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22
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.
SwingWrapper: Retiling Triangle Meshes for Better EdgeBreaker Compression
, 2003
"... We focus on the lossy compression of manifold triangle meshes. Our SwingWrapper approach partitions the surface of an original mesh M into simply connected regions, called triangloids. From these, we generate a new mesh M'. Each triangle of M' is an approximation of a triangloid of M. By c ..."
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Cited by 35 (11 self)
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We focus on the lossy compression of manifold triangle meshes. Our SwingWrapper approach partitions the surface of an original mesh M into simply connected regions, called triangloids. From these, we generate a new mesh M'. Each triangle of M' is an approximation of a triangloid of M. By construction, the connectivity of M' is fairly regular and can be compressed to less than a bit per triangle using EdgeBreaker or one of the other recently developed schemes. The locations of the vertices of M' are compactly encoded with our new prediction technique, which uses a single correction parameter per vertex. SwingWrapper strives to reach a userdefined output file size rather than to guarantee a given error bound. For a variety of popular models, a rate of 0.4 bits/triangle yields an L2 distortion of about 0.01% of the bounding box diagonal. The proposed solution may also be used to encode crude meshes for adaptive transmission or for controlling subdivision surfaces.
Remesh: An interactive environment to edit and repair triangle meshes
 in SMI ’06: Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006 (SMI’06
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EdgeSharpener: Recovering sharp features in triangulations of nonadaptively remeshed surfaces
, 2003
"... 3D scanners, isosurface extraction procedures, and several recent geometric compression schemes sample surfaces of 3D shapes in a regular fashion, without any attempt to align the samples with the sharp edges and corners of the original shape. Consequently, the interpolating triangle meshes chamfer ..."
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Cited by 21 (4 self)
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3D scanners, isosurface extraction procedures, and several recent geometric compression schemes sample surfaces of 3D shapes in a regular fashion, without any attempt to align the samples with the sharp edges and corners of the original shape. Consequently, the interpolating triangle meshes chamfer these sharp features and thus exhibit significant errors. The new EdgeSharpener filter introduced here identifies the chamfer edges and subdivides them and their incident triangles by inserting new vertices and by forcing these vertices to lie on intersections of planes that locally approximate the smooth surfaces that meet at these sharp features.
Bilateral recovering of sharp edges on featureinsensitive sampled meshes,”
 IEEE Transactions on Visualization and Computer Graphics,
, 2006
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Freeform Shape Representations for Efficient Geometry Processing
"... The most important concepts for the handling and storage of freeform shapes in geometry processing applications are parametric representations and volumetric representations. Both have their specific advantages and drawbacks. While the algebraic complexity of volumetric representations S = {(x, y, z ..."
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Cited by 12 (4 self)
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The most important concepts for the handling and storage of freeform shapes in geometry processing applications are parametric representations and volumetric representations. Both have their specific advantages and drawbacks. While the algebraic complexity of volumetric representations S = {(x, y, z)  f(x, y, z) = 0} is independent from the shape complexity, the domain Ω of a parametric representation f: Ω → S usually has to have the same structure as the surface S itself (which sometimes makes it necessary to update the domain when the surface is modified). On the other hand, the topology of a parametrically defined surface can be controlled explicitly while in a volumetric representation, the surface topology can change accidentally during deformation. A volumetric representation reduces distance queries or inside/outside tests to mere function evaluations but the geodesic neighborhood relation between surface points is difficult to resolve. As a consequence, it seems promising to combine parametric and volumetric representations to effectively exploit both advantages. In this talk, a number of applications is presented and discussed where such a combination leads to efficient and numerically stable algorithms for the solution of various geometry processing tasks. These applications include surface remeshing, mesh fairing, global error control for mesh decimation and smoothing, and topology control for levelset surfaces.
Tetsplat: Realtime rendering and volume clipping of large unstructured tetrahedral meshes
 In Proceedings of IEEE Visualization 2004
, 2004
"... Figure 1: Screen shots from interactive visualization of an unstructured 275Mb mesh with more than 5 million tetrahedra and 13 field values. Our method is the first to guarantee realtime performance regardless of rendering hardware (here a P4 1.7GHz, Radeon 8700) and size of the unstructured tetrah ..."
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Cited by 9 (0 self)
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Figure 1: Screen shots from interactive visualization of an unstructured 275Mb mesh with more than 5 million tetrahedra and 13 field values. Our method is the first to guarantee realtime performance regardless of rendering hardware (here a P4 1.7GHz, Radeon 8700) and size of the unstructured tetrahedral mesh. Images show realtime volumetric clipping by CSG intersection with a sphere probe (left), cutting plane (two center) and a box probe (right). We present a novel approach to interactive visualization and exploration of large unstructured tetrahedral meshes. These massive 3D meshes are used in missioncritical CFD and structural mechanics simulations, and typically sample multiple field values on several millions of unstructured grid points. Our method relies on the preprocessing of the tetrahedral mesh to partition it into nonconvex boundaries and internal fragments that are subsequently encoded into compressed multiresolution data representations. These compact hierarchical data structures are then adaptively rendered and probed in realtime on a commodity PC. Our pointbased rendering algorithm, which is inspired by QSplat, employs a simple but highly efficient splatting technique that guarantees interactive framerates regardless of the size of the input mesh and the available rendering hardware. It furthermore allows for realtime probing of the volumetric dataset through constructive solid geometry operations as well as interactive editing of color transfer functions for an arbitrary number of field values. Thus, the presented visualization technique allows endusers for the first time to interactively render and explore very large unstructured tetrahedral meshes on relatively inexpensive hardware.
Topologyfree cutandpaste editing over meshes
 In Geometric Modeling and Processing 2004
, 2004
"... Existing cutandpaste editing methods over meshes are inapplicable to regions with nonzero genus. To overcome this drawback, we propose a novel method in this paper. Firstly, a base surface passing through the boundary vertices of the selected region is constructed using the boundary triangulation ..."
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Cited by 9 (2 self)
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Existing cutandpaste editing methods over meshes are inapplicable to regions with nonzero genus. To overcome this drawback, we propose a novel method in this paper. Firstly, a base surface passing through the boundary vertices of the selected region is constructed using the boundary triangulation technique. Considering the connectivity between the neighboring vertices, a new detail encoding technique is then presented based on surface parameterization. Finally, the detail representation is transferred onto the target surface via the base surface. This strategy of creating a base surface as a detail carrier allows us to paste features of nonzero genus onto the target surface. By taking the physical relationship of adjacent vertices into account, our detail encoding method produces more natural and less distorted results. Therefore, our elegant method not only can eliminate the dependence on the topology of the selected feature, but also reduces the distortion effectively during pasting. 1.
Meshing NonUniformly Sampled and Incomplete Data Based on
 Displaced T Spline Level Sets,” Proc. IEEE Int’l Conf. Shape Modeling and Applications
, 2007
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Evolution of Tspline Level Sets for Meshing Nonuniformly Sampled and Incomplete Data
, 2008
"... Given a large set of unorganized point sample data, we propose a new framework for computing a triangular mesh representing an approximating piecewise smooth surface. The data may be non–uniformly distributed, noisy, and they may contain holes. This framework is based on the combination of two type ..."
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Cited by 5 (3 self)
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Given a large set of unorganized point sample data, we propose a new framework for computing a triangular mesh representing an approximating piecewise smooth surface. The data may be non–uniformly distributed, noisy, and they may contain holes. This framework is based on the combination of two types of surface representations: triangular meshes, and Tspline level sets, which are implicit surfaces defined by refinable spline functions allowing Tjunctions. Our method contains three main steps. Firstly, we construct an implicit representation of a smooth (C² in our case) surface, by using an evolution process of Tspline level sets, such that the implicit surface captures the topology and outline of the object to be reconstructed. The initial mesh with high quality is obtained through the marching triangulation of the implicit surface. Secondly, we project each data point to the initial mesh, and get a scalar displacement field. Detailed features will be captured by the displaced mesh. Finally, we present an additional evolution process, which combines datadriven velocities and featurepreserving bilateral filters, in order to reproduce sharp features. We also show that various shape constraints, such as distance field constraints, range constraints and volume constraints can be naturally added to our framework, which is helpful to obtain a desired reconstruction result, especially when the given data contains noise and inaccuracies.