# 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

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#### 15 Citations

Consistent Correspondence between Arbitrary Manifold Surfaces

- Mathematics, Computer Science
- 2007 IEEE 11th International Conference on Computer Vision
- 2007

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

- Physics, Computer Science
- Comput. Graph. Forum
- 2020

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

- Computer Science, Medicine
- IEEE Transactions on Visualization and Computer Graphics
- 2011

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

- Mathematics, Computer Science
- 2017 30th SIBGRAPI Conference on Graphics, Patterns and Images (SIBGRAPI)
- 2017

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

- Computer Science
- ACM Trans. Graph.
- 2019

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

- Computer Science, Medicine
- IEEE Transactions on Visualization and Computer Graphics
- 2011

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

- Computer Science
- 2007

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

- Computer Science
- Comput. Animat. Virtual Worlds
- 2007

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

- Computer Science, Mathematics
- ACM Trans. Graph.
- 2020

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

- Mathematics
- 2009

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 shape… Expand

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