Linear Surface Reconstruction from Discrete Fundamental Forms on Triangle Meshes

@article{Wang2012LinearSR,
  title={Linear Surface Reconstruction from Discrete Fundamental Forms on Triangle Meshes},
  author={Yue Wang and B. Liu and Y. Tong},
  journal={Comput. Graph. Forum},
  year={2012},
  volume={31},
  pages={2277-2287}
}
We present a linear algorithm to reconstruct the vertex coordinates for a surface mesh given its edge lengths and dihedral angles, unique up to rotation and translation. A local integrability condition for the existence of an immersion of the mesh in 3D Euclidean space is provided, mirroring the fundamental theorem of surfaces in the continuous setting (i.e., Gauss’s equation and the Mainardi-Codazzi equations) if we regard edge lengths as the discrete first fundamental form and dihedral angles… CONTINUE READING
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