Discrete differential geometry of triangle tiles and algebra of closed trajectories
<|reference_start|>Discrete differential geometry of triangle tiles and algebra of closed trajectories: This paper proposes a new mathematical framework that can be applied to biological problems such as analysis of the structures of proteins and protein complexes. In particular, it gives a new method for encoding the three-dimensional structure of a protein into a binary sequence, where proteins are approximated by a folded tetrahedron sequence. It also gives a new algebraic framework for describing molecular complexes and their interactions.   For simplicity, we shall explain the framework in the case of two-dimensional objects. Then, the binary code of a plane curve is obtained as the ``second derivative'' of the curve and ``fusion and fission'' of closed trajectories is described algebraically.<|reference_end|>
@article{morikawa2006discrete,
    title={Discrete differential geometry of triangle tiles and algebra of closed
  trajectories},
    author={Naoto Morikawa},
    journal={arXiv preprint arXiv:math/0607051},
    year={2006},
    archivePrefix={arXiv},
    eprint={math/0607051},
    primaryClass={math.CO cs.DM math.MG}
}