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393
Interactive MultiResolution Modeling on Arbitrary Meshes
, 1998
"... During the last years the concept of multiresolution modeling has gained special attention in many fields of computer graphics and geometric modeling. In this paper we generalize powerful multiresolution techniques to arbitrary triangle meshes without requiring subdivision connectivity. Our major o ..."
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Cited by 307 (34 self)
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During the last years the concept of multiresolution modeling has gained special attention in many fields of computer graphics and geometric modeling. In this paper we generalize powerful multiresolution techniques to arbitrary triangle meshes without requiring subdivision connectivity. Our major observation is that the hierarchy of nested spaces which is the structural core element of most multiresolution algorithms can be replaced by the sequence of intermediate meshes emerging from the application of incremental mesh decimation. Performing such schemes with local frame coding of the detail coefficients already provides effective and efficient algorithms to extract multiresolution information from unstructured meshes. In combination with discrete fairing techniques, i.e., the constrained minimization of discrete energy functionals, we obtain very fast mesh smoothing algorithms which are able to reduce noise from a geometrically specified frequency band in a multiresolution decomposition. Putting mesh hierarchies, local frame coding and multilevel smoothing together allows us to propose a flexible and intuitive paradigm for interactive detailpreserving mesh modification. We show examples generated by our mesh modeling tool implementation to demonstrate its functionality.
Spherical Wavelets: Efficiently Representing Functions on the Sphere
, 1995
"... Wavelets have proven to be powerful bases for use in numerical analysis and signal processing. Their power lies in the fact that they only require a small number of coefficients to represent general functions and large data sets accurately. This allows compression and efficient computations. Classic ..."
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Cited by 286 (14 self)
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Wavelets have proven to be powerful bases for use in numerical analysis and signal processing. Their power lies in the fact that they only require a small number of coefficients to represent general functions and large data sets accurately. This allows compression and efficient computations. Classical constructions have been limited to simple domains such as intervals and rectangles. In this paper we present a wavelet construction for scalar functions defined on the sphere. We show how biorthogonal wavelets with custom properties can be constructed with the lifting scheme. The bases are extremely easy to implement and allow fully adaptive subdivisions. We give examples of functions defined on the sphere, such as topographic data, bidirectional reflection distribution functions, and illumination, and show how they can be efficiently represented with spherical wavelets.
Progressive Geometry Compression
, 2000
"... We propose a new progressive compression scheme for arbitrary topology, highly detailed and densely sampled meshes arising from geometry scanning. We observe that meshes consist of three distinct components: geometry, parameter, and connectivity information. The latter two do not contribute to the r ..."
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Cited by 239 (13 self)
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We propose a new progressive compression scheme for arbitrary topology, highly detailed and densely sampled meshes arising from geometry scanning. We observe that meshes consist of three distinct components: geometry, parameter, and connectivity information. The latter two do not contribute to the reduction of error in a compression setting. Using semiregular meshes, parameter and connectivity information can be virtually eliminated. Coupled with semiregular wavelet transforms, zerotree coding, and subdivision based reconstruction we see improvements in error by a factor four (12dB) compared to other progressive coding schemes. CR Categories and Subject Descriptors: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling  hierarchy and geometric transformations; G.1.2 [Numerical Analysis]: Approximation  approximation of surfaces and contours, wavelets and fractals; I.4.2 [Image Processing and Computer Vision]: Compression (Coding)  Approximate methods Additional K...
Interpolating Subdivision for Meshes with Arbitrary Topology
"... Subdivision is a powerful paradigm for the generation of surfaces of arbitrary topology. Given an initial triangular mesh the goal is to produce a smooth and visually pleasing surface whose shape is controlled by the initial mesh. Of particular interest are interpolating schemes since they match the ..."
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Cited by 236 (24 self)
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Subdivision is a powerful paradigm for the generation of surfaces of arbitrary topology. Given an initial triangular mesh the goal is to produce a smooth and visually pleasing surface whose shape is controlled by the initial mesh. Of particular interest are interpolating schemes since they match the original data exactly, and play an important role in fast multiresolution and wavelet techniques. Dyn, Gregory, and Levin introduced the Butterfly scheme, which yields C 1 surfaces in the topologically regular setting. Unfortunately it exhibits undesirable artifacts in the case of an irregular topology. We examine these failures and derive an improved scheme, which retains the simplicity of the Butterfly scheme, is interpolating, and results in smoother surfaces.
Subdivision surfaces in character animation
 In Proceedings of the 25th annual conference on Computer graphics and interactive techniques, SIGGRAPH ’98
, 1998
"... The creation of believable and endearing characters in computer graphics presents a number of technical challenges, including the modeling, animation and rendering of complex shapes such as heads, hands, and clothing. Traditionally, these shapes have been modeled with NURBS surfaces despite the seve ..."
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Cited by 233 (1 self)
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The creation of believable and endearing characters in computer graphics presents a number of technical challenges, including the modeling, animation and rendering of complex shapes such as heads, hands, and clothing. Traditionally, these shapes have been modeled with NURBS surfaces despite the severe topological restrictions that NURBS impose. In order to move beyond these restrictions, we have recently introduced subdivision surfaces into our production environment. Subdivision surfaces are not new, but their use in highend CG production has been limited. Here we describe a series of developments that were required in order for subdivision surfaces to meet the demands of highend production. First, we devised a practical technique for constructing provably smooth variableradius fillets and blends. Second, we developed methods for using subdivision surfaces in clothing simulation including a new algorithm for efficient collision detection. Third, we developed a method for constructing smooth scalar fields on subdivision surfaces, thereby enabling the use of a wider class of programmable shaders. These developments, which were used extensively in our recently completed short film Geri’s game, have become a highly valued feature of our production environment.
Subdivision for Modeling and Animation
 SIGGRAPH ’99 Courses, no. 37. ACM SIGGRAPH
, 1999
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Interactive Multiresolution Mesh Editing
"... We describe a multiresolution representation for meshes based on subdivision. Subdivision is a natural extension of the existing patchbased surface representations. At the same time subdivision algorithms can be viewed as operating directly on polygonal meshes, which makes them a useful tool for me ..."
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Cited by 208 (18 self)
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We describe a multiresolution representation for meshes based on subdivision. Subdivision is a natural extension of the existing patchbased surface representations. At the same time subdivision algorithms can be viewed as operating directly on polygonal meshes, which makes them a useful tool for mesh manipulation. Combination of subdivision and smoothing algorithms of Taubin [26] allows us to construct a set of algorithms for interactive multiresolution editing of complex meshes of arbitrary topology. Simplicity of the essential algorithms for re nement and coarsi cation allows to make them local and adaptive, considerably improving their efficiency. We have built a scalable interactive multiresolution editing system based on such algorithms.
Interpolatory Subdivision on Open Quadrilateral Nets with Arbitrary Topology
 Computer Graphics Forum
, 1996
"... A simple interpolatory subdivision scheme for quadrilateral nets with arbitrary topology is presented which generates C 1 surfaces in the limit. The scheme satisfies important requirements for practical applications in computer graphics and engineering. These requirements include the necessity to ..."
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Cited by 154 (10 self)
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A simple interpolatory subdivision scheme for quadrilateral nets with arbitrary topology is presented which generates C 1 surfaces in the limit. The scheme satisfies important requirements for practical applications in computer graphics and engineering. These requirements include the necessity to generate smooth surfaces with local creases and cusps. The scheme can be applied to open nets in which case it generates boundary curves that allow a C 0 join of several subdivision patches. Due to the local support of the scheme, adaptive refinement strategies can be applied. We present a simple device to preserve the consistency of such adaptively refined nets. Keywords: Curve and surface modeling, Interpolatory subdivision, Adaptive meshrefinement 1 Introduction The problem we address in this paper is the generation of smooth interpolating surfaces of arbitrary topological type in the context of practical applications. Such applications range from the design of freeform surfaces an...
Compressed Progressive Meshes.
 IEEE Transactions on Visualization and Computer Graphics.
, 2000
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Building Your Own Wavelets at Home
"... Wavelets have been making an appearance in many pure and applied areas of science and engineering. Computer graphics with its many and varied computational problems has been no exception to this rule. In these notes we will attempt to motivate and explain the basic ideas behind wavelets and what mak ..."
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Cited by 150 (13 self)
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Wavelets have been making an appearance in many pure and applied areas of science and engineering. Computer graphics with its many and varied computational problems has been no exception to this rule. In these notes we will attempt to motivate and explain the basic ideas behind wavelets and what makes them so successful in application areas. The main