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√3subdivision
 IN PROCEEDINGS OF ACM SIGGRAPH
, 2000
"... A new stationary subdivision scheme is presented which performs slower topological refinement than the usual dyadic split operation. The number of triangles increases in every step by a factor of 3 instead of 4. Applying the subdivision operator twice causes a uniform refinement with trisection of ..."
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Cited by 138 (4 self)
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A new stationary subdivision scheme is presented which performs slower topological refinement than the usual dyadic split operation. The number of triangles increases in every step by a factor of 3 instead of 4. Applying the subdivision operator twice causes a uniform refinement with trisection of every original edge (hence the name 3subdivision) while two dyadic splits would quadsect every original edge. Besides the finer gradation of the hierarchy levels, the new scheme has several important properties: The stencils for the subdivision rules have minimum size and maximum symmetry. The smoothness of the limit surface is C2 everywhere except for the extraordinary points where it is C1. The convergence analysis of the scheme is presented based on a new general technique which also applies to the analysis of other subdivision schemes. The new splitting operation enables locally adaptive refinement under builtin preservation of the mesh consistency without temporary crackfixing between neighboring faces from different refinement levels. The size of the surrounding mesh area which is affected by selective refinement is smaller than for the dyadic split operation. We further present a simple extension of the new subdivision scheme which makes it applicable to meshes with boundary and allows us to generate sharp feature lines.
General Object Reconstruction based on Simplex Meshes
, 1999
"... In this paper, we propose a general tridimensional reconstruction algorithm of range and volumetric images, based on deformable simplex meshes. Simplex meshes are topologically dual of triangulations and have the advantage of permitting smooth deformations in a simple and e cient manner. Our reconst ..."
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Cited by 134 (18 self)
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In this paper, we propose a general tridimensional reconstruction algorithm of range and volumetric images, based on deformable simplex meshes. Simplex meshes are topologically dual of triangulations and have the advantage of permitting smooth deformations in a simple and e cient manner. Our reconstruction algorithm can handle surfaces without any restriction on their shape or topology. The di erent tasks performed during the reconstruction include the segmentation of given objects in the scene, the extrapolation of missing data, and the control of smoothness, density, and geometric quality of the reconstructed meshes. The reconstruction takes place in two stages. First, the initialization stage creates a simplex mesh in the vicinity of the data model either manually or using an automatic procedure. Then, after a few iterations, the mesh topology can be modi ed by creating holes or by increasing its genus. Finally, aniterativere nement algorithm decreases the distance of the mesh from the data while preserving high geometric and topological quality. Several reconstruction examples are provided with quantitative and qualitative results.
Subdivision Surfaces: A New Paradigm For ThinShell FiniteElement Analysis
 INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
, 2000
"... We develop a new paradigm for thinshell finiteelement analysis based on the use of subdivision surfaces for: i) describing the geometry of the shell in its undeformed configuration, and ii) generating smooth interpolated displacement fields possessing bounded energy within the strict framework ..."
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Cited by 133 (30 self)
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We develop a new paradigm for thinshell finiteelement analysis based on the use of subdivision surfaces for: i) describing the geometry of the shell in its undeformed configuration, and ii) generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the KirchhoffLove theory of thin shells. The particular subdivision strategy adopted here is Loop's scheme, with extensions such as required to account for creases and displacement boundary conditions. The displacement fields obtained by subdivision are H 2 and, consequently, have a finite KirchhoffLove energy. The resulting finite elements contain three nodes and element integrals are computed by a onepoint quadrature. The displacement field of the shell is interpolated from nodal displacements only. In particular, no nodal rotations are used in the interpolation. The interpolation scheme induced by subdivision is nonlocal, i. e., the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighboring elements. However, the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface.
Flows on Surfaces of Arbitrary Topology
, 2003
"... In this paper we introduce a method to simulate fluid flows on smooth surfaces of arbitrary topology: an effect never seen before. We achieve this by combining a twodimensional stable fluid solver with an atlas of parametrizations of a CatmullClark surface. The contributions of this paper are: (i) ..."
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Cited by 92 (0 self)
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In this paper we introduce a method to simulate fluid flows on smooth surfaces of arbitrary topology: an effect never seen before. We achieve this by combining a twodimensional stable fluid solver with an atlas of parametrizations of a CatmullClark surface. The contributions of this paper are: (i) an extension of the Stable Fluids solver to arbitrary curvilinear coordinates, (ii) an elegant method to handle crosspatch boundary conditions and (iii) a set of new external forces custom tailored for surface flows. Our techniques can also be generalized to handle other types of processes on surfaces modeled by partial differential equations, such as reactiondiffusion. Some of our simulations allow a user to interactively place densities and apply forces to the surface, then watch their effects in realtime. We have also computed higher resolution animations of surface flows offline.
CutandPaste Editing of Multiresolution Surfaces
, 2002
"... Cutting and pasting to combine different elements into a common structure are widely used operations that have been successfully adapted to many media types. Surface design could also benefit from the availability of a general, robust, and efficient cutandpaste tool, especially during the initial s ..."
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Cited by 79 (5 self)
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Cutting and pasting to combine different elements into a common structure are widely used operations that have been successfully adapted to many media types. Surface design could also benefit from the availability of a general, robust, and efficient cutandpaste tool, especially during the initial stages of design when a large space of alternatives needs to be explored. Techniques to support cutandpaste operations for surfaces have been proposed in the past, but have been of limited usefulness due to constraints on the type of shapes supported and the lack of realtime interaction. In this paper, we describe a set of algorithms based on multiresolution subdivision surfaces that perform at interactive rates and enable intuitive cutandpaste operations.
4–8 Subdivision
, 2000
"... In this paper we introduce 4–8 subdivision, a new scheme that generalizes the fourdirectional box spline of class � � to surfaces of arbitrary topological type. The crucial advantage of the proposed scheme is that it uses bisection refinement as an elementary refinement operation, rather than more c ..."
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Cited by 66 (6 self)
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In this paper we introduce 4–8 subdivision, a new scheme that generalizes the fourdirectional box spline of class � � to surfaces of arbitrary topological type. The crucial advantage of the proposed scheme is that it uses bisection refinement as an elementary refinement operation, rather than more commonly used face or vertex splits. In the uniform case, bisection refinement results in doubling, rather than quadrupling of the number of faces in a mesh. Adaptive bisection refinement, automatically generates conforming variableresolution meshes in contrast to face and vertex split methods which require an postprocessing step to make an adaptively refined mesh conforming. The fact that the size of faces decreases more gradually with refinement allows one to have greater control over the resolution of a refined mesh. It also makes it possible to achieve higher smoothness while using small stencils (the size of the stencils used by our scheme is similar to Loop subdivision). We show that the subdivision surfaces produced by the 4–8 scheme are � � continuous almost everywhere, except at extraordinary vertices where they are is �continuous.
Seamless Texture Mapping of Subdivision Surfaces by Model Pelting and Texture Blending
"... Subdivision surfaces solve numerous problems related to the geometry of character and animation models. However, unlike on parametrised surfaces there is no natural choice of texture coordinates on subdivision surfaces. Existing algorithms for generating texture coordinates on nonparametrised surfa ..."
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Cited by 65 (0 self)
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Subdivision surfaces solve numerous problems related to the geometry of character and animation models. However, unlike on parametrised surfaces there is no natural choice of texture coordinates on subdivision surfaces. Existing algorithms for generating texture coordinates on nonparametrised surfaces often find solutions that are locally acceptable but globally are unsuitable for use by artists wishing to paint textures. In addition, for topological reasons there is not necessarily any choice of assignment of texture coordinates to control points that can satisfactorily be interpolated over the entire surface. We introduce a technique, pelting, for finding both optimal and intuitive texture mapping over almost all of an entire subdivision surface and then show how to combine multiple texture mappings together to produce a seamless result.
Evaluation of Loop Subdivision Surfaces
 In Proceedings of SIGGRAPH ’98
, 1998
"... This paper describes a technique to evaluate Loop subdivision surfaces at arbitrary parameter values. The method is a straightforward extension of our evaluation work for CatmullClark surfaces. The same ideas are applied here, with the differences being in the details only. 1 ..."
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Cited by 51 (1 self)
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This paper describes a technique to evaluate Loop subdivision surfaces at arbitrary parameter values. The method is a straightforward extension of our evaluation work for CatmullClark surfaces. The same ideas are applied here, with the differences being in the details only. 1
A simple manifoldbased construction of surfaces of arbitrary smoothness
 ACM Trans. Graph
"... Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or direct commercial advantage and that copies show this notice on the first page or initial screen of a display alon ..."
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Cited by 50 (4 self)
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Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or direct commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee.
Quad/Triangle Subdivision
, 2002
"... In this paper we introduce a new subdivision operator that unifies triangular and quadrilateral subdivision schemes. Designers often want the added flexibility of having both quads and triangles in their models. It is also well known that triangle meshes generate poor limit surfaces when using a q ..."
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Cited by 45 (2 self)
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In this paper we introduce a new subdivision operator that unifies triangular and quadrilateral subdivision schemes. Designers often want the added flexibility of having both quads and triangles in their models. It is also well known that triangle meshes generate poor limit surfaces when using a quad scheme, while quadonly meshes behave poorly with triangular schemes. Our new scheme is a generalization of the well known CatmullClark and Loop subdivision algorithms. We show that our surfaces are C everywhere and provide a proof that it is impossible to construct a C scheme at the quad/triangle boundary. However, we provide rules that produce surfaces with bounded curvature at the regular quad/triangle boundary and provide optimal masks that minimize the curvature divergence elsewhere. We demonstrate the visual quality of our surfaces with several examples.