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57
Fitting Smooth Surfaces to Dense Polygon Meshes
 Proceedings of SIGGRAPH 96
, 1996
"... Recent progress in acquiring shape from range data permits the acquisition of seamless millionpolygon meshes from physical models. In this paper, we present an algorithm and system for converting dense irregular polygon meshes of arbitrary topology into tensor product Bspline surface patches with ..."
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Cited by 240 (5 self)
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Recent progress in acquiring shape from range data permits the acquisition of seamless millionpolygon meshes from physical models. In this paper, we present an algorithm and system for converting dense irregular polygon meshes of arbitrary topology into tensor product Bspline surface patches with accompanying displacement maps. This choice of representation yields a coarse but efficient model suitable for animation and a fine but more expensive model suitable for rendering. The first step in our process consists of interactively painting patch boundaries over a rendering of the mesh. In many applications, interactive placement of patch boundaries is considered part of the creative process and is not amenable to automation. The next step is gridded resampling of eachboundedsection of the mesh. Our resampling algorithm lays a grid of springs acrossthe polygonmesh, then iterates between relaxing this grid and subdividing it. This grid provides a parameterization for the mesh section, w...
A Hierarchical Approach to Interactive Motion Editing for Humanlike Figures
, 1999
"... This paper presents a technique for adapting existing motion of a humanlike character to have the desired features that are specified by a set of constraints. This problem can be typically formulated as a spacetime constraint problem. Our approach combines a hierarchical curve fitting technique wit ..."
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Cited by 228 (16 self)
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This paper presents a technique for adapting existing motion of a humanlike character to have the desired features that are specified by a set of constraints. This problem can be typically formulated as a spacetime constraint problem. Our approach combines a hierarchical curve fitting technique with a new inverse kinematics solver. Using the kinematics solver, we can adjust the configuration of an articulated figure to meet the constraints in each frame. Through the fitting technique, the motion displacement of every joint at each constrained frame is interpolated and thus smoothly propagated to frames. We are able to adaptively add motion details to satisfy the constraints within a specified tolerance by adopting a multilevel Bspline representation which also provides a speedup for the interpolation. The performance of our system is further enhanced by the new inverse kinematics solver. We present a closedform solution to compute the joint angles of a limb linkage. This analytical m...
Automatic reconstruction of Bspline surfaces of arbitrary topological type
 SIGGRAPH'96
, 1996
"... Creating freeform surfaces is a challenging task even with advanced geometric modeling systems. Laser range scanners offer a promising alternative for model acquisition—the 3D scanning of existing objects or clay maquettes. The problem of converting the dense point sets produced by laser scanners in ..."
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Cited by 173 (0 self)
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Creating freeform surfaces is a challenging task even with advanced geometric modeling systems. Laser range scanners offer a promising alternative for model acquisition—the 3D scanning of existing objects or clay maquettes. The problem of converting the dense point sets produced by laser scanners into useful geometric models is referred to as surface reconstruction. In this paper, we present a procedure for reconstructing a tensor product Bspline surface from a set of scanned 3D points. Unlike previous work which considers primarily the problem of fitting a single Bspline patch, our goal is to directly reconstruct a surface of arbitrary topological type. We must therefore define the surface as a network of Bspline patches. A key ingredient in our solution is a scheme for automatically constructing both a network of patches and a parametrization of the data points over these patches. In addition, we define the Bspline surface using a surface spline construction, and demonstrate that such an approach leads to an efficient procedure for fitting the surface while maintaining tangent plane continuity. We explore adaptive refinement of the patch network in order to satisfy userspecified error tolerances, and demonstrate our method on both synthetic and real data.
Scattered Data Interpolation with Multilevel Splines
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 1997
"... This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel Bsplines are introduced to compute a C²continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarsetofine hierarchy of control lattices to generate a sequen ..."
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Cited by 159 (10 self)
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This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel Bsplines are introduced to compute a C²continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarsetofine hierarchy of control lattices to generate a sequence of bicubic Bspline functions whose sum approaches the desired interpolation function. Large performance gains are realized by using Bspline refinement to reduce the sum of these functions into one equivalent Bspline function. Experimental results demonstrate that highfidelity reconstruction is possible from a selected set of sparse and irregular samples.
Displaced subdivision surfaces
 Siggraph 2000, Computer Graphics Proceedings, Annual Conference Series, pages 85–94. ACM Press / ACM SIGGRAPH
, 2000
"... In this paper we introduce a new surface representation, the displaced subdivision surface. It represents a detailed surface model as a scalarvalued displacement over a smooth domain surface. Our representation defines both the domain surface and the displacement function using a unified subdivisio ..."
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Cited by 158 (2 self)
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In this paper we introduce a new surface representation, the displaced subdivision surface. It represents a detailed surface model as a scalarvalued displacement over a smooth domain surface. Our representation defines both the domain surface and the displacement function using a unified subdivision framework, allowing for simple and efficient evaluation of analytic surface properties. We present a simple, automatic scheme for converting detailed geometric models into such a representation. The challenge in this conversion process is to find a simple subdivision surface that still faithfully expresses the detailed model as its offset. We demonstrate that displaced subdivision surfaces offer a number of benefits, including geometry compression, editing, animation, scalability, and adaptive rendering. In particular, the encoding of fine detail as a scalar function makes the representation extremely compact. Additional Keywords: geometry compression, multiresolution geometry, displacement maps, bump maps, multiresolution editing, animation.
Discrete Fairing
 In Proceedings of the Seventh IMA Conference on the Mathematics of Surfaces
, 1997
"... We address the general problem of, given a triangular net of arbitrary topology in IR 3 , find a refined net which contains the original vertices and yields an improved approximation of a smooth and fair interpolating surface. The (topological) mesh refinement is performed by uniform subdivision o ..."
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Cited by 96 (17 self)
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We address the general problem of, given a triangular net of arbitrary topology in IR 3 , find a refined net which contains the original vertices and yields an improved approximation of a smooth and fair interpolating surface. The (topological) mesh refinement is performed by uniform subdivision of the original triangles while the (geometric) position of the newly inserted vertices is determined by variational methods, i.e., by the minimization of a functional measuring a discrete approximation of bending energy. The major problem in this approach is to find an appropriate parameterization for the refined net's vertices such that second divided differences (derivatives) tightly approximate intrinsic curvatures. We prove the existence of a unique optimal solution for the minimization of discrete functionals that involve squared second order derivatives. Finally, we address the efficient computation of fair nets. 1 Introduction One of the main problems in geometric modeling is the gen...
An automatic modeling of human bodies from sizing parameters
 In SI3D ’03: Proceedings of the 2003 symposium on Interactive 3D graphics
, 2003
"... In this paper, we present an automatic, runtime modeler for modeling realistic, animatable human bodies. A user can generate a new model or modify an existing one simply by inputting a number of sizing parameters. We approach the problem by forming deformation functions that are devoted to the gener ..."
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Cited by 55 (13 self)
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In this paper, we present an automatic, runtime modeler for modeling realistic, animatable human bodies. A user can generate a new model or modify an existing one simply by inputting a number of sizing parameters. We approach the problem by forming deformation functions that are devoted to the generation of appropriate shape and proportion of the body geometry by taking the parameters as input. Starting from a number of 3D scanned data of human body models as examples, we derive these functions by using radial basis interpolation. A prerequisite of such formulation is to have correspondence among example models in the database. We obtain the correspondence by fitting a template onto each scanned data. Throughout the paper, body geometry is considered to have two distinct entities, namely rigid and elastic component of the deformation. The rigid deformation is represented by the corresponding joint parameters, which will determine the linear approximation of the physique. The elastic deformation is essentially vertex displacements, which, when added to the rigid deformation, depicts the detail shape of the body. Having these interpolators formulated, the runtime modeling can be reduced to the function evaluation and application of the evaluated results to the template model. We demonstrate our method by applying different parameters to generate a wide range of different body models.
Multiresolution Surface Representation Based on Displacement Volumes
 EUROGRAPHICS
, 2003
"... We propose a new representation for multiresolution models which uses volume elements enclosed between the different resolution levels to encode the detail information. Keeping these displacement volumes locally constant during a deformation of the base surface leads to a natural behaviour of the de ..."
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Cited by 48 (5 self)
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We propose a new representation for multiresolution models which uses volume elements enclosed between the different resolution levels to encode the detail information. Keeping these displacement volumes locally constant during a deformation of the base surface leads to a natural behaviour of the detail features. The corresponding reconstruction operator can be implemented efficiently by a hierarchical iterative relaxation scheme, providing close to interactive response times for moderately complex models. Based on this representation we implement a multiresolution editing tool for irregular polygon meshes that allows the designer to freely edit the base surface of a multiresolution model without having to care about selfintersections in the respective detailed surface. We demonstrate the effectiveness and robustness of the reconstruction by several examples with realworld data.
A Remeshing Approach to Multiresolution Modeling
, 2004
"... Providing a thorough mathematical foundation, multiresolution modeling is the standard approach for global surface deformations that preserve fine surface details in an intuitive and plausible manner. A given shape is decomposed into a smooth lowfrequency base surface and highfrequency detail in ..."
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Cited by 43 (6 self)
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Providing a thorough mathematical foundation, multiresolution modeling is the standard approach for global surface deformations that preserve fine surface details in an intuitive and plausible manner. A given shape is decomposed into a smooth lowfrequency base surface and highfrequency detail information. Adding these details back onto a deformed version of the base surface results in the desired modification. Using a suitable detail encoding, the connectivity of the base surface is not restricted to be the same as that of the original surface. We propose
Discrete fairing and variational subdivision for freeform surface design
 The Visual Computer
, 2000
"... Abstract The representation of freeform surfaces by sufficiently refined polygonal meshes has become common in many geometric modeling applications where complicated objects have to be handled. While working with triangle meshes is flexible and efficient, there are difficulties arising prominently ..."
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Cited by 40 (2 self)
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Abstract The representation of freeform surfaces by sufficiently refined polygonal meshes has become common in many geometric modeling applications where complicated objects have to be handled. While working with triangle meshes is flexible and efficient, there are difficulties arising prominently from the lack of infinitesimal smoothness and the prohibitive complexity of highly detailed 3Dmodels. In this paper we discuss the generation of fair triangle meshes which are optimal with respect to some discretized curvature energy functional. The key issues are the proper definition of discrete curvature, the smoothing of high resolution meshes by filter operators, and the efficient generation of optimal meshes by solving a sparse linear system that characterizes the global minimum of an energy functional. Results and techniques from differential geometry, variational surface design (fairing), and numerical analysis are combined to find efficient and robust algorithms that generate smooth meshes of arbitrary topology which interpolate or approximate a given set of data points.