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Anisotropic Polygonal Remeshing
"... In this paper, we propose a novel polygonal remeshing technique that exploits a key aspect of surfaces: the intrinsic anisotropy of natural or manmade geometry. In particular, we use curvature directions to drive the remeshing process, mimicking the lines that artists themselves would use when cre ..."
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Cited by 166 (16 self)
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In this paper, we propose a novel polygonal remeshing technique that exploits a key aspect of surfaces: the intrinsic anisotropy of natural or manmade geometry. In particular, we use curvature directions to drive the remeshing process, mimicking the lines that artists themselves would use when creating 3D models from scratch. After extracting and smoothing the curvature tensor field of an input genus0 surface patch, lines of minimum and maximum curvatures are used to determine appropriate edges for the remeshed version in anisotropic regions, while spherical regions are simply pointsampled since there is no natural direction of symmetry locally. As a result our technique generates polygon meshes mainly composed of quads in anisotropic regions, and of triangles in spherical regions. Our approach provides the flexibility to produce meshes ranging from isotropic to anisotropic, from coarse to dense, and from uniform to curvature adapted.
Laplacian Surface Editing
, 2004
"... Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. We p ..."
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Cited by 162 (20 self)
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Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. We provide such a representation of a surface, based on the Laplacian of the mesh, by encoding each vertex relative to its neighborhood. The Laplacian of the mesh is enhanced to be invariant to locally linearized rigid transformations and scaling. Based on this Laplacian representation, we develop useful editing operations: interactive freeform deformation in a region of interest based on the transformation of a handle, transfer and mixing of geometric details between two surfaces, and transplanting of a partial surface mesh onto another surface. The main computation involved in all operations is the solution of a sparse linear system, which can be done at interactive rates. We demonstrate the effectiveness of our approach in several examples, showing that the editing operations change the shape while respecting the structural geometric detail.
Explicit Surface Remeshing
, 2003
"... We present a new remeshing scheme based on the idea of improving mesh quality by a series of local modifications of the mesh geometry and connectivity. Our contribution to the family of local modification techniques is an areabased smoothing technique. Areabased smoothing allows the control of bo ..."
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Cited by 60 (7 self)
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We present a new remeshing scheme based on the idea of improving mesh quality by a series of local modifications of the mesh geometry and connectivity. Our contribution to the family of local modification techniques is an areabased smoothing technique. Areabased smoothing allows the control of both triangle quality and vertex sampling over the mesh, as a function of some criteria, e.g. the mesh curvature. To perform local modifications of arbitrary genus meshes we use dynamic patchwise parameterization. The parameterization is constructed and updated onthefly as the algorithm progresses with local updates. As a postprocessing stage, we introduce a new algorithm to improve the regularity of the mesh connectivity. The algorithm is able to create an unstructured mesh with a very small number of irregular vertices. Our remeshing scheme is robust, runs at interactive speeds and can be applied to arbitrary complex meshes.
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
 COMPUTERAIDED GEOMETRIC DESIGN
, 2005
"... In this paper, we propose a new quadrilateral remeshing method for manifolds of arbitrary genus that is at once general, flexible, and efficient. Our technique is based on the use of smooth harmonic scalar fields defined over the mesh. Given such a field, we compute its gradient field and a second v ..."
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Cited by 57 (1 self)
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In this paper, we propose a new quadrilateral remeshing method for manifolds of arbitrary genus that is at once general, flexible, and efficient. Our technique is based on the use of smooth harmonic scalar fields defined over the mesh. Given such a field, we compute its gradient field and a second vector field that is everywhere orthogonal to the gradient. We then trace integral lines through these vector fields to sample the mesh. The two nets of integral lines together are used to form the polygons of the output mesh. Curvaturesensitive spacing of the lines provides for anisotropic meshes that adapt to the local shape. Our scalar field construction allows users to exercise extensive control over the structure of the final mesh. The entire process is performed without computing an explicit parameterization of the surface, and is thus applicable to manifolds of any genus without the need for cutting the surface into patches.
Isotropic remeshing of surfaces: A local parameterization approach
 In Proceedings of 12th International Meshing Roundtable
, 2003
"... We present a method for isotropic remeshing of arbitrary genus surfaces. The method is based on a mesh adaptation process, namely, a sequence of local modifications performed on a copy of the original mesh, while referring to the original mesh geometry. The algorithm has three stages. In the first s ..."
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Cited by 39 (4 self)
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We present a method for isotropic remeshing of arbitrary genus surfaces. The method is based on a mesh adaptation process, namely, a sequence of local modifications performed on a copy of the original mesh, while referring to the original mesh geometry. The algorithm has three stages. In the first stage the required number or vertices are generated by iterative simplification or refinement. The second stage performs an initial vertex partition using an areabased relaxation method. The third stage achieves precise isotropic vertex sampling prescribed by a given density function on the mesh. We use a modification of Lloyd’s relaxation method to construct a weighted centroidal Voronoi tessellation of the mesh. We apply these iterations locally on small patches of the mesh that are parameterized into the 2D plane. This allows us to handle arbitrary complex meshes with any genus and any number of boundaries. The efficiency and the accuracy of the remeshing process is achieved using a patchwise parameterization technique.
An Incremental Approach to Feature Aligned Quad Dominant Remeshing
, 2008
"... In this paper we present a new algorithm which turns an unstructured triangle mesh into a quaddominant mesh with edges aligned to the principal directions of the underlying geometry. Instead of computing a globally smooth parameterization or integrating curvature lines along a tangent vector field, ..."
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Cited by 16 (3 self)
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In this paper we present a new algorithm which turns an unstructured triangle mesh into a quaddominant mesh with edges aligned to the principal directions of the underlying geometry. Instead of computing a globally smooth parameterization or integrating curvature lines along a tangent vector field, we simply apply an iterative relaxation scheme which incrementally aligns the mesh edges to the principal directions. The quaddominant mesh is eventually obtained by dropping the notaligned diagonals from the triangle mesh. A postprocessing stage is introduced to further improve the results. The major advantage of our algorithm is its conceptual simplicity since it is merely based on elementary mesh operations such as edge collapse, flip, and split. The resulting meshes exhibit a very good alignment to surface features and rather uniform distribution of mesh vertices. This makes them very wellsuited, e.g., as CatmullClark Subdivision control meshes.
Feature sensitive mesh segmentation
 In ACM symposium on Solid and physical modeling (2006), ACM
, 2006
"... Copyright © 2006 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for commercial advantage and that copies bear this notice and ..."
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Cited by 14 (5 self)
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Copyright © 2006 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee.
Anisotropic mesh adaptation for evolving triangulated surfaces
 In: Proc. 15th International Meshing Roundtable. (2006
, 1989
"... Summary. Dynamic surfaces arise in many applications, such as free surfaces in multiphase ows and moving interfaces in uidsolid interactions. In many applications, an explicit surface triangulation is used to track the dynamic surfaces, posing signi cant challenges in adapting their meshes, especia ..."
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Cited by 13 (2 self)
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Summary. Dynamic surfaces arise in many applications, such as free surfaces in multiphase ows and moving interfaces in uidsolid interactions. In many applications, an explicit surface triangulation is used to track the dynamic surfaces, posing signi cant challenges in adapting their meshes, especially if large curvatures and sharp features may dynamically appear or vanish as the surfaces evolve. In this paper, we present an anisotropic mesh adaptation technique to meet these challenges. Our technique strives for optimal aspect ratios of the triangulation to reduce interpolation errors and to capture geometric features based on a novel extension of the quadricbased surface analysis. Our adaptation algorithm combines the operations of vertex redistribution, edge ipping, edge contraction, and edge splitting. Experimental results demonstrate the e ectiveness of our anisotropic adaptation techniques for static and dynamic surfaces. Key words: Mesh adaptation; anisotropic meshes; dynamic surfaces; feature preservation 1
Perceptually driven interactive geometry remeshing
 In ACM I3D’06 (2006
"... Figure 1: Bump mapped vase (a) created using a normal map and geometric model. The shading calculation transforms the normal map into a color pattern which is gathered into a color map (b). The perceptual properties of the color map are then evaluated using a visual discrimination metric. The bright ..."
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Cited by 8 (2 self)
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Figure 1: Bump mapped vase (a) created using a normal map and geometric model. The shading calculation transforms the normal map into a color pattern which is gathered into a color map (b). The perceptual properties of the color map are then evaluated using a visual discrimination metric. The brighter region in the map (c) indicates stronger visual masking. This map is then used to guide the placement of vertex samples (d) in the geometry remeshing stage. Visual patterns on the surface of an object, such as two dimensional texture, are taken into consideration as part of the geometry remeshing process. Given a parameterized mesh and a texture map, the visual perceptual properties of the texture are first computed using a visual difference metric. This precomputation is then used to guide the distribution of samples to the surface mesh. The system automatically distributes few samples to texture areas with strong visual masking properties and more samples to texture areas with weaker visual masking properties. In addition, due to contrast considerations, brighter areas receive fewer samples than do darker surface features. Because of the properties of the human visual system, especially visual masking, the artifacts in the rendered mesh are invisible to the human observer. For a fixed number of polygons, this approach also improves the quality of the rendered mesh since the distribution of the samples is guided by the principles of visual perception. The utility of the system is demonstrated by showing that it can also account for other observable patterns on the surface, besides two dimensional texture, such as those produced by bump mapping, lighting variations, reflection models, and interreflections.
Quadrangulating a Mesh using Laplacian Eigenvectors
, 2005
"... Resampling raw surface meshes is one of the most fundamental operations used by nearly all digital geometry processing systems. The vast majority of work in the past has focused on triangular remeshing; the equally important problem of resampling surfaces with quadrilaterals has remained largely un ..."
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Cited by 8 (0 self)
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Resampling raw surface meshes is one of the most fundamental operations used by nearly all digital geometry processing systems. The vast majority of work in the past has focused on triangular remeshing; the equally important problem of resampling surfaces with quadrilaterals has remained largely unaddressed. Despite the relative lack of attention, the need for quality quadrangular resampling methods is of central importance in a number of important areas of graphics. Quadrilaterals are the preferred primitive in many cases, such as CatmullClark subdivision surfaces, fluid dynamics, and texture atlasing. We propose a fundamentally new approach to the problem of quadrangulating manifold polygon meshes. By applying a Morsetheoretic analysis to the eigenvectors of the mesh Laplacian, we have developed an algorithm that can correctly quadrangulate any manifold, no matter its genus. Because of the properties of the Laplacian operator, the resulting quadrangular patches are wellshaped and arise directly from intrinsic properties of the surface, rather than from arbitrary heuristics. We demonstrate that this quadrangulation of the surface provides a base complex that is wellsuited to semiregular remeshing of the initial surface into a fully conforming mesh composed exclusively of quadrilaterals.