surface Interpolartion with Tension Control, ACM Transcations on Graphics, Vol. 9, No. 2, pp. 160-169, April 1990
An Heuristic Analysis of the Classification of Bivariate.. - Dodgson (2005) (Correct)
No context found.
Dyn, N., Levin, D., Gregory, J.A.: A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics 9 (1990) 160-- 169
Compressing Volumes and Animations - Rossignac (2004) (Correct)
No context found.
N. Dyn, D. Levin, and J. A. Gregory, "A butterfly subdivision scheme for surface interpolation with tension control," ACM Transactions on Graphics, vol. 9, no. 2, pp. 160--169, 1990.
Bender: A Virtual Ribbon for Deforming 3D Shapes in.. - Llamas, Powell.. (2005) (Correct)
No context found.
N. Dyn, D. Levin, and J. A. Gregory. A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control. ACM Transactions on Graphics (TOG), 9(2), 1990.
Interpolatory Rank-1 Vector Subdivision Schemes - Costanza Conti And (Correct)
No context found.
N. Dyn, J. A. Gregory, and D. Levin. A butterfly subdivision scheme for surface interpolation. ACM Trans. Graphics, 9:160--169, 1990.
Curved PN Triangles - Alex Vlachos Jorg (2001) (9 citations) (Correct)
No context found.
Nira Dyn, David Levin, and John A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics, 9(2):160--169, April 1990.
Mean Square Error For Biorthogonal M-Channel Wavelet Coder - PAYAN, ANTONINI (2005) (Correct)
No context found.
N. Dyn, D. Levin, and J. Gregory, "A butterfly subdivision scheme for surface interpolation with tension control," ACM Transaction. on Graphics, vol. 9,2, pp. 160--169, 1990.
Interactive Display of Surfaces Using Subdivision.. - Duchaineau.. (2001) (1 citation) (Correct)
No context found.
Nira Dyn, David Levin, and John A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics, 9(2):160--169, April 1990.
Bicubic Subdivision-Surface Wavelets for Large-Scale .. - Bertram.. (2000) (5 citations) (Correct)
No context found.
N. Dyn, D. Levin, and J.A. Gregory, A butterfly subdivision scheme for surface interpolation with tension control,ACM 169.
Modeling Images of Natural 3D Surfaces: Overview and.. - Jalobeanu, Kuehnel.. (Correct)
No context found.
N. Dyn, J. Gregory, and D. Levin, "A butterfly subdivision scheme for surface interpolation with tension control," ACM Trans. Graph., vol. 9, pp. 160--169, 1990.
Multiresolution Analysis for Surfaces of Arbitrary.. - Lounsbery, Derose, Warren (1997) (151 citations) (Correct)
No context found.
DYN, N., LEVIN, D., AND GREGORY, J. 1990. A butterfly subdivision scheme for surface interpolation with tension control. ACM Trans. Graph. 9, 2, (April) 160--169.
Subdivision Interpolating Implicit Surfaces - Jin, Sun, Peng (2003) (Correct)
No context found.
Dyn N, Gregory J, Levin D. Butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics 1990;9(2):160--9.
Models for Character Animation - Gordon Collins And (Correct)
No context found.
Nira Dyn, David Levin, and John A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics, 9(2):160--169, April 1990. ISSN 0730-0301.
Subdivision Models in a Freeform Sketching System - Wai Kit Addy (Correct)
No context found.
Nira Dyn, David Levin, and John A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics, 9(2):160--169, 1990.
Graphics Hardware (2003) - Doggett Heidrich Mark (Correct)
No context found.
Nira Dyn, David Levine, and John A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics (TOG), 9(2):160--169, 1990.
Characteristics of Dual - Triangular Subdivision Dodgson (Correct)
No context found.
Dyn, N., D. Levin and J. A. Gregory, A butterfly subdivision scheme for surface interpolation with tension control, ACM Trans. on Graphics 9 (1990) 160--169.
Compression of Normal Meshes - Andrei Khodakovsky And (2003) (3 citations) (Correct)
No context found.
DYN, N., LEVIN, D., AND GREGORY, J. A. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics 9, 2 (1990), 160--169.
Fractal 3D Modeling of Asteroids Using Wavelets on Arbitrary.. - Jalobeanu (Correct)
No context found.
N. Dyn, J. Gregory, and D. Levin. A butterfly subdivision scheme for surface interpolation with tension control. ACM Trans. Graph., 9:160--169, 1990.
Time Critical Isosurface Refinement and Smoothing - Pascucci, Bajaj (2000) (1 citation) (Correct)
No context found.
N. Dyn, D. Levin, and J. A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Trans. on Graphics, 9(2):160--169, 1990.
Real-Time Dynamic Wrinkles - Larboulette, Cani (2004) (Correct)
No context found.
N. Dyn, D. Levine, and J. A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics, 9(2):160--169, Apr. 1990.
Surface Simplification and 3D Geometry Compression - Rossignac (Correct)
No context found.
N. Dyn, D. Levin, and J. A. Gregory, A butterfly subdivision scheme for surface interpolation with tension control. ACM Trans. Graph., volume 9, no. 2, pages 160-- 169, 1990.
Interactive Rendering of Translucent Deformable Objects - Mertens, Kautz, Bekaert, .. (2003) (1 citation) (Correct)
No context found.
Nira Dyn, David Levin, and John A. Gregory. A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control. ACM Transactions on Graphics, 9(2):160--169, April 1990.
A Meshing Scheme for Memory Efficient Adaptive.. - Amor, Boo.. (2000) (Correct)
No context found.
N. Dyn, D. Levin, J.A. Gregory, A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control, ACM Trans. on Graphics, vol. 9, no. 2, pp. 160-169, 1990.
Multiresolution Mesh Representation: Models and Data Structures - De Floriani, Magillo (2002) (Correct)
No context found.
N. Dyn, D. Levin, and J.A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Trans. on Graphics 9(2), 1990, 160--169.
Non-Interpolatory Hermite Subdivision Schemes - Han, Yu, Xue (2003) (Correct)
No context found.
N. Dyn, D. Levin, and J. A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transaction on Graphics, 9(2), April 1990.
Multidimensional Interpolatory Subdivision Schemes - Riemenschneider, Shen (1996) (25 citations) (Correct)
No context found.
N. Dyn, J. A. Gregory and D. Levin, A butterfly subdivision scheme for surface interpolation with tension control, ACM Trans. on Graphics, 9 (1990), pp. 160-169.
Classification and Construction of Bivariate Subdivision Schemes - Han (2002) (1 citation) (Correct)
No context found.
N. Dyn, J. A. Gregory, and D. Levin, A butterfly subdivision scheme for surface interpolation with tension control, ACM Trans. on Graphics 9 (1990), 160--169.
Discrete Smooth Interpolation: - Constrained Discrete Fairing (1999) (Correct)
No context found.
N. Dyn, D. Leven, and J. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics, 9(2):160--169, 1990.
Diagrammatic Tools for Generating Biorthogonal Multiresolutions - Samavati, Bartels (2003) (Correct)
No context found.
Nira Dyn, David Levin, and John A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics, 9(2):160--169, April 1990.
Quasi 4--8 Subdivision - Luiz Velho Visgraf (2001) (1 citation) (Correct)
No context found.
Nira Dyn, David Levin, and John A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics, 9(2):160-- 169, April 1990. ISSN 0730-0301.
Quasi 4--8 Subdivision - Luiz Velho Visgraf (2001) (1 citation) (Correct)
No context found.
N. Dyn, D. Levin, and J. A. Gregory. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions on Graphics, 9(2):160--169, April 1990.
Subdivision Surfaces - Can they be Useful for Geometric.. - Gonsor, Neamtu (2001) (Correct)
No context found.
Dyn, N., D. Levin, and J. Gregory, A butterfly subdivision scheme for surface interpolation with tension control, ACM Trans. Graphics 9 (1990), 160--169.
Haptic Subdivision: an Approach to Defining.. - Zhang, Payandeh, Dill (2002) (Correct)
No context found.
N. Dyn, D. Levin, and J. A. Gregory, "A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control", ACM Transaction on Graphics, Volume 9, Number 2, April 1990, pp 160-169.
Levels of Detail for Crowds and Groups - O'Sullivan, Cassell.. (2002) (Correct)
No context found.
N. Dyn, J.A. Gregory and D. Levin. "A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control", ACM Transactions on Graphics 9 (2) pp 160-- 190 (1990). 2
First 50 documents Next 50
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC