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84
Featurebased surface parameterization and texture mapping
 ACM Transactions on Graphics
, 2005
"... and precomputation of solid textures. The stretch caused by a given parameterization determines the sampling rate on the surface. In this article, we present an automatic parameterization method for segmenting a surface into patches that are then flattened with little stretch. Many objects consist o ..."
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Cited by 90 (5 self)
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and precomputation of solid textures. The stretch caused by a given parameterization determines the sampling rate on the surface. In this article, we present an automatic parameterization method for segmenting a surface into patches that are then flattened with little stretch. Many objects consist of regions of relatively simple shapes, each of which has a natural parameterization. Based on this observation, we describe a threestage featurebased patch creation method for manifold surfaces. The first two stages, genus reduction and feature identification, are performed with the help of distancebased surface functions. In the last stage, we create one or two patches for each feature region based on a covariance matrix of the feature’s surface points. To reduce stretch during patch unfolding, we notice that stretch is a 2 × 2 tensor, which in ideal situations is the identity. Therefore, we use the GreenLagrange tensor to measure and to guide the optimization process. Furthermore, we allow the boundary vertices of a patch to be optimized by adding scaffold triangles. We demonstrate our featurebased patch creation and patch unfolding methods for several textured models. Finally, to evaluate the quality of a given parameterization, we describe an imagebased error measure that takes into account stretch, seams, smoothness, packing efficiency, and surface visibility.
Approximate convex decomposition of polyhedra
 In Proc. of ACM Symposium on Solid and Physical Modeling
, 2005
"... Decomposition is a technique commonly used to partition complex models into simpler components. While decomposition into convex components results in pieces that are easy to process, such decompositions can be costly to construct and can result in representations with an unmanageable number of compo ..."
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Cited by 50 (3 self)
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Decomposition is a technique commonly used to partition complex models into simpler components. While decomposition into convex components results in pieces that are easy to process, such decompositions can be costly to construct and can result in representations with an unmanageable number of components. In this paper, we explore an alternative partitioning strategy that decomposes a given model into “approximately convex ” pieces that may provide similar benefits as convex components, while the resulting decomposition is both significantly smaller (typically by orders of magnitude) and can be computed more efficiently. Indeed, for many applications, an approximate convex decomposition (ACD) can more accurately represent the important structural features of the model by providing a mechanism for ignoring less significant features, such as surface texture. We describe a technique for computing ACDs of threedimensional polyhedral solids and surfaces of arbitrary genus. We provide results illustrating that our approach results in high quality decompositions with very few components and applications showing that comparable or better results can be obtained using ACD decompositions in place of exact convex decompositions (ECD) that are several orders of magnitude larger. 1 ECD Figure 1: The approximate convex decompositions (ACD) of the Armadillo and the David models consist of a small number of nearly convex components that characterize the important features of the models better than the exact convex decompositions (ECD) that have orders of magnitude more components. The Armadillo (500K edges, 12.1MB) has a solid ACD with 98 components (14.2MB) that was computed in 232 seconds while the solid “ECD ” has more than 726,240 components (20+ GB) and could not be completed because disk space was exhausted after nearly 4 hours of computation. The David (750K edges, 18MB) has a surface ACD with 66 components (18.1MB) while the surface ECD has 85,132 components (20.1MB). 1
Topologybased Simplification for Feature Extraction from 3D Scalar Fields
"... This paper describes a topological approach for simplifying continuous functions defined on volumetric domains. The MorseSmale complex provides a segmentation of the domain into monotonic regions having uniform gradient flow behavior. We present a combinatorial algorithm that simplifies the Morse ..."
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Cited by 45 (21 self)
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This paper describes a topological approach for simplifying continuous functions defined on volumetric domains. The MorseSmale complex provides a segmentation of the domain into monotonic regions having uniform gradient flow behavior. We present a combinatorial algorithm that simplifies the MorseSmale complex by repeated application of two atomic operations that removes pairs of critical points. The simplification procedure leaves important critical points untouched, and is therefore useful for extracting features. We present a visualization of the simplified topology.
A Practical Approach to MorseSmale Complex Computation: Scalability and Generality
"... Abstract—The MorseSmale (MS) complex has proven to be a useful tool in extracting and visualizing features from scalarvalued data. However, efficient computation of the MS complex for large scale data remains a challenging problem. We describe a new algorithm and easily extensible framework for co ..."
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Cited by 36 (9 self)
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Abstract—The MorseSmale (MS) complex has proven to be a useful tool in extracting and visualizing features from scalarvalued data. However, efficient computation of the MS complex for large scale data remains a challenging problem. We describe a new algorithm and easily extensible framework for computing MS complexes for large scale data of any dimension where scalar values are given at the vertices of a closurefinite and weak topology (CW) complex, therefore enabling computation on a wide variety of meshes such as regular grids, simplicial meshes, and adaptive multiresolution (AMR) meshes. A new divideandconquer strategy allows for memoryefficient computation of the MS complex and simplification onthefly to control the size of the output. In addition to being able to handle various data formats, the framework supports implementationspecific optimizations, for example, for regular data. We present the complete characterization of critical point cancellations in all dimensions. This technique enables the topology based analysis of large data on offtheshelf computers. In particular we demonstrate the first full computation of the MS complex for a 1 billion/1024 3 node grid on a laptop computer with 2Gb memory. Index Terms—Topologybased analysis, MorseSmale complex, large scale data. 1
Efficient Computation of MorseSmale Complexes for ThreeDimensional Scalar Functions
, 2007
"... The MorseSmale complex is an efficient representation of the gradient behavior of a scalar function, and critical points paired by the complex identify topological features and their importance. We present an algorithm that constructs the MorseSmale complex in a series of sweeps through the data, ..."
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Cited by 32 (14 self)
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The MorseSmale complex is an efficient representation of the gradient behavior of a scalar function, and critical points paired by the complex identify topological features and their importance. We present an algorithm that constructs the MorseSmale complex in a series of sweeps through the data, identifying various components of the complex in a consistent manner. All components of the complex, both geometric and topological, are computed, providing a complete decomposition of the domain. Efficiency is maintained by representing the geometry of the complex in terms of point sets.
Computing geometryaware handle and tunnel loops in 3d models
 ACM Trans. Graph
"... Many applications such as topology repair, model editing, surface parameterization, and feature recognition benefit from computing loops on surfaces that wrap around their ‘handles ’ and ‘tunnels’. Computing such loops while optimizing their geometric lengths is difficult. On the other hand, computi ..."
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Cited by 30 (2 self)
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Many applications such as topology repair, model editing, surface parameterization, and feature recognition benefit from computing loops on surfaces that wrap around their ‘handles ’ and ‘tunnels’. Computing such loops while optimizing their geometric lengths is difficult. On the other hand, computing such loops without considering geometry is easy but may not be very useful. In this paper we strike a balance by computing topologically correct loops that are also geometrically relevant. Our algorithm is a novel application of the concepts from topological persistence introduced recently in computational topology. The usability of the computed loops is demonstrated with some examples in feature identification and topology simplification.
A topological approach to simplification of threedimensional scalar functions
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS (SPECIAL ISSUE IEEE VISUALIZATION
, 2006
"... This paper describes an efficient combinatorial method for simplification of topological features in a 3D scalar function. The MorseSmale complex, which provides a succinct representation of a function’s associated gradient flow field, is used to identify topological features and their significance ..."
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Cited by 28 (13 self)
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This paper describes an efficient combinatorial method for simplification of topological features in a 3D scalar function. The MorseSmale complex, which provides a succinct representation of a function’s associated gradient flow field, is used to identify topological features and their significance. The simplification process, guided by the MorseSmale complex, proceeds by repeatedly applying two atomic operations that each remove a pair of critical points from the complex. Efficient storage of the complex results in execution of these atomic operations at interactive rates. Visualization of the simplified complex shows that the simplification preserves significant topological features and removes small features and noise.
Topology repair of solid models using skeletons
 IEEE Transactions on Visualization and Computer Graphics
, 2007
"... Abstract—We present a method for repairing topological errors on solid models in the form of small surface handles, which often arise from surface reconstruction algorithms. We utilize a skeleton representation that offers a new mechanism for identifying and measuring handles. Our method presents tw ..."
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Cited by 27 (3 self)
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Abstract—We present a method for repairing topological errors on solid models in the form of small surface handles, which often arise from surface reconstruction algorithms. We utilize a skeleton representation that offers a new mechanism for identifying and measuring handles. Our method presents two unique advantages over previous approaches. First, handle removal is guaranteed not to introduce invalid geometry or additional handles. Second, by using an adaptive grid structure, our method is capable of processing huge models efficiently at high resolutions. Index Terms—Topology repair, skeleton, thinning, octree. Ç
Topologically Clean Distance Fields
"... Analysis of the results obtained from material simulations is important in the physical sciences. Our research was motivated by the need to investigate the properties of a simulated porous solid as it is hit by a projectile. This paper describes two techniques for the generation of distance fields c ..."
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Cited by 25 (16 self)
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Analysis of the results obtained from material simulations is important in the physical sciences. Our research was motivated by the need to investigate the properties of a simulated porous solid as it is hit by a projectile. This paper describes two techniques for the generation of distance fields containing a minimal number of topological features, and we use them to identify features of the material. We focus on distance fields defined on a volumetric domain considering the distance to a given surface embedded within the domain. Topological features of the field are characterized by its critical points. Our first method begins with a distance field that is computed using a standard approach, and simplifies this field using ideas from Morse theory. We present a procedure for identifying and extracting a feature set through analysis of the MS complex, and apply it to find the invariants in the clean distance field. Our second method proceeds by advancing a front, beginning at the surface, and locally controlling the creation of new critical points. We demonstrate the value of topologically clean distance fields for the analysis of filament structures in porous solids. Our methods produce a curved skeleton representation of the filaments that helps material scientists to perform a detailed qualitative and quantitative analysis of pores, and hence infer important material properties. Furthermore, we provide a set of criteria for finding the “difference ” between two skeletal structures, and use this to examine how the structure of the porous solid changes over several timesteps in the simulation of the particle impact.