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66
Rapid Evaluation of CatmullClark Subdivision Surfaces
, 2002
"... Using subdivision as a basic primitive for the construction of arbitrary topology, smooth, freeform surfaces is attractive for content destined for display on devices with greatly varying rendering performance. Subdivision naturally supports level of detail rendering and powerful compression algori ..."
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Cited by 44 (1 self)
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Using subdivision as a basic primitive for the construction of arbitrary topology, smooth, freeform surfaces is attractive for content destined for display on devices with greatly varying rendering performance. Subdivision naturally supports level of detail rendering and powerful compression algorithms. While the underlying algorithms are conceptually simple it is difficult to implement player engines which achieve optimal performance on modern CPUs such as the Intel Pentium family. In this
Hierarchical Representation of Timevarying Volume Data with 4√2 Subdivision and Quadrilinear Bspline Wavelets
, 2002
"... ... levels of detail are widely used for largescale two and threedimensional data sets. We present a fourdimensional multiresolution approach for timevarying volume data. This approach supports a hierarchy with spatial and temporal scalability. The ..."
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Cited by 29 (1 self)
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... levels of detail are widely used for largescale two and threedimensional data sets. We present a fourdimensional multiresolution approach for timevarying volume data. This approach supports a hierarchy with spatial and temporal scalability. The
Hybrid meshes: Multiresolution using regular and irregular refinement
, 2002
"... A hybrid mesh is a multiresolution surface representation that combines advantages from regular and irregular meshes. Irregular operations allow a hybrid mesh to change topology throughout the hierarchy and approximate detailed features at multiple scales. A preponderance of regular refinements allo ..."
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Cited by 29 (2 self)
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A hybrid mesh is a multiresolution surface representation that combines advantages from regular and irregular meshes. Irregular operations allow a hybrid mesh to change topology throughout the hierarchy and approximate detailed features at multiple scales. A preponderance of regular refinements allows for efficient datastructures and processing algorithms. We provide a user driven procedure for creating a hybrid mesh from scanned geometry and present a progressive hybrid mesh compression algorithm.
Tuning Subdivision by Minimising Gaussian Curvature Variation Near Extraordinary Vertices
 Computer Graphics Forum
, 2006
"... We present a method for tuning primal stationary subdivision schemes to give the best possible behaviour near extraordinary vertices with respect to curvature variation. ..."
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Cited by 17 (4 self)
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We present a method for tuning primal stationary subdivision schemes to give the best possible behaviour near extraordinary vertices with respect to curvature variation.
On the Support of Recursive Subdivision
 ACM TRANSACTIONS ON GRAPHICS
, 2002
"... We study the support of subdivision schemes, that is, the area of the subdivision surface that will be affected by the displacement of a single control point. Our main results cover the regular case, where the mesh induces a regular Euclidean tessellation of the parameter space. If n is the ratio ..."
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Cited by 17 (3 self)
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We study the support of subdivision schemes, that is, the area of the subdivision surface that will be affected by the displacement of a single control point. Our main results cover the regular case, where the mesh induces a regular Euclidean tessellation of the parameter space. If n is the ratio of similarity between the tessellation at step k and step k 1 of the subdivision, we show that this number determines if the support is polygonal or fractal. In particular if n = 2, as it is in the most schemes, the support is a polygon whose vertices can be easily determined. If n 2, as for example in the # 3scheme, the support is usually fractal and on its boundary we can identify sets like the classic ternary Cantor set.
Matrixvalued symmetric templates for interpolatory surface subdivisions
 I. Regular vertices, Appl. Comput. Harmon. Anal
"... The objective of this paper is to introduce a general procedure for deriving interpolatory surface subdivision schemes with “symmetric subdivision templates ” (SSTs) for regular vertices. While the precise definition of “symmetry ” will be clarified in the paper, the property of SSTs is instrumental ..."
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Cited by 14 (9 self)
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The objective of this paper is to introduce a general procedure for deriving interpolatory surface subdivision schemes with “symmetric subdivision templates ” (SSTs) for regular vertices. While the precise definition of “symmetry ” will be clarified in the paper, the property of SSTs is instrumental to facilitate application of the standard procedure for finding symmetric weights for taking weighted averages to accommodate extraordinary (or irregular) vertices in surface subdivisions, a topic to be studied in a continuation paper. By allowing the use of matrices as weights, the SSTs introduced in this paper may be constructed to overcome the size barrier limited to scalarvalued interpolatory subdivision templates, and thus avoiding the unnecessary surface oscillation artifacts. On the other hand, while the old vertices in a (scalar) interpolatory subdivision scheme do not require a subdivision template, we will see that this is not the case for the matrixvalued setting. Here, we employ the same definition of interpolation subdivisions as in the usual scalar consideration, simply by requiring the old vertices to be stationary in the definition of matrixvalued interpolatory subdivisions. Hence, there would be another complication when the templates are extended to accommodate extraordinary vertices
PointSampled Cell Complexes
"... A piecewise smooth surface, possibly with boundaries, sharp edges, corners, or other features is defined by a set of samples. The basic idea is to model surface patches, curve segments and points explicitly, and then to glue them together based on explicit connectivity information. The geometry is d ..."
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Cited by 14 (1 self)
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A piecewise smooth surface, possibly with boundaries, sharp edges, corners, or other features is defined by a set of samples. The basic idea is to model surface patches, curve segments and points explicitly, and then to glue them together based on explicit connectivity information. The geometry is defined as the set of stationary points of a projection operator, which is generalized to allow modeling curves with samples, and extended to account for the connectivity information. Additional tangent constraints can be used to model shapes with continuous tangents across edges and corners.
Stellar Subdivision Grammars
, 2003
"... In this paper we develop a new description for subdivision surfaces based on a graph grammar formalism. Subdivision schemes are specified by a context sensitive grammar in which production rules represent topological and geometrical transformations to the surface’s control mesh. This methodology can ..."
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Cited by 12 (2 self)
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In this paper we develop a new description for subdivision surfaces based on a graph grammar formalism. Subdivision schemes are specified by a context sensitive grammar in which production rules represent topological and geometrical transformations to the surface’s control mesh. This methodology can be used for all known subdivision surface schemes. Moreover, it gives an effective representation that allows simple implementation and is suitable for adaptive computations.