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157
Geometry images
 IN PROC. 29TH SIGGRAPH
, 2002
"... Surface geometry is often modeled with irregular triangle meshes. The process of remeshing refers to approximating such geometry using a mesh with (semi)regular connectivity, which has advantages for many graphics applications. However, current techniques for remeshing arbitrary surfaces create onl ..."
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Cited by 276 (22 self)
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Surface geometry is often modeled with irregular triangle meshes. The process of remeshing refers to approximating such geometry using a mesh with (semi)regular connectivity, which has advantages for many graphics applications. However, current techniques for remeshing arbitrary surfaces create only semiregular meshes. The original mesh is typically decomposed into a set of disklike charts, onto which the geometry is parametrized and sampled. In this paper, we propose to remesh an arbitrary surface onto a completely regular structure we call a geometry image. It captures geometry as a simple 2D array of quantized points. Surface signals like normals and colors are stored in similar 2D arrays using the same implicit surface parametrization — texture coordinates are absent. To create a geometry image, we cut an arbitrary mesh along a network of edge paths, and parametrize the resulting single chart onto a square. Geometry images can be encoded using traditional image compression algorithms, such as waveletbased coders.
Least Squares Conformal Maps for Automatic Texture Atlas Generation
, 2002
"... A Texture Atlas is an efficient color representation for 3D Paint Systems. The model to be textured is decomposed into charts homeomorphic to discs, each chart is parameterized, and the unfolded charts are packed in texture space. Existing texture atlas methods for triangulated surfaces suffer from ..."
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Cited by 250 (6 self)
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A Texture Atlas is an efficient color representation for 3D Paint Systems. The model to be textured is decomposed into charts homeomorphic to discs, each chart is parameterized, and the unfolded charts are packed in texture space. Existing texture atlas methods for triangulated surfaces suffer from several limitations, requiring them to generate a large number of small charts with simple borders. The discontinuities between the charts cause artifacts, and make it difficult to paint large areas with regular patterns.
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 172 (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
Intrinsic Parameterizations of Surface Meshes
, 2002
"... Parameterization of discrete surfaces is a fundamental and widelyused operation in graphics, required, for instance, for texture mapping or remeshing. As 3D data becomes more and more detailed, there is an increased need for fast and robust techniques to automatically compute leastdistorted para ..."
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Cited by 166 (13 self)
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Parameterization of discrete surfaces is a fundamental and widelyused operation in graphics, required, for instance, for texture mapping or remeshing. As 3D data becomes more and more detailed, there is an increased need for fast and robust techniques to automatically compute leastdistorted parameterizations of large meshes. In this paper, we present new theoretical and practical results on the parameterization of triangulated surface patches.
Wang Tiles for Image and Texture Generation
, 2003
"... We present a simple stochastic system for nonperiodically tiling the plane with a small set of Wang Tiles. The tiles may be filled with texture, patterns, or geometry that when assembled create a continuous representation. The primary advantage of using Wang Tiles is that once the tiles are filled, ..."
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Cited by 128 (4 self)
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We present a simple stochastic system for nonperiodically tiling the plane with a small set of Wang Tiles. The tiles may be filled with texture, patterns, or geometry that when assembled create a continuous representation. The primary advantage of using Wang Tiles is that once the tiles are filled, large expanses of nonperiodic texture (or patterns or geometry) can be created as needed very efficiently at runtime. Wang Tiles
Global Conformal Surface Parameterization
, 2003
"... We solve the problem of computing global conformal parameterizations for surfaces with nontrivial topologies. The parameterization is global in the sense that it preserves the conformality everywhere except for a few points, and has no boundary of discontinuity. We analyze the structure of the space ..."
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Cited by 114 (22 self)
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We solve the problem of computing global conformal parameterizations for surfaces with nontrivial topologies. The parameterization is global in the sense that it preserves the conformality everywhere except for a few points, and has no boundary of discontinuity. We analyze the structure of the space of all global conformal parameterizations of a given surface and find all possible solutions by constructing a basis of the underlying linear solution space. This space has a natural structure solely determined by the surface geometry, so our computing result is independent of connectivity, insensitive to resolution, and independent of the algorithms to discover it. Our algorithm is based on the properties of gradient fields of conformal maps, which are closedness, harmonity, conjugacy, duality and symmetry. These properties can be formulated by sparse linear systems, so the method is easy to implement and the entire process is automatic. We also introduce a novel topological modification method to improve the uniformity of the parameterization. Based on the global conformal parameterization of a surface, we can construct a conformal atlas and use it to build conformal geometry images which have very accurate reconstructed normals.
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 111 (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.
Fundamentals of Spherical Parameterization for 3D Meshes
 PROCEEDINGS OF THE 2006 SYMPOSIUM ON INTERACTIVE 3D GRAPHICS AND GAMES, MARCH 1417, 2006
, 2003
"... Parametrization of 3D mesh data is important for many graphics applications, in particular for texture mapping, remeshing and morphing. Closed manifold genus0 meshes are topologically equivalent to a sphere, hence this is the natural parameter domain for them. Parametrizing a triangle mesh onto the ..."
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Cited by 104 (25 self)
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Parametrization of 3D mesh data is important for many graphics applications, in particular for texture mapping, remeshing and morphing. Closed manifold genus0 meshes are topologically equivalent to a sphere, hence this is the natural parameter domain for them. Parametrizing a triangle mesh onto the sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the spherical triangles induced by the mesh connectivity do not overlap. Satisfying the nonoverlapping requirement is the most difficult and critical component of this process. We present a generalization of the method of barycentric coordinates for planar parametrization which solves the spherical parametrization problem, prove its correctness by establishing a connection to spectral graph theory and describe efficient numerical methods for computing these parametrizations.
Globally Smooth Parameterizations with Low Distortion
, 2003
"... Good parameterizations are of central importance in many digital geometry processing tasks. Typically the behavior of such processing algorithms is related to the smoothness of the parameterization and how much distortion it contains, i.e., how rapidly the derivatives of the parameterization change. ..."
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Cited by 79 (2 self)
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Good parameterizations are of central importance in many digital geometry processing tasks. Typically the behavior of such processing algorithms is related to the smoothness of the parameterization and how much distortion it contains, i.e., how rapidly the derivatives of the parameterization change. Since a parameterization maps a bounded region of the plane to the surface, a parameterization for a surface which is not homeomorphic to a disc must be made up of multiple pieces. We present a novel parameterization algorithm for arbitrary topology surface meshes which computes a globally smooth parameterization with low distortion. We optimize the patch layout subject to criteria such as shape quality and parametric distortion, which are used to steer a mesh simplification approach for base complex construction. Global smoothness is achieved through simultaneous relaxation over all patches, with suitable transition functions between patches incorporated into the relaxation procedure. We demonstrate the quality of our parameterizations through numerical evaluation of distortion measures; the rate distortion behavior of semiregular remeshes produced with these parameterizations; and a comparison with globally smooth subdivision methods. The numerical algorithms required to compute the parameterizations are robust and run on the order of minutes even for large meshes.