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127
Poisson Surface Reconstruction
, 2006
"... We show that surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial partitioning or blending, and is therefore highly resilient to data noise. Unlike radial basis function ..."
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Cited by 369 (5 self)
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We show that surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial partitioning or blending, and is therefore highly resilient to data noise. Unlike radial basis function schemes, our Poisson approach allows a hierarchy of locally supported basis functions, and therefore the solution reduces to a well conditioned sparse linear system. We describe a spatially adaptive multiscale algorithm whose time and space complexities are proportional to the size of the reconstructed model. Experimenting with publicly available scan data, we demonstrate reconstruction of surfaces with greater detail than previously achievable.
Multilevel Partition of Unity Implicits
 ACM TRANSACTIONS ON GRAPHICS
, 2003
"... We present a shape representation, the multilevel partition of unity implicit surface, that allows us to construct surface models from very large sets of points. There are three key ingredients to our approach: 1) piecewise quadratic functions that capture the local shape of the surface, 2) weighti ..."
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Cited by 218 (7 self)
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We present a shape representation, the multilevel partition of unity implicit surface, that allows us to construct surface models from very large sets of points. There are three key ingredients to our approach: 1) piecewise quadratic functions that capture the local shape of the surface, 2) weighting functions (the partitions of unity) that blend together these local shape functions, and 3) an octree subdivision method that adapts to variations in the complexity of the local shape. Our approach
ShapeShop: SketchBased Solid Modeling with BlobTrees
, 2005
"... Various systems have explored the idea of inferring 3D models from sketched 2D outlines. In all of these systems the underlying modeling methodology limits the complexity of models that can be created interactively. The ShapeShop sketchbased modeling system utilizes Hierarchical Implicit Volume M ..."
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Cited by 81 (18 self)
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Various systems have explored the idea of inferring 3D models from sketched 2D outlines. In all of these systems the underlying modeling methodology limits the complexity of models that can be created interactively. The ShapeShop sketchbased modeling system utilizes Hierarchical Implicit Volume Models (BlobTrees) as an underlying shape representation. The BlobTree framework supports interactive creation of complex, detailed solid models with arbitrary topology. A new technique is described for inflating 2D contours into rounded threedimensional implicit volumes. Sketchbased modeling operations are defined that combine these basic shapes using standard blending and CSG operators. Since the underlying volume hierarchy is by definition a construction history, individual sketched components can be nonlinearly edited and removed. For example, holes can be interactively dragged through a shape. ShapeShop also provides 2D drawing assistance using a new curvesketching system based on variational contours. A wide range of models can be sketched with ShapeShop, from cartoonlike characters to detailed mechanical parts. Examples are shown which demonstrate significantly higher model complexity than existing systems.
A Multiscale Approach to 3D Scattered Data Interpolation with Compactly Supported Basis Functions
, 2003
"... In this paper, we propose a hierarchical approach to 3D scattered data interpolation with compactly supported basis functions. Our numerical experiments suggest that the approach integrates the best aspects of scattered data fitting with locally and globally supported basis functions. Employing loca ..."
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Cited by 61 (3 self)
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In this paper, we propose a hierarchical approach to 3D scattered data interpolation with compactly supported basis functions. Our numerical experiments suggest that the approach integrates the best aspects of scattered data fitting with locally and globally supported basis functions. Employing locally supported functions leads to an efficient computational procedure, while a coarsetofine hierarchy makes our method insensitive to the density of scattered data and allows us to restore large parts of missed data. Given a point
Realtime shape editing using radial basis functions
 Computer Graphics Forum
, 2005
"... Current surfacebased methods for interactive freeform editing of high resolution 3D models are very powerful, but at the same time require a certain minimum tessellation or sampling quality in order to guarantee sufficient robustness. In contrast to this, space deformation techniques do not depend ..."
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Cited by 59 (10 self)
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Current surfacebased methods for interactive freeform editing of high resolution 3D models are very powerful, but at the same time require a certain minimum tessellation or sampling quality in order to guarantee sufficient robustness. In contrast to this, space deformation techniques do not depend on the underlying surface representation and hence are affected neither by its complexity nor by its quality aspects. However, while analogously to surfacebased methods high quality deformations can be derived from variational optimization, the major drawback lies in the computation and evaluation, which is considerably more expensive for volumetric space deformations. In this paper we present techniques which allow us to use triharmonic radial basis functions for realtime freeform shape editing. An incremental leastsquares method enables us to approximately solve the involved linear systems in a robust and efficient manner and by precomputing a special set of deformation basis functions we are able to significantly reduce the perframe costs. Moreover, evaluating these linear basis functions on the GPU finally allows us to deform highly complex polygon meshes or pointbased models at a rate of 30M vertices or 13M splats per second, respectively. 1.
Leastsquares meshes
 In Shape Modeling International (SMI
, 2004
"... Figure 1: LSmesh: a mesh constructed from a given connectivity graph and a sparse set of control points with geometry. In this example the connectivity is taken from the camel mesh. In (a) the LSmesh is constructed with 100 control points and in (c) with 2000 control points. The connectivity graph ..."
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Cited by 46 (5 self)
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Figure 1: LSmesh: a mesh constructed from a given connectivity graph and a sparse set of control points with geometry. In this example the connectivity is taken from the camel mesh. In (a) the LSmesh is constructed with 100 control points and in (c) with 2000 control points. The connectivity graph contains 39074 vertices (without any geometric information). (b) and (d) show closeups on the head; the control points are marked by red balls. In this paper we introduce Leastsquares Meshes: meshes with a prescribed connectivity that approximate a set of control points in a leastsquares sense. The given mesh consists of a planar graph with arbitrary connectivity and a sparse set of control points with geometry. The geometry of the mesh is reconstructed by solving a sparse linear system. The linear system not only defines a surface that approximates the given control points, but it also distributes the vertices over the surface in a fair way. That is, each vertex lies as close as possible to the center of gravity of its immediate neighbors. The Leastsquares Meshes (LSmeshes) are a visually smooth and fair approximation of the given control points. We show that the connectivity of the mesh contains geometric information that affects the shape of the reconstructed surface. Finally, we discuss the applicability of LSmeshes to approximation of given surfaces, smooth completion, mesh editing and progressive transmission.
Controllable smoke animation with guiding objects
 ACM Transactions on Graphics
, 2005
"... This article addresses the problem of controlling the density and dynamics of smoke (a gas phenomenon) so that the synthetic appearance of the smoke (gas) resembles a still or moving object. Both the smoke region and the target object are represented as implicit functions. As a part of the target im ..."
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Cited by 46 (3 self)
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This article addresses the problem of controlling the density and dynamics of smoke (a gas phenomenon) so that the synthetic appearance of the smoke (gas) resembles a still or moving object. Both the smoke region and the target object are represented as implicit functions. As a part of the target implicit function, a shape transformation is generated between an initial smoke region and the target object. In order to match the smoke surface with the target surface, we impose carefully designed velocity constraints on the smoke boundary during a dynamic fluid simulation. The velocity constraints are derived from an iterative functional minimization procedure for shape matching. The dynamics of the smoke is formulated using a novel compressible fluid model which can effectively absorb the discontinuities in the velocity field caused by imposed velocity constraints while reproducing realistic smoke appearances. As a result, a smoke region can evolve into a regular object and follow the motion of the object, while maintaining its smoke appearance.
Spatial Keyframing for Performancedriven Animation
, 2005
"... This paper introduces spatial keyframing, a technique for performancedriven character animation. In traditional temporal keyframing, key poses are defined at specific points in time: i.e., we define a map from a set of key times to the configuration space of the character and then extend this map t ..."
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Cited by 41 (4 self)
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This paper introduces spatial keyframing, a technique for performancedriven character animation. In traditional temporal keyframing, key poses are defined at specific points in time: i.e., we define a map from a set of key times to the configuration space of the character and then extend this map to the entire timeline by interpolation. By contrast, in spatial keyframing key poses are defined at specific key positions in a 3D space where the character lives; the mapping from the 3D space to the configuration space is again defined by interpolation. The user controls a character by adjusting the position of a control cursor in the 3D space; the pose of the character is given as a blend of nearby key poses. The user thus can make expressive motion in real time and the resulting motion can be recorded and interpreted as an animation sequence. Although similar ideas are present in previous systems, our system is unique in that the designer can quickly design a new set of keyframes from scratch, and make an animation without motion capture data or special input devices. Our technique is especially useful for imaginary characters other than human figures because we do not rely on motioncapture data. We also introduce several applications of the basic idea and give examples showing the expressiveness of the approach.
3D Scattered Data Approximation with Adaptive Compactly Supported Radial Basis Functions
"... In this paper, we develop an adaptive RBF fitting procedure for a high quality approximation of a set of points scattered over a piecewise smooth surface. We use compactly supported RBFs whose centers are randomly chosen from the points. The randomness is controlled by the point density and surface ..."
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Cited by 38 (2 self)
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In this paper, we develop an adaptive RBF fitting procedure for a high quality approximation of a set of points scattered over a piecewise smooth surface. We use compactly supported RBFs whose centers are randomly chosen from the points. The randomness is controlled by the point density and surface geometry. For each RBF, its support size is chosen adaptively according to surface geometry at a vicinity of the RBF center. All these lead to a noiserobust high quality approximation of the set. We also adapt our basic technique for shape reconstruction from registered range scans by taking into account measurement confidences. Finally, an interesting link between our RBF fitting procedure and partition of unity approximations is established and discussed.