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65
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 342 (24 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.
Texture Synthesis on Surfaces
 ACM SIGGRAOH 2001
, 2001
"... Many natural and manmade surface patterns are created by interactions between texture elements and surface geometry. We believe that the best way to create such patterns is to synthesize a texture directly on the surface of the model. Given a texture sample in the form of an image, we create a simi ..."
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Cited by 186 (5 self)
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Many natural and manmade surface patterns are created by interactions between texture elements and surface geometry. We believe that the best way to create such patterns is to synthesize a texture directly on the surface of the model. Given a texture sample in the form of an image, we create a similar texture over an irregular mesh hierarchy that has been placed on a given surface. Our method draws upon texture synthesis methods that use image pyramids, and we use a mesh hierarchy to serve in place of such pyramids. First, we create a hierarchy of points from low to high density over a given surface, and we connect these points to form a hierarchy of meshes. Next, the user specifies a vector field over the surface that indicates the orientation of the texture. The mesh vertices on the surface are then sorted in such a way that visiting the points in order will follow the vector field and will sweep across the surface from one end to the other. Each point is then visited in turn to determine its color. The color of a particular point is found by examining the color of neighboring points and finding the best match to a similar pixel neighborhood in the given texture sample. The color assignment is done in a coarsetofine manner using the mesh hierarchy. A texture created this way fits the surface naturally and seamlessly.
MultiChart Geometry Images
, 2003
"... We introduce multichart geometry images, a new representation for arbitrary surfaces. It is created by resampling a surface onto a regular 2D grid. Whereas the original scheme of Gu et al. maps the entire surface onto a single square, we use an atlas construction to map the surface piecewise onto c ..."
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Cited by 117 (4 self)
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We introduce multichart geometry images, a new representation for arbitrary surfaces. It is created by resampling a surface onto a regular 2D grid. Whereas the original scheme of Gu et al. maps the entire surface onto a single square, we use an atlas construction to map the surface piecewise onto charts of arbitrary shape. We demonstrate that this added flexibility reduces parametrization distortion and thus provides greater geometric fidelity, particularly for shapes with long extremities, high genus, or disconnected components. Traditional atlas constructions suffer from discontinuous reconstruction across chart boundaries, which in our context create unacceptable surface cracks. Our solution is a novel zippering algorithm that creates a watertight surface. In addition, we present a new atlas chartification scheme based on clustering optimization.
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.
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, intersurface 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, intersurface 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.
Seamster: Inconspicuous lowdistortion texture seam layout
 In: Proc. IEEE Visualization 2002
, 2002
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Optimally cutting a surface into a disk
 Discrete & Computational Geometry
, 2002
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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 intersurface mapping, and demonstrates a variety of parameterization applications.
Optimal system of loops on an orientable surface
 DISCRETE COMPUT. GEOM
, 2005
"... Every compact orientable boundaryless surface M can be cut along simple loops with a common point v0, pairwise disjoint except at v0, so that the resulting surface is a topological disk; such a set of loops is called a system of loops for M. The resulting disk may be viewed as a polygon in which the ..."
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Cited by 43 (4 self)
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Every compact orientable boundaryless surface M can be cut along simple loops with a common point v0, pairwise disjoint except at v0, so that the resulting surface is a topological disk; such a set of loops is called a system of loops for M. The resulting disk may be viewed as a polygon in which the sides are pairwise identified on the surface; it is called a polygonal schema. Assuming that M is a combinatorial surface, and that each edge has a given length, we are interested in a shortest (or optimal) system of loops homotopic to a given one, drawn on the vertexedge graph of M. We prove that each loop of such an optimal system is a shortest loop among all simple loops in its homotopy class. We give an algorithm to build such a system, which has polynomial running time if the lengths of the edges are uniform. As a byproduct, we get an algorithm with the same running time to compute a shortest simple loop homotopic to a given simple loop.
Texture Synthesis for 3D Shape Representation
 IEEE Transactions on Visualization and Computer Graphics
"... Considerable evidence suggests that a viewer’s perception of the 3D shape of a polygonallydefined object can be significantly affected (either masked or enhanced) by the presence of a surface texture pattern. However investigations into the specific mechanisms of texture’s effect on shape perceptio ..."
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Cited by 41 (3 self)
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Considerable evidence suggests that a viewer’s perception of the 3D shape of a polygonallydefined object can be significantly affected (either masked or enhanced) by the presence of a surface texture pattern. However investigations into the specific mechanisms of texture’s effect on shape perception are still ongoing and the question of how to design and apply a texture pattern to a surface in order to best facilitate shape perception remains open. Recently, we have suggested that for anisotropic texture patterns, the accuracy of shape judgments may be significantly affected by the orientation of the surface texture pattern anisotropy with respect to the principal directions of curvature over the surface. However it has been difficult, until this time, to conduct controlled studies specifically investigating the effect of texture orientation on shape perception because there has been no simple and reliable method for texturing an arbitrary doubly curved surface with a specified input pattern such that the dominant orientation of the pattern everywhere follows a predefined directional vector field over the surface, while seams and projective distortion of the pattern are avoided. In this paper, we present a straightforward and highly efficient method for achieving such a texture and describe how it can potentially be used to enhance shape representation. Specifically, we describe a novel, efficient, automatic algorithm for