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241
Geodesic Remeshing Using Front Propagation
, 2006
"... In this paper, we propose a complete framework for 3D geometry modeling and processing that uses only fast geodesic computations. The basic building block for these techniques is a novel greedy algorithm to perform a uniform or adaptive remeshing of a triangulated surface. Our other contributions in ..."
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Cited by 52 (7 self)
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In this paper, we propose a complete framework for 3D geometry modeling and processing that uses only fast geodesic computations. The basic building block for these techniques is a novel greedy algorithm to perform a uniform or adaptive remeshing of a triangulated surface. Our other contributions include a parameterization scheme based on barycentric coordinates, an intrinsic algorithm for computing geodesic centroidal tessellations, and a fast and robust method to flatten a genus-0 surface patch. On large meshes (more than 500,000 vertices), our techniques speed up computation by over one order of magnitude in comparison to classical remeshing and parameterization methods. Our methods are easy to implement and do not need multilevel solvers to handle complex models that may contain poorly shaped triangles.
Constrained Delaunay Tetrahedralizations and Provably Good Boundary Recovery
- In Eleventh International Meshing Roundtable
, 2002
"... In two dimensions, a constrained Delaunay triangulation (CDT) respects a set of segments that constrain the edges of the triangulation, while still maintaining most of the favorable properties of ordinary Delaunay triangulations (such as maximizing the minimum angle). CDTs solve the problem of enfor ..."
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Cited by 44 (1 self)
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In two dimensions, a constrained Delaunay triangulation (CDT) respects a set of segments that constrain the edges of the triangulation, while still maintaining most of the favorable properties of ordinary Delaunay triangulations (such as maximizing the minimum angle). CDTs solve the problem of enforcing boundary conformity---ensuring that triangulation edges cover the boundaries (both interior and exterior) of the domain being modeled. This paper discusses the three-dimensional analogue, constrained Delaunay tetrahedralizations (also called CDTs), and their advantages in mesh generation. CDTs maintain most of the favorable properties of ordinary Delaunay tetrahedralizations, but they are more difficult to work with, because some sets of constraining segments and facets simply do not have CDTs. However, boundary conformity can always be enforced by judicious insertion of additional vertices, combined with CDTs. This approach has three advantages over other methods for boundary recovery: it usually requires fewer additional vertices to be inserted, it yields provably good bounds on edge lengths (i.e. edges are not made unnecessarily short), and it interacts well with provably good Delaunay refinement methods for tetrahedral mesh generation.
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 44 (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 error-driven 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
Sparse Voronoi Refinement
- IN PROCEEDINGS OF THE 15TH INTERNATIONAL MESHING ROUNDTABLE
, 2006
"... ... a conformal Delaunay mesh in arbitrary dimension with guaranteed mesh size and quality. Our algorithm runs in output-sensitive time O(nlog(L/s) + m), with constants depending only on dimension and on prescribed element shape quality bounds. For a large class of inputs, including integer coordina ..."
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Cited by 42 (26 self)
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... a conformal Delaunay mesh in arbitrary dimension with guaranteed mesh size and quality. Our algorithm runs in output-sensitive time O(nlog(L/s) + m), with constants depending only on dimension and on prescribed element shape quality bounds. For a large class of inputs, including integer coordinates, this matches the optimal time bound of Θ(n log n + m). Our new technique uses interleaving: we maintain a sparse mesh as we mix the recovery of input features with the addition of Steiner vertices for quality improvement.
Quality Meshing with Weighted Delaunay Refinement
- SIAM J. Comput
, 2002
"... Delaunay meshes with bounded circumradius to shortest edge length ratio have been proposed in the past for quality meshing. The only poor quality tetrahedra called slivers that can occur in such a mesh can be eliminated by the sliver exudation method. This method has been shown to work for periodic ..."
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Cited by 40 (7 self)
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Delaunay meshes with bounded circumradius to shortest edge length ratio have been proposed in the past for quality meshing. The only poor quality tetrahedra called slivers that can occur in such a mesh can be eliminated by the sliver exudation method. This method has been shown to work for periodic point sets, but not with boundaries. Recently a randomized point-placement strategy has been proposed to remove slivers while conforming to a given boundary. In this paper we present a deterministic algorithm for generating a weighted Delaunay mesh which respects the input boundary and has no poor quality tetrahedron including slivers. This success is achieved by combining the weight pumping method for sliver exudation and the Delaunay refinement method for boundary conformation. We show that an incremental weight pumping can be mixed seamlessly with vertex insertions in our weighted Delaunay refinement paradigm. 1
Aggressive Tetrahedral Mesh Improvement
- In Proc. of the 16th Int. Meshing Roundtable
, 2007
"... Summary. We present a tetrahedral mesh improvement schedule that usually creates meshes whose worst tetrahedra have a level of quality substantially better than those produced by any previous method for tetrahedral mesh generation or “mesh clean-up. ” Our goal is to aggressively optimize the worst t ..."
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Cited by 39 (4 self)
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Summary. We present a tetrahedral mesh improvement schedule that usually creates meshes whose worst tetrahedra have a level of quality substantially better than those produced by any previous method for tetrahedral mesh generation or “mesh clean-up. ” Our goal is to aggressively optimize the worst tetrahedra, with speed a secondary consideration. Mesh optimization methods often get stuck in bad local optima (poor-quality meshes) because their repertoire of mesh transformations is weak. We employ a broader palette of operations than any previous mesh improvement software. Alongside the best traditional topological and smoothing operations, we introduce a topological transformation that inserts a new vertex (sometimes deleting others at the same time). We describe a schedule for applying and composing these operations that rarely gets stuck in a bad optimum. We demonstrate that all three techniques—smoothing, vertex insertion, and traditional transformations—are substantially more effective than any two alone. Our implementation usually improves meshes so that all dihedral angles are between 31 ◦ and 149 ◦ , or (with a different objective function) between 23 ◦ and 136 ◦. 1
Provably good sampling and meshing of surfaces
- Graphical Models
, 2005
"... The notion of ε-sample, introduced by Amenta and Bern, has proven to be a key concept in the theory of sampled surfaces. Of particular interest is the fact that, if E is an ε-sample of a C2-continuous surface S for a sufficiently small ε, then the Delaunay triangulation of E restricted to S is a goo ..."
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Cited by 37 (9 self)
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The notion of ε-sample, introduced by Amenta and Bern, has proven to be a key concept in the theory of sampled surfaces. Of particular interest is the fact that, if E is an ε-sample of a C2-continuous surface S for a sufficiently small ε, then the Delaunay triangulation of E restricted to S is a good approximation of S, both in a topological and in a geometric sense. Hence, if one can construct an ε-sample, one also gets a good approximation of the surface. Moreover, correct reconstruction is ensured by various algorithms. In this paper, we introduce the notion of loose ε-sample. We show that the set of loose ε-samples contains and is asymptotically identical to the set of ε-samples. The main advantage of loose ε-samples over ε-samples is that they are easier to check and to construct. We also present a simple algorithm that constructs provably good surface samples and meshes. Given a C2-continuous surface S without boundary, the algorithm generates a sparse ε-sample E and at the same time a triangulated surface Del|S(E). The triangulated surface has the same topological type as S, is close to S for the Hausdorff distance and can provide good approximations of normals, areas and curvatures. A notable feature of the algorithm is that the surface needs only to be known through an oracle that, given a line segment, detects whether the segment intersects the surface and, in the affirmative, returns the intersection points. This makes the algorithm useful in a wide variety of contexts and for a large class of surfaces. Key-words: Surface mesh generation, ε-sampling, surface approximation, restricted Delaunay triangulation, mesh refinement
Animating Wrinkles on Clothes
- Proc. IEEE Visualization ’99
, 1999
"... This paper describes a method to simulate realistic wrinkles on clothes without fine mesh and large computational overheads. Cloth has very little in-plane deformations, as most of the deformations come from buckling. This can be looked at as area conservation property of cloth. The area conservatio ..."
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Cited by 37 (1 self)
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This paper describes a method to simulate realistic wrinkles on clothes without fine mesh and large computational overheads. Cloth has very little in-plane deformations, as most of the deformations come from buckling. This can be looked at as area conservation property of cloth. The area conservation formulation of the method modulates the user defined wrinkle pattern, based on deformation of individual triangle. The methodology facilitates use of small in-plane deformation stiffnesses and a coarse mesh for the numeri-cal simulation, this makes cloth simulation fast and robust. More-over, the ability to design wrinkles (even on generalized deformable models) makes this method versatile for synthetic image genera-tion. The method inspired from cloth wrinkling problem, being ge-ometric in nature, can be extended to other wrinkling phenomena.
Grid generation and optimization based on centroidal Voronoi tessellations
- Appl. Math. Comput
"... www.elsevier.com/locate/amc ..."
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Mesh Generation for Domains with Small Angles
- Proc. 16th Annu. Sympos. Comput. Geom
, 2000
"... Nonmanifold geometric domains having small angles present special problems for triangular and tetrahedral mesh generators. Although small angles inherent in the input geometry cannot be removed, one would like to find a way to triangulate a domain without creating any new small angles. Unfortunately ..."
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Cited by 36 (1 self)
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Nonmanifold geometric domains having small angles present special problems for triangular and tetrahedral mesh generators. Although small angles inherent in the input geometry cannot be removed, one would like to find a way to triangulate a domain without creating any new small angles. Unfortunately, this problem is not always soluble. I discuss how mesh generation algorithms based on Delaunay refinement can be modified to ensure that they always produce a mesh, and to ensure that poor quality triangles or tetrahedra appear only near small input angles. 1 Introduction The Delaunay refinement algorithms for triangular mesh generation introduced by Jim Ruppert [4] and Paul Chew [1] are almost entirely satisfying in theory and in practice. However, one unresolved problem has limited their applicability: they do not always mesh domains with small angles well---or at all---especially if these domains are nonmanifold. This problem is not just true of Delaunay refinement algorithms; it ste...
