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111
Surface Parameterization: a Tutorial and Survey
 In Advances in Multiresolution for Geometric Modelling, Mathematics and Visualization
, 2005
"... Summary. This paper provides a tutorial and survey of methods for parameterizing surfaces with a view to applications in geometric modelling and computer graphics. We gather various concepts from differential geometry which are relevant to surface mapping and use them to understand the strengths and ..."
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Cited by 180 (5 self)
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Summary. This paper provides a tutorial and survey of methods for parameterizing surfaces with a view to applications in geometric modelling and computer graphics. We gather various concepts from differential geometry which are relevant to surface mapping and use them to understand the strengths and weaknesses of the many methods for parameterizing piecewise linear surfaces and their relationship to one another. 1
Crossparameterization and compatible remeshing of 3D models
 ACM Trans. Graph
, 2004
"... Figure 1: Applications: (left) texture transfer and morphing; (right) threesided blending. Many geometry processing applications, such as morphing, shape blending, transfer of texture or material properties, and fitting template meshes to scan data, require a bijective mapping between two or more m ..."
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Cited by 112 (5 self)
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Figure 1: Applications: (left) texture transfer and morphing; (right) threesided blending. Many geometry processing applications, such as morphing, shape blending, transfer of texture or material properties, and fitting template meshes to scan data, require a bijective mapping between two or more models. This mapping, or crossparameterization, typically needs to preserve the shape and features of the parameterized models, mapping legs to legs, ears to ears, and so on. Most of the applications also require the models to be represented by compatible meshes, i.e. meshes with identical connectivity, based on the crossparameterization. In this paper we introduce novel methods for shape preserving crossparameterization and compatible remeshing. Our crossparameterization method computes a lowdistortion bijective mapping between models that satisfies user prescribed constraints. Using this mapping, the remeshing algorithm preserves the userdefined feature vertex correspondence and the shape correlation between the models. The remeshing algorithm generates output meshes with significantly fewer elements compared to previous techniques, while accurately approximating the input geometry. As demonstrated by the examples, the compatible meshes we construct are ideally suitable for morphing and other geometry processing applications.
Intersurface mapping
 ACM TRANSACTIONS ON GRAPHICS
, 2004
"... We consider the problem of creating a map between two arbitrary triangle meshes. Whereas previous approaches compose parametrizations over a simpler intermediate domain, we directly create and optimize a continuous map between the meshes. Map distortion is measured with a new symmetric metric, and ..."
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Cited by 65 (4 self)
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We consider the problem of creating a map between two arbitrary triangle meshes. Whereas previous approaches compose parametrizations over a simpler intermediate domain, we directly create and optimize a continuous map between the meshes. Map distortion is measured with a new symmetric metric, and is minimized during interleaved coarsetofine refinement of both meshes. By explicitly favoring low intersurface distortion, we obtain maps that naturally align corresponding shape elements. Typically, the user need only specify a handful of feature correspondences for initial registration, and even these constraints can be removed during optimization. Our method robustly satisfies hard constraints if desired. Intersurface mapping is shown using geometric and attribute morphs. Our general framework can also be applied to parametrize surfaces onto simplicial domains, such as coarse meshes (for semiregular remeshing), and octahedron and toroidal domains (for geometry image remeshing). In these settings, we obtain better parametrizations than with previous specialized techniques, thanks to our finegrain optimization.
Mesh Parameterization: Theory and Practice
 SIGGRAPH ASIA 2008 COURSE NOTES
, 2008
"... Mesh parameterization is a powerful geometry processing tool with numerous computer graphics applications, from texture mapping to animation transfer. This course outlines its mathematical foundations, describes recent methods for parameterizing meshes over various domains, discusses emerging tools ..."
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Cited by 37 (2 self)
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Mesh parameterization is a powerful geometry processing tool with numerous computer graphics applications, from texture mapping to animation transfer. This course outlines its mathematical foundations, describes recent methods for parameterizing meshes over various domains, discusses emerging tools like global parameterization and intersurface mapping, and demonstrates a variety of parameterization applications.
Ambient occlusion and edge cueing for enhancing real time molecular visualization
 IEEE Transaction on Visualization and Computer Graphics
, 2006
"... Abstract — The paper presents a set of combined techniques to enhance the realtime visualization of simple or complex molecules (up to order of 10 6 atoms) space fill mode. The proposed approach includes an innovative technique for efficient computation and storage of ambient occlusion terms, a sma ..."
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Cited by 33 (0 self)
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Abstract — The paper presents a set of combined techniques to enhance the realtime visualization of simple or complex molecules (up to order of 10 6 atoms) space fill mode. The proposed approach includes an innovative technique for efficient computation and storage of ambient occlusion terms, a small set of GPU accelerated procedural impostors for spacefill and ballandstick rendering, and novel edgecueing techniques. As a result, the user’s understanding of the threedimensional structure under inspection is strongly increased (even for still images), while the rendering still occurs in real time. 1
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 31 (2 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
A fast and simple stretchminimizing mesh parameterization
 in Proc. Shape Modeling International
, 2004
"... Figure 1: Texture mapping of the Mannequin Head model with three mesh parameterizations used in our method. (a) Texture and model. (b) Floater's shape preserving parameterization [6] is used as an initial mesh parameterization. (c) After a single optimization pass. (d) Our optimal lowstretch p ..."
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Cited by 31 (2 self)
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Figure 1: Texture mapping of the Mannequin Head model with three mesh parameterizations used in our method. (a) Texture and model. (b) Floater's shape preserving parameterization [6] is used as an initial mesh parameterization. (c) After a single optimization pass. (d) Our optimal lowstretch parameterization. We propose a fast and simple method for generating a lowstretch mesh parameterization. Given a triangle mesh, we start from the Floater shape preserving parameterization and then improve the parameterization gradually. At each improvement step, we optimize the parameterization generated at the previous step by minimizing a weighted quadratic energy where the weights are chosen in order to minimize the parameterization stretch. This optimization procedure does not generate triangle ips if the boundary of the parameter domain is a convex polygon. Moreover already the rst optimization step produces a highquality mesh parameterization. We compare our parameterization procedure with several stateofart mesh parameterization methods and demonstrate its speed and high efciency in parameterizing large and geometrically complex models.
Discrete Surface Ricci Flow
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
"... This work introduces a unified framework for discrete surface Ricci flow algorithms, including spherical, Euclidean, and hyperbolic Ricci flows, which can design Riemannian metrics on surfaces with arbitrary topologies by userdefined Gaussian curvatures. Furthermore, the target metrics are conform ..."
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Cited by 26 (18 self)
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This work introduces a unified framework for discrete surface Ricci flow algorithms, including spherical, Euclidean, and hyperbolic Ricci flows, which can design Riemannian metrics on surfaces with arbitrary topologies by userdefined Gaussian curvatures. Furthermore, the target metrics are conformal (anglepreserving) to the original metrics. Ricci flow conformally deforms the Riemannian metric on a surface according to its induced curvature, such that the curvature evolves like a heat diffusion process. Eventually, the curvature becomes the user defined curvature. Discrete Ricci flow algorithms are based on a variational framework. Given a mesh, all possible metrics form a linear space, and all possible curvatures form a convex polytope. The Ricci energy is defined on the metric space, which reaches its minimum at the desired metric. The Ricci flow is the negative gradient flow of the Ricci energy. Furthermore, the Ricci energy can be optimized using Newton’s method more efficiently. Discrete Ricci flow algorithms are rigorous and efficient. Our experimental results demonstrate the efficiency, accuracy and flexibility of the algorithms. They have the potential for a wide range of applications in graphics, geometric modeling, and medical imaging. We demonstrate their practical values by global surface parameterizations.
Shape compression using spherical geometry images
 in Advances in Multiresolution for Geom. Modelling
, 2005
"... We recently introduced an algorithm for spherical parametrization and remeshing, which allows resampling of a genuszero surface onto a regular 2D grid, a spherical geometry image. These geometry images offer several advantages for shape compression. First, simple extension rules extend the square i ..."
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Cited by 25 (1 self)
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We recently introduced an algorithm for spherical parametrization and remeshing, which allows resampling of a genuszero surface onto a regular 2D grid, a spherical geometry image. These geometry images offer several advantages for shape compression. First, simple extension rules extend the square image domain to cover the infinite plane, thereby providing a globally smooth surface parametrization. The 2D grid structure permits use of ordinary image wavelets, including higherorder wavelets with polynomial precision. The coarsest wavelets span the entire surface and thus encode the lowest frequencies of the shape. Finally, the compression and decompression algorithms operate on ordinary 2D arrays, and are thus ideally suited for hardware acceleration. In this paper, we detail two waveletbased approaches for shape compression using spherical geometry images, and provide comparisons with previous compression schemes. 1