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Reconstruction and Representation of 3D Objects with Radial Basis Functions
 Computer Graphics (SIGGRAPH ’01 Conf. Proc.), pages 67–76. ACM SIGGRAPH
, 2001
"... We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from pointcloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs al ..."
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Cited by 500 (1 self)
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We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from pointcloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs allow us to model large data sets, consisting of millions of surface points, by a single RBFpreviously an impossible task. A greedy algorithm in the fitting process reduces the number of RBF centers required to represent a surface and results in significant compression and further computational advantages. The energyminimisation characterisation of polyharmonic splines result in a "smoothest" interpolant. This scaleindependent characterisation is wellsuited to reconstructing surfaces from nonuniformly sampled data. Holes are smoothly filled and surfaces smoothly extrapolated. We use a noninterpolating approximation when the data is noisy. The functional representation is in effect a solid model, which means that gradients and surface normals can be determined analytically. This helps generate uniform meshes and we show that the RBF representation has advantages for mesh simplification and remeshing applications. Results are presented for realworld rangefinder data.
Efficient implementation of Marching Cubes' cases with topological guarantees
 Journal of Graphics Tools
, 2003
"... Marching Cubes' methods first offered visual access to experimental and theoretical data. The implementation of this method usually relies on a small lookup table. Many enhancements and optimizations of Marching Cubes still use it. However, this lookup table can lead to cracks and inconsistent ..."
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Cited by 66 (5 self)
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Marching Cubes' methods first offered visual access to experimental and theoretical data. The implementation of this method usually relies on a small lookup table. Many enhancements and optimizations of Marching Cubes still use it. However, this lookup table can lead to cracks and inconsistent topology. This paper introduces a full implementation of Chernyaev's technique to ensure a topologically correct result, i.e. a manifold mesh for any input data. It completes the original paper for the ambiguity resolution and for the feasibility of the implementation. Moreover, the cube interpolation provided here can be used in a wider range of methods. The source code is available online.
A survey of the marching cubes algorithm
, 2006
"... A survey of the development of the marching cubes algorithm [W. Lorensen, H. Cline, Marching cubes: a high resolution 3D surface construction algorithm. Computer Graphics 1987; 21(4):163–9], a wellknown cellbycell method for extraction of isosurfaces from scalar volumetric data sets, is presented ..."
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Cited by 44 (0 self)
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A survey of the development of the marching cubes algorithm [W. Lorensen, H. Cline, Marching cubes: a high resolution 3D surface construction algorithm. Computer Graphics 1987; 21(4):163–9], a wellknown cellbycell method for extraction of isosurfaces from scalar volumetric data sets, is presented. The paper’s primary aim is to survey the development of the algorithm and its computational properties, extensions, and limitations (including the attempts to resolve its limitations). A rich body of publications related to this aim are included. Representative applications and spinoff work are also considered and related techniques are briefly discussed.
Particlebased simulation of granular materials
 In ACM SIGGRAPH/Eurographics Symposium on Computer Animation
, 2005
"... Granular materials, such as sand and grains, are ubiquitous. Simulating the 3D dynamic motion of such materials represents a challenging problem in graphics because of their unique physical properties. In this paper we present a simple and effective method for granular material simulation. By incor ..."
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Cited by 38 (1 self)
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Granular materials, such as sand and grains, are ubiquitous. Simulating the 3D dynamic motion of such materials represents a challenging problem in graphics because of their unique physical properties. In this paper we present a simple and effective method for granular material simulation. By incorporating techniques from physical models, our approach describes granular phenomena more faithfully than previous methods. Granular material is represented by a large collection of nonspherical particles which may be in persistent contact. The particles represent discrete elements of the simulated material. One major advantage of using discrete elements is that the topology of particle interaction can evolve freely. As a result, highly dynamic phenomena, such as splashing and avalanches, can be conveniently generated by this meshless approach without sacricing physical accuracy. We generalize this discrete model to rigid bodies by distributing particles over their surfaces. In this way, twoway coupling between granular materials and rigid bodies is achieved.
Lapped solid textures: filling a model with anisotropic textures. SIGGRAPH
, 2008
"... map channel). Note that the input solid textures include surface textures as well as interior textures. We present a method for representing solid objects with spatiallyvarying oriented textures by repeatedly pasting solid texture exemplars. The underlying concept is to extend the 2D texture patchpa ..."
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Cited by 18 (3 self)
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map channel). Note that the input solid textures include surface textures as well as interior textures. We present a method for representing solid objects with spatiallyvarying oriented textures by repeatedly pasting solid texture exemplars. The underlying concept is to extend the 2D texture patchpasting approach of lapped textures to 3D solids using a tetrahedral mesh and 3D texture patches. The system places texture patches according to the userdefined volumetric tensor fields over the mesh to represent oriented textures. We have also extended the original technique to handle nonhomogeneous textures for creating solid models whose textural patterns change gradually along the depth fields. We identify several texture types considering the amount of anisotropy and spatial variation and provide a tailored user interface for each. With our simple framework, largescale realistic solid models can be created easily with little memory and computational cost. We demonstrate the effectiveness of our approach with several examples including trees, fruits, and vegetables.
Surface Interpolation From Sparse CrossSections Using Region Correspondence
, 1999
"... The ability to estimate a surface from a set of crosssections allows calculation of the enclosed volume and the display of the surface in threedimensions (3D). This process has increasingly been used to derive useful information from medical data. However, extracting the crosssections (segmentin ..."
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Cited by 14 (2 self)
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The ability to estimate a surface from a set of crosssections allows calculation of the enclosed volume and the display of the surface in threedimensions (3D). This process has increasingly been used to derive useful information from medical data. However, extracting the crosssections (segmenting) can be very difficult, and automatic segmentation methods are not sufficiently robust to deal with all situations. Hence, it is an advantage if the surface reconstruction algorithm can work effectively on a small number of crosssections. In addition, crosssections of medical data are often quite complex. In this paper, an algorithm is presented which can interpolate a surface through sparse, complex crosssections. This is an extension of maximal disc guided interpolation [25], which is itself based on shape based interpolation [8, 21]. The performance of this algorithm is demonstrated on various types of medical data (Xray Computed Tomography, Magnetic Resonance Imaging and threedimen...
Edge transformations for improving mesh quality of marching cubes
 IEEE TVCG
"... Abstract—Marching Cubes is a popular choice for isosurface extraction from regular grids due to its simplicity, robustness, and efficiency. One of the key shortcomings of this approach is the quality of the resulting meshes, which tend to have many poorly shaped and degenerate triangles. This issue ..."
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Cited by 14 (5 self)
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Abstract—Marching Cubes is a popular choice for isosurface extraction from regular grids due to its simplicity, robustness, and efficiency. One of the key shortcomings of this approach is the quality of the resulting meshes, which tend to have many poorly shaped and degenerate triangles. This issue is often addressed through postprocessing operations such as smoothing. As we demonstrate in experiments with several data sets, while these improve the mesh, they do not remove all degeneracies and incur an increased and unbounded error between the resulting mesh and the original isosurface. Rather than modifying the resulting mesh, we propose a method to modify the grid on which Marching Cubes operates. This modification greatly increases the quality of the extracted mesh. In our experiments, our method did not create a single degenerate triangle, unlike any other method we experimented with. Our method incurs minimal computational overhead, requiring at most twice the execution time of the original Marching Cubes algorithm in our experiments. Most importantly, it can be readily integrated in existing Marching Cubes implementations and is orthogonal to many Marching Cubes enhancements (particularly, performance enhancements such as outofcore and acceleration structures). Index Terms—Meshing, marching cubes. Ç 1
Marching Diamonds for Unstructured Meshes
"... We present a higherorder approach to the extraction of isosurfaces from unstructured meshes. Existing methods use linear interpolation along each mesh edge to find isosurface intersections. In contrast, our method determines intersections by performing barycentric interpolation over diamonds form ..."
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Cited by 12 (0 self)
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We present a higherorder approach to the extraction of isosurfaces from unstructured meshes. Existing methods use linear interpolation along each mesh edge to find isosurface intersections. In contrast, our method determines intersections by performing barycentric interpolation over diamonds formed by the tetrahedra incident to each edge. Our method produces smoother, more accurate isosurfaces. Additionally, interpolating over diamonds, rather than linearly interpolating edge endpoints, enables us to identify up to two isosurface intersections per edge. This paper details how our new technique extracts isopoints, and presents a simple connection strategy for forming a triangle mesh isosurface.
Transitive inverseconsistent manifold registration
 in Proc. Int. Conf. Inf. Process. Med. Imag., 2005
"... Abstract. This paper presents a new registration method called Transitive InverseConsistent Manifold Registration (TICMR). The TICMR method jointly estimates correspondence maps between groups of three manifolds embedded in a higher dimensional image space while minimizing inverse consistency and t ..."
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Cited by 9 (2 self)
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Abstract. This paper presents a new registration method called Transitive InverseConsistent Manifold Registration (TICMR). The TICMR method jointly estimates correspondence maps between groups of three manifolds embedded in a higher dimensional image space while minimizing inverse consistency and transitivity errors. Registering three manifolds at once provides a means for minimizing the transitivity error which is not possible when registering only two manifolds. TICMR is an iterative method that uses the closest point projection operator to define correspondences between manifolds as they are nonrigidly registered. Examples of the TICMR method are presented for matching groups of three contours and groups of three surfaces. The contour registration is regularized by minimizing the change in bending energy of the curves while the surface registration is regularized by minimizing the change in elastic energy of the surfaces. The notions of inverse consistency error (ICE) and transitivity error (TE) are extended from volume registration to manifold registration by using a closest point projection operator. For the experiments in this paper, the TICMR method reduces the average ICE by 200 times (contour) / 6 times (surface) and the average TE by 40 times (contour) / 24 times (surface) compared to registering with a curvature constraint alone. Furthermore, the TICMR is shown to avoid some local minimum that are not avoided when registering with a curvature constraint alone. 1
Interactive 3D Flow Visualization Based on Textures and Geometric Primitives
, 2004
"... This thesis presents research in the area of flow visualization. The theoretical framework is based on the notion that flow visualization methodology can be classified into four main areas: direct, geometric, texturebased, and featurebased flow visualization. Our work focuses on the direct, geomet ..."
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Cited by 8 (0 self)
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This thesis presents research in the area of flow visualization. The theoretical framework is based on the notion that flow visualization methodology can be classified into four main areas: direct, geometric, texturebased, and featurebased flow visualization. Our work focuses on the direct, geometric, and texturebased categories, with special emphasis on texturebased approaches. After presenting the stateoftheart, we discuss a technique for resampling of CFD simulation data. The resampling tool addresses both the perceptual problems resulting from a brute force hedgehog visualization and flow field coverage problems. These challenges are handled by giving the user control of the resolution of the resampling grid in object space and giving the user precise control of where to place the vector glyphs. Afterward, we present a novel technique for visualization of unsteady flow on surfaces from computational fluid dynamics. The method generates dense representations of timedependent vector fields with high spatiotemporal correlation. While the 3D vector fields are associated with arbitrary triangular surface meshes, the generation and advection of texture properties is confined to image space. Frame rates of up to 60 frames per second are realized by exploiting graphics card hardware. We apply this algorithm to unsteady flow on boundary surfaces of, large, complex meshes from computational fluid dynamics