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Mean value coordinates for closed triangular meshes
Open accessAbstract
Constructing a function that interpolates a set of values defined at vertices of a mesh is a fundamental operation in computer graphics. Such an interpolant has many uses in applications such as shading, parameterization and deformation. For closed polygons, mean value coordinates have been proven to be an excellent method for constructing such an interpolant. In this paper, we generalize mean value coordinates from closed 2D polygons to closed triangular meshes. Given such a mesh P , we show that these coordinates are continuous everywhere and smooth on the interior of P . The coordinates are linear on the triangles of P and can reproduce linear functions on the interior of P . To illustrate their usefulness, we conclude by considering several interesting applications including constructing volumetric textures and surface deformation.
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Cited by
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Sukumar, N., & Srivastava, A. (2022) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2021.114333 · Cited by 426
Harmonic coordinates for character articulation
Joshi, P., Meyer, M., DeRose, T., Green, B., & Sanocki, T. (2007) · ACM Transactions on Graphics · doi:10.1145/1276377.1276466 · Cited by 401
Bounded biharmonic weights for real-time deformation
Jacobson, A., Baran, I., Popović, J., & Sorkine, O. (2011) · ACM SIGGRAPH 2011 papers · doi:10.1145/1964921.1964973 · Cited by 258
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Metadata
- Authors
- Ju, T., Schaefer, S., & Warren, J.
- Venue
- ACM Transactions on Graphics
- Published
- 2005-07
- Volume
- 24
- Issue
- 3
- Pages
- 561-566
- ISSN
- 0730-0301 (ISSN-L)
- 1557-7368
- OpenAlex
- W2160692760
- Cited by
- 564
- References
- 0
- FWCI
- 30.73
- Type
- journal article
- Language
- en
- Open access
- bronze
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