Manifold Parameterization

@inproceedings{Zhang2006ManifoldP,
  title={Manifold Parameterization},
  author={Lei Zhang and Ligang Liu and Zhongping Ji and Guo-jin Wang},
  booktitle={Computer Graphics International},
  year={2006}
}
Manifold parameterization considers the problem of parameterizing a given triangular mesh onto another mesh surface, which could be particularly plane or sphere surfaces. [...] Key Method The connectivity graph of source mesh is used to approximate the geometry of target mesh using least squares meshes. A subset of user specified vertices are constrained to have the geometry information of the target mesh.Expand
Consistent Correspondence between Arbitrary Manifold Surfaces
TLDR
A novel mean-value Laplacian fitting scheme is proposed, which aims at computing a shape-preserving (conformal) correspondence directly in 3D-to-3D space, efficiently avoiding local optimum caused by the nearest-point search, and achieving good results even with only a few marker points. Expand
Mesh Parametrization Driven by Unit Normal Flow
TLDR
Based on mesh deformation, this work derives and defines a novel geometric flow: ‘unit normal flow (UNF)’ and proves that if UNF converges, it will deform a surface to a constant mean curvature (CMC) surface, such as planes and spheres. Expand
Partwise Cross-Parameterization via Nonregular Convex Hull Domains
TLDR
A novel partwise framework for cross-parameterization between 3D mesh models, which exploits properties of the convex hull, e.g., good approximation ability and linear convex representation for interior vertices. Expand
Least-Squares Morphing of Dynamic Meshes
TLDR
This paper presents a method for morphing of two dynamic meshes: mesh sequences representing the keyframes of animated shapes over time, entirely mesh-based and does not demand the generation of skeletons, mesh segmentation or the use of any additional control structures. Expand
Distortion-minimizing injective maps between surfaces
TLDR
This work provides a formulation that yields a map between two disk-topology meshes, which is continuous and injective by construction and which locally minimizes intrinsic distortion, and demonstrates that, despite the challenges inherent to the more involved setting, discrete surface-to-surface maps can be optimized effectively. Expand
Template-Based 3D Model Fitting Using Dual-Domain Relaxation
TLDR
The usefulness of the template fitting method to the application of consistent surface parameterization (also known as cross-parameterization) is demonstrated and the method is shown to encourage near-equilateral mesh elements and significantly reduces the occurrence of triangle foldovers. Expand
Dual Laplacian morphing for triangular meshes
TLDR
A novel morphing approach for 3D triangular meshes with the same topology that can generate visual pleasing and physical plausible morphing sequences and avoid the shrinkage and kinks appeared in the linear interpolation method. Expand
Dual Laplacian morphing for triangular meshes
TLDR
A novel morphing approach for 3D triangular meshes with the same topology that can generate visual pleasing and physical plausible morphing sequences and avoid the shrinkage and kinks appeared in the linear interpolation method. Expand
Inter-surface maps via constant-curvature metrics
TLDR
A novel approach to represent maps between two discrete surfaces of the same genus and to minimize intrinsic mapping distortion, built upon the fact that such metrics exist on surfaces of arbitrary topology, without the need for any cuts or cones. Expand
Three-dimensional morphing of similar shapes using a template mesh
Shape morphing is the process of transforming a source shape into a target shape, through a series of intermediate shapes. There are two important problems to be considered in three-dimensional shapeExpand
...
1
2
...

References

SHOWING 1-10 OF 23 REFERENCES
Fundamentals of spherical parameterization for 3D meshes
TLDR
A generalization of the method of barycentric coordinates for planar parameterization which solves the spherical parameterization problem is described, its correctness is proved by establishing a connection to spectral graph theory and how to compute these parameterizations is shown. Expand
Least-squares meshes
TLDR
The least-squares meshes (LS-meshes) are a visually smooth and fair approximation of the given control points and it is shown that the connectivity of the mesh contains geometric information that affects the shape of the reconstructed surface. Expand
MAPS: multiresolution adaptive parameterization of surfaces
TLDR
An irregular connectivity mesh representative of a surface having an arbitrary topology is processed to generate a parameterization which maps points in a coarse base domain to points in the mesh, such that the original mesh can be reconstructed from the base domain and the parameterization. Expand
Geometry images
TLDR
This paper proposes to remesh an arbitrary surface onto a completely regular structure the authors call a geometry image, which captures geometry as a simple 2D array of quantized points. Expand
Spherical parametrization and remeshing
TLDR
This work introduces a robust technique for directly parametrizing a genus-zero surface onto a spherical domain, and proposes a scheme for sampling the spherical domain using uniformly subdivided polyhedral domains, namely the tetrahedron, octahedrons, and cube. Expand
Spherical Parametrization and Remeshing
Recently, Gu et al. [2002] introduced geometry images, in which geometry is resampled into a completely regular 2D grid. The process involves cutting the surface into a disk using a network of cutExpand
Multiresolution mesh morphing
TLDR
This work presents a new method for user controlled morphing of two homeomorphic triangle meshes of arbitrary topology using the MAPS algorithm to parameterize both meshes over simple base domains and an additional harmonic map bringing the latter into correspondence. Expand
Cross-parameterization and compatible remeshing of 3D models
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 twoExpand
Consistent mesh parameterizations
TLDR
This paper proposes an algorithm which establishes parameterizations for a set of models which share the same base domain and respect features, and demonstrates the versatility of this algorithm with a number of examples. Expand
Spanning tree seams for reducing parameterization distortion of triangulated surfaces
  • A. Sheffer
  • Mathematics
  • Proceedings SMI. Shape Modeling International 2002
  • 2002
Providing a two-dimensional parameterization of three-dimensional tessellated surfaces is beneficial to many applications in computer graphics, finite-element surface meshing, surface reconstructionExpand
...
1
2
3
...