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76
QuadCover – Surface Parameterization using Branched Coverings.
 COMPUT. GRAPH. FORUM
, 2007
"... We introduce an algorithm for automatic computation of global parameterizations on arbitrary simplicial 2manifolds whose parameter lines are guided by a given frame field, for example by principal curvature frames. The parameter lines are globally continuous, and allow a remeshing of the surface in ..."
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Cited by 98 (11 self)
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We introduce an algorithm for automatic computation of global parameterizations on arbitrary simplicial 2manifolds whose parameter lines are guided by a given frame field, for example by principal curvature frames. The parameter lines are globally continuous, and allow a remeshing of the surface into quadrilaterals. The algorithm converts a given frame field into a single vector field on a branched covering of the 2manifold, and generates an integrable vector field by a Hodge decomposition on the covering space. Except for an optional smoothing and alignment of the initial frame field, the algorithm is fully automatic and generates high quality quadrilateral meshes.
Harmonic guidance for surface deformation
 In Proc. of Eurographics 05
, 2005
"... We present an interactive method for applying deformations to a surface mesh while preserving its global shape and local properties. Two surface editing scenarios are discussed, which conceptually differ in the specification of deformations: Either interpolation constraints are imposed explicitly, e ..."
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Cited by 66 (14 self)
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We present an interactive method for applying deformations to a surface mesh while preserving its global shape and local properties. Two surface editing scenarios are discussed, which conceptually differ in the specification of deformations: Either interpolation constraints are imposed explicitly, e.g., by dragging a subset of vertices, or, deformation of a reference surface is mimicked. The contribution of this paper is a novel approach for interpolation of local deformations over the manifold and for efficiently establishing correspondence to a reference surface from only few pairs of markers. As a general tool for both scenarios, a harmonic field is constructed to guide the interpolation of constraints and to find correspondence required for deformation transfer. We show that our approach fits nicely in a unified mathematical framework, where the same type of linear operator is applied in all phases, and how this approach can be used to create an intuitive and interactive editing tool. Figure 1: A simple edit: The visualized harmonic field is used as guidance for bending the cactus (left). Here, the field is defined by one source (red) at the tip of the left arm and one sink (blue) below the middle of the trunk. The result is shown in the center image. Notice the different propagation of the rotation compared to the edit on the right, where three sources on all arms were chosen (without picture). 1.
Rotational Symmetry Field Design on Surfaces
"... tensor smoothed as a 4RoSy field, (c) topological editing operations applied to (b), and (d) more global smoothing performed on (b). Notice that treating the curvature tensor as a 4RoSy field (b) leads to fewer unnatural singularities and therefore less visual artifacts than as a 2RoSy field (a). ..."
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Cited by 63 (8 self)
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tensor smoothed as a 4RoSy field, (c) topological editing operations applied to (b), and (d) more global smoothing performed on (b). Notice that treating the curvature tensor as a 4RoSy field (b) leads to fewer unnatural singularities and therefore less visual artifacts than as a 2RoSy field (a). In addition, both topological editing (c) and global smoothing (d) can be used to remove more singularities from (b). However, topological editing (c) provides local control while excessive global smoothing (d) can cause hatch directions to deviate from their natural orientations (neck and chest). Designing rotational symmetries on surfaces is a necessary task for a wide variety of graphics applications, such as surface parameterization and remeshing, painterly rendering and penandink sketching, and texture synthesis. In these applications, the topology of a rotational symmetry field such as singularities and separatrices can have a direct impact on the quality of the results. In this paper, we present a design system that provides control over the topology of rotational symmetry fields on surfaces. As the foundation of our system, we provide comprehensive analysis for rotational symmetry fields on surfaces and present efficient algorithms to identify singularities and separatrices. We also describe design operations that allow a rotational symmetry field to be created and modified in an intuitive fashion by using the idea of basis fields and relaxation. In particular, we provide control over the topology of a rotational symmetry field by allowing the user to remove singularities from the field or to move them to more desirable locations.
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 56 (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.
Interactive tensor field design and visualization on surfaces
 Online]. Available: http://eecs.oregonstate.edu/library/files/2005106/tenflddesn.pdf
, 2005
"... Abstract—Designing tensor fields in the plane and on surfaces is a necessary task in many graphics applications, such as painterly rendering, penandink sketching of smooth surfaces, and anisotropic remeshing. In this article, we present an interactive design system that allows a user to create a w ..."
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Cited by 49 (19 self)
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Abstract—Designing tensor fields in the plane and on surfaces is a necessary task in many graphics applications, such as painterly rendering, penandink sketching of smooth surfaces, and anisotropic remeshing. In this article, we present an interactive design system that allows a user to create a wide variety of symmetric tensor fields over 3D surfaces either from scratch or by modifying a meaningful input tensor field such as the curvature tensor. Our system converts each user specification into a basis tensor field and combines them with the input field to make an initial tensor field. However, such a field often contains unwanted degenerate points which cannot always be eliminated due to topological constraints of the underlying surface. To reduce the artifacts caused by these degenerate points, our system allows the user to move a degenerate point or to cancel a pair of degenerate points that have opposite tensor indices. These operations provide control over the number and location of the degenerate points in the field. We observe that a tensor field can be locally converted into a vector field so that there is a onetoone correspondence between the set of degenerate points in the tensor field and the set of singularities in the vector field. This conversion allows us to effectively perform degenerate point pair cancellation and movement by using similar operations for vector fields. In addition, we adapt the imagebased flow visualization technique to tensor fields, therefore allowing interactive display of tensor fields on surfaces. We demonstrate the capabilities of our tensor field design system with painterly rendering, penandink sketching of surfaces, and anisotropic remeshing. Index Terms—Tensor field design, tensor field visualization, nonphotorealistic rendering, surfaces, remeshing, tensor field topology. 1
Volumetric Parameterization and Trivariate Bspline Fitting using Harmonic Functions
"... We present a methodology based on discrete volumetric harmonic functions to parameterize a volumetric model in a way that it can be used to fit a single trivariate Bspline to data so that simulation attributes can also be modeled. The resulting model representation is suitable for isogeometric anal ..."
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Cited by 45 (3 self)
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We present a methodology based on discrete volumetric harmonic functions to parameterize a volumetric model in a way that it can be used to fit a single trivariate Bspline to data so that simulation attributes can also be modeled. The resulting model representation is suitable for isogeometric analysis [Hughes T.J. 2005]. Input data consists of both a closed triangle mesh representing the exterior geometric shape of the object and interior triangle meshes that can represent material attributes or other interior features. The trivariate Bspline geometric and attribute representations are generated from the resulting parameterization, creating trivariate Bspline material property representations over the same parameterization in a way that is related to [Martin and Cohen 2001] but is suitable for application to a much larger family of shapes and attributes. The technique constructs a Bspline representation with guaranteed quality of approximation to the original data. Then we focus attention on a model of simulation interest, a femur, consisting of hard outer cortical bone and inner trabecular bone. The femur is a reasonably complex object to model with a single trivariate Bspline since the shape overhangs make it impossible to model by sweeping planar slices. The representation is used in an elastostatic isogeometric analysis, demonstrating its ability to suitably represent objects for isogeometric analysis.
Recent advances in remeshing of surfaces
 Shape Analysis and Structuring, Mathematics and Visualization
, 2008
"... Summary. Remeshing is a key component of many geometric algorithms, including modeling, editing, animation and simulation. As such, the rapidly developing field of geometry processing has produced a profusion of new remeshing techniques over the past few years. In this paper we survey recent develop ..."
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Cited by 45 (1 self)
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Summary. Remeshing is a key component of many geometric algorithms, including modeling, editing, animation and simulation. As such, the rapidly developing field of geometry processing has produced a profusion of new remeshing techniques over the past few years. In this paper we survey recent developments in remeshing of surfaces, focusing mainly on graphics applications. We classify the techniques into five categories based on their end goal: structured, compatible, high quality, feature and errordriven remeshing. We limit our description to the main ideas and intuition behind each technique, and a brief comparison between some of the techniques. We also list some open questions and directions for future research. 1
Shape Analysis Using the Auto Diffusion Function
 Comp. Graph. Forum
"... Scalar functions defined on manifold triangle meshes is a starting point for many geometry processing algorithms such as mesh parametrization, skeletonization, and segmentation. In this paper, we propose the Auto Diffusion Function (ADF) which is a linear combination of the eigenfunctions of the Lap ..."
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Cited by 42 (0 self)
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Scalar functions defined on manifold triangle meshes is a starting point for many geometry processing algorithms such as mesh parametrization, skeletonization, and segmentation. In this paper, we propose the Auto Diffusion Function (ADF) which is a linear combination of the eigenfunctions of the LaplaceBeltrami operator in a way that has a simple physical interpretation. The ADF of a given 3D object has a number of further desirable properties: Its extrema are generally at the tips of features of a given object, its gradients and level sets follow or encircle features, respectively, it is controlled by a single parameter which can be interpreted as feature scale, and, finally, the ADF is invariant to rigid and isometric deformations. We describe the ADF and its properties in detail and compare it to other choices of scalar functions on manifolds. As an example of an application, we present a pose invariant, hierarchical skeletonization and segmentation algorithm which makes direct use of the ADF.
Spectral quadrangulation with orientation and alignment control
 IN ACM SIGGRAPH ASIA
, 2008
"... This paper presents a new quadrangulation algorithm, extending the spectral surface quadrangulation approach where the coarse quadrangular structure is derived from the MorseSmale complex of an eigenfunction of the Laplacian operator on the input mesh. In contrast to the original scheme, we provi ..."
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Cited by 37 (10 self)
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This paper presents a new quadrangulation algorithm, extending the spectral surface quadrangulation approach where the coarse quadrangular structure is derived from the MorseSmale complex of an eigenfunction of the Laplacian operator on the input mesh. In contrast to the original scheme, we provide flexible explicit controls of the shape, size, orientation and feature alignment of the quadrangular faces. We achieve this by proper selection of the optimal eigenvalue (shape), by adaption of the area term in the Laplacian operator (size), and by adding special constraints to the Laplace eigenproblem (orientation and alignment). By solving a generalized eigenproblem we can generate a scalar field on the mesh whose MorseSmale complex is of high quality and satisfies all the user requirements. The final quadrilateral mesh is generated from the MorseSmale complex by computing a globally smooth parametrization. Here we additionally introduce edge constraints to preserve user specified feature lines accurately.