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31
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 78 (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.
A flexible kernel for adaptive mesh refinement on GPU
 Computer Graphics Forum
, 2008
"... We present a flexible GPU kernel for adaptive onthefly refinement of meshes with arbitrary topology. By simply reserving a small amount of GPU memory to store a set of adaptive refinement patterns, onthefly refinement is performed by the GPU, without any preprocessing nor additional topology dat ..."
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Cited by 15 (1 self)
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We present a flexible GPU kernel for adaptive onthefly refinement of meshes with arbitrary topology. By simply reserving a small amount of GPU memory to store a set of adaptive refinement patterns, onthefly refinement is performed by the GPU, without any preprocessing nor additional topology data structure. The level of adaptive refinement can be controlled by specifying a pervertex depthtag, in addition to usual position, normal, color and texture coordinates. This depthtag is used by the kernel to instanciate the correct refinement pattern, which will map a refined connectivity on the input coarse polygon. Finally, the refined patch produced for each triangle can be displaced by the vertex shader, using any kind of geometric refinement, such as Bezier patch smoothing, scalar valued displacement, procedural geometry synthesis or subdivision surfaces. This refinement engine does neither require multipass rendering nor any use of fragment processing nor special preprocess of the input mesh structure. It can be implemented on any GPU with vertex shading capabilities.
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.
Spherical manifolds for adaptive resolution surface modeling
 In Graphite (accepted
, 2005
"... Figure 1: Creating a surface with spherical topology. a) Sketch mesh (22 faces) and first subdivision level mesh embedded in the spherical domain. b) Initial geometry of sketch mesh and resulting surface (129 overlapping surface patches). c) Geometry specifying the next hierarchical level (average p ..."
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Cited by 6 (3 self)
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Figure 1: Creating a surface with spherical topology. a) Sketch mesh (22 faces) and first subdivision level mesh embedded in the spherical domain. b) Initial geometry of sketch mesh and resulting surface (129 overlapping surface patches). c) Geometry specifying the next hierarchical level (average patch overlap, 3.4) This geometry is created by drawing on the surface in b). d) The resulting surface, colored by hierarchical level. e) Editing the first hierarchical level to produce arms and legs. f) Adding and editing a second hierarchical level. We present a surface modeling technique that supports adaptive resolution and hierarchical editing for surfaces of spherical topology. The resulting surface is analytic, Ck, and has a continuous local parameterization defined at every point. To manipulate these surfaces we describe a userinterface based on multiple, overlapping subdivisionstyle meshes.
Biorthogonal wavelets for subdivision volumes
 In: Proceedings of the Seventh ACM Symposium on Solid Modeling and Applications
, 2002
"... Figure 1: Volume subdivision, manipulation, and fitting. A lattice (top left) is recursively subdivided and reshaped at the fourth subdivision level. This shape is lowpass filtered by removing fineresolution wavelet coefficients (bottom right). We present a biorthogonal wavelet construction based ..."
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Cited by 5 (0 self)
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Figure 1: Volume subdivision, manipulation, and fitting. A lattice (top left) is recursively subdivided and reshaped at the fourth subdivision level. This shape is lowpass filtered by removing fineresolution wavelet coefficients (bottom right). We present a biorthogonal wavelet construction based on CatmullClarkstyle subdivision volumes, like multilinear cell averaging (MLCA). Our wavelet transform is the threedimensional extension of a previously developed construction of subdivisionsurface wavelets that was used for multiresolution modeling of largescale isosurfaces. Subdivision surfaces provide a flexible modeling tool for geometries of arbitrary topology and for functions defined thereon. Wavelet representations add the ability to compactly represent largescale geometries at multiple levels of detail. Our wavelet construction based on subdivision volumes extends these concepts to trivariate geometries, such as timevarying surfaces, freeform deformations, and solid models with nonuniform material properties.
Subdivision surface for CADan overview
 ComputerAided Design Volume 37, Issue 7
, 2005
"... Subdivision surfaces refer to a class of modelling schemes that define an object through recursive subdivision starting from an initial control mesh. Similar to Bsplines, the final surface is defined by the vertices of the initial control mesh. These surfaces were initially conceived as an extensio ..."
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Cited by 5 (0 self)
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Subdivision surfaces refer to a class of modelling schemes that define an object through recursive subdivision starting from an initial control mesh. Similar to Bsplines, the final surface is defined by the vertices of the initial control mesh. These surfaces were initially conceived as an extension of splines in modelling objects with a control mesh of arbitrary topology. They exhibit a number of advantages over traditional splines. Today one can find a variety of subdivision schemes for geometric design and graphics applications. This paper provides an overview of subdivision surfaces with a particular emphasis on schemes generalizing splines. Some common issues on subdivision surface modelling are addressed. Several key topics, such as scheme construction, property analysis, parametric evaluation and subdivision surface fitting, are discussed. Some other important topics are also summarized for potential future research and development. Several examples are provided to highlight the modelling capability of subdivision surfaces for CAD applications.
Isogeometric Finite Element Analysis Based on CatmullClark Subdivision Solids
 In Proceedings of Symposium on Geometry Processing, Computer Graphics Forum
"... We present a volumetric isogeometric finite element analysis based on CatmullClark solids. This concept allows one to use the same representation for the modeling, the physical simulation, and the visualization, which optimizes the design process and narrows the gap between CAD and CAE. In our met ..."
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Cited by 5 (1 self)
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We present a volumetric isogeometric finite element analysis based on CatmullClark solids. This concept allows one to use the same representation for the modeling, the physical simulation, and the visualization, which optimizes the design process and narrows the gap between CAD and CAE. In our method the boundary of the solid model is a CatmullClark surface with optional corners and creases to support the modeling phase. The crucial point in the simulation phase is the need to perform efficient integration for the elements. We propose a method similar to the standard subdivision surface evaluation technique, such that numerical quadrature can be used. Experiments show that our approach converges faster than methods based on trilinear and triquadratic elements.However, the topological structure of CatmullClark elements is as simple as the structure of linear elements. Furthermore, the CatmullClark elements we use are C2continuous on the boundary and in the interior except for irregular vertices and edges. Categories and Subject Descriptors (according to ACM CCS): 1.
Fair webs
, 2007
"... Fair webs are energyminimizing curve networks. Obtained via an extension of cubic splines or splines in tension to networks of curves, they are efficiently computable and possess a variety of interesting applications. We present properties of fair webs and their discrete counterparts, i.e., fair ..."
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Cited by 5 (1 self)
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Fair webs are energyminimizing curve networks. Obtained via an extension of cubic splines or splines in tension to networks of curves, they are efficiently computable and possess a variety of interesting applications. We present properties of fair webs and their discrete counterparts, i.e., fair polygon networks. Applications of fair curve and polygon networks include fair surface design and approximation under constraints such as obstacle avoidance or guaranteed error bounds, aesthetic remeshing, parameterization and texture mapping, and surface restoration in geometric models.
Subdivision surfaces with creases and truncated multiple knot lines
 Computer Graphics Forum
"... We deal with subdivision schemes based on arbitrary degree Bsplines. We focus on extraordinary knots which exhibit various levels of complexity in terms of both valency and multiplicity of knot lines emanating from such knots. The purpose of truncated multiple knot lines is to model creases which f ..."
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Cited by 2 (2 self)
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We deal with subdivision schemes based on arbitrary degree Bsplines. We focus on extraordinary knots which exhibit various levels of complexity in terms of both valency and multiplicity of knot lines emanating from such knots. The purpose of truncated multiple knot lines is to model creases which fair out. Our construction supports any degree and any knot line multiplicity and provides a modelling framework familiar to users used to Bsplines and NURBS systems.
Sharpen&Bend: Recovering curved sharp edges in triangle meshes produced by featureinsensitive sampling
 IEEE Transactions on Visualization and Computer Graphics
, 2005
"... triangle meshes produced by featureinsensitive sampling ..."
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Cited by 1 (1 self)
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triangle meshes produced by featureinsensitive sampling