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Cross-parameterization and compatible remeshing of 3-D models
- ACM Trans. Graph
, 2004
"... Figure 1: Applications: (left) texture transfer and morphing; (right) three-sided 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 143 (5 self)
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Figure 1: Applications: (left) texture transfer and morphing; (right) three-sided 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 cross-parameterization. In this paper we introduce novel methods for shape preserving cross-parameterization and compatible remeshing. Our crossparameterization method computes a low-distortion bijective mapping between models that satisfies user prescribed constraints. Using this mapping, the remeshing algorithm preserves the user-defined 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.
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 100 (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 semi-regular 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.
Mesh parameterization methods and their applications
- FOUNDATIONS AND TRENDSÂŐ IN COMPUTER GRAPHICS AND VISION
, 2006
"... We present a survey of recent methods for creating piecewise linear mappings between triangulations in 3D and simpler domains such as planar regions, simplicial complexes, and spheres. We also discuss emerging tools such as global parameterization, inter-surface mapping, and parameterization with co ..."
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Cited by 69 (2 self)
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We present a survey of recent methods for creating piecewise linear mappings between triangulations in 3D and simpler domains such as planar regions, simplicial complexes, and spheres. We also discuss emerging tools such as global parameterization, inter-surface mapping, and parameterization with constraints. We start by describing the wide range of applications where parameterization tools have been used in recent years. We then briefly review the pertinent mathematical background and terminology, before proceeding to survey the existing parameterization techniques. Our survey summarizes the main ideas of each technique and discusses its main properties, comparing it to other methods available. Thus it aims to provide guidance to researchers and developers when assessing the suitability of different methods for various applications. This survey focuses on the practical aspects of the methods available, such as time complexity and robustness and shows multiple examples of parameterizations generated using different methods, allowing the reader to visually evaluate and compare the results.
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 54 (5 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 inter-surface mapping, and demonstrates a variety of parameterization applications.
Curvature Maps for Local Shape Comparison
- In Shape Modeling International
, 2005
"... The ability to identify similarities between shapes is important for applications such as medical diagnosis, object registration and alignment, and shape retrieval. In this paper we present a method, the Curvature Map, that uses surface curvature properties in a region around a point to create a uni ..."
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Cited by 49 (5 self)
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The ability to identify similarities between shapes is important for applications such as medical diagnosis, object registration and alignment, and shape retrieval. In this paper we present a method, the Curvature Map, that uses surface curvature properties in a region around a point to create a unique signature for that point. These signatures can then be compared to determine the similarity of one point to another. To gather curvature information around a point we explore two techniques, rings (which use the local topology of the mesh) and Geodesic Fans (which trace geodesics along the mesh from the point). We explore a variety of comparison functions and provide experimental evidence for which ones provide the best discriminatory power. We show that Curvature Maps are both more robust and provide better discrimination than simply comparing the curvature at individual points.
An Adaptable Surface Parameterization Method
- In Proceedings of the 12th International Meshing Roundtable
, 2003
"... Parameterizations of triangulated surfaces are used in an increasing number of mesh processing applications for various purposes. Although demands vary, they are often required to preserve the surface metric and thus minimize angle, area and length deformation. However, most of the existing techniqu ..."
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Cited by 43 (3 self)
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Parameterizations of triangulated surfaces are used in an increasing number of mesh processing applications for various purposes. Although demands vary, they are often required to preserve the surface metric and thus minimize angle, area and length deformation. However, most of the existing techniques primarily target at angle preservation while disregarding global area deformation.
Interactive modeling of topologically complex geometric detail
- ACM Trans. Graph
, 2004
"... Volume textures aligned with a surface can be used to add topologically complex geometric detail to objects in an efficient way, while retaining an underlying simple surface structure. Adding a volume texture to a surface requires more than a conventional two-dimensional parameterization: a part of ..."
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Cited by 29 (1 self)
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Volume textures aligned with a surface can be used to add topologically complex geometric detail to objects in an efficient way, while retaining an underlying simple surface structure. Adding a volume texture to a surface requires more than a conventional two-dimensional parameterization: a part of the space surrounding the surface has to be parameterized. Another problem with using volume textures for adding geometric detail is the difficulty in rendering implicitly represented surfaces, especially when they are changed interactively. In this paper we present algorithms for constructing and rendering volume-textured surfaces. We demonstrate a number of interactive operations that these algorithms enable.
IGARASHI T.: Illumination brush: Interactive design of all-frequency lighting
- In Proc. Pacific Conference on Computer Graphics and Applications (2007), IEEE Computer Society
"... We present an appearance-based user interface for artists to efficiently design customized image-based lighting environments. 1 Our approach avoids typical iterations of parameter editing, rendering, and confirmation by providing a set of intuitive user interfaces for directly specifying the desired ..."
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Cited by 19 (0 self)
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We present an appearance-based user interface for artists to efficiently design customized image-based lighting environments. 1 Our approach avoids typical iterations of parameter editing, rendering, and confirmation by providing a set of intuitive user interfaces for directly specifying the desired appearance of the model in the scene. Then the system automatically creates the lighting environment by solving the inverse shading problem. To obtain a realistic image, all-frequency lighting is used with a spherical radial basis function (SRBF) representation. Rendering is performed using precomputed radiance transfer (PRT) to achieve a responsive speed. User experiments demonstrated the effectiveness of the proposed system compared to a previous approach. 1.
Sketch-Based Procedural Surface Modeling and Compositing Using Surface Trees
- EUROGRAPHICS
, 2008
"... We present a system for creating and manipulating layered procedural surface editing operations, which is motivated by the limited support for iterative design in free-form modeling. A combination of sketch-based and traditional modeling tools are used to design soft displacements, sharp creases, ex ..."
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Cited by 17 (4 self)
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We present a system for creating and manipulating layered procedural surface editing operations, which is motivated by the limited support for iterative design in free-form modeling. A combination of sketch-based and traditional modeling tools are used to design soft displacements, sharp creases, extrusions along 3D paths, and topological holes and handles. Using local parameterizations, these edits are combined in a dynamic hierarchy, enabling procedural operations like linked copy-and-paste and drag-and-drop layer-based editing. Such dynamic, layered "surface compositing" is formalized as a Surface Tree, an analog of CSG trees which generalizes previous hierarchical surface modeling techniques. By "anchoring" tree nodes in the parameter space of lower layers, our surface tree implementation can better preserve the semantics of an edit as the underlying surface changes. Details of our implementation are described, including an efficient procedural mesh data structure.
Template-Based Mesh Completion
, 2005
"... Meshes generated by range scanners and other acquisition tools are often incomplete and typically contain multiple connected components with irregular boundaries and complex holes. This paper introduces a robust algorithm for completion of such meshes using a mapping between the incomplete mesh and ..."
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Cited by 15 (1 self)
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Meshes generated by range scanners and other acquisition tools are often incomplete and typically contain multiple connected components with irregular boundaries and complex holes. This paper introduces a robust algorithm for completion of such meshes using a mapping between the incomplete mesh and a template model. The mapping is computed using a novel framework for bijective parameterization of meshes with gaps and holes. We employ this mapping to correctly glue together the components of the input mesh and to close the holes. The template is used to fill in the topological and geometric information missing in the input. The completed models are guaranteed to have the same topology as the template. Furthermore, if no appropriate template exists or if only topologically correct completion is required a standard canonical shape can be used as a template. As part of our completion method we propose a boundary-mapping technique useful for mesh editing operations such as merging, blending, and detail transfer. We demonstrate that by using this technique we can automatically perform complex editing operations that previously required a large amount of user interaction.
