Iterated medial triangle subdivision in surfaces of constant curvature
Brunck FR. 2023. Iterated medial triangle subdivision in surfaces of constant curvature. Discrete and Computational Geometry. 70(3), 1059–1089.
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Abstract
Consider a geodesic triangle on a surface of constant curvature and subdivide it recursively into four triangles by joining the midpoints of its edges. We show the existence of a uniform δ>0
such that, at any step of the subdivision, all the triangle angles lie in the interval (δ,π−δ)
. Additionally, we exhibit stabilising behaviours for both angles and lengths as this subdivision progresses.
Publishing Year
Date Published
2023-07-05
Journal Title
Discrete and Computational Geometry
Acknowledgement
Open access funding provided by the Institute of Science and Technology (IST Austria).
Volume
70
Issue
3
Page
1059-1089
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eISSN
IST-REx-ID
Cite this
Brunck FR. Iterated medial triangle subdivision in surfaces of constant curvature. Discrete and Computational Geometry. 2023;70(3):1059-1089. doi:10.1007/s00454-023-00500-5
Brunck, F. R. (2023). Iterated medial triangle subdivision in surfaces of constant curvature. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00500-5
Brunck, Florestan R. “Iterated Medial Triangle Subdivision in Surfaces of Constant Curvature.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-023-00500-5.
F. R. Brunck, “Iterated medial triangle subdivision in surfaces of constant curvature,” Discrete and Computational Geometry, vol. 70, no. 3. Springer Nature, pp. 1059–1089, 2023.
Brunck FR. 2023. Iterated medial triangle subdivision in surfaces of constant curvature. Discrete and Computational Geometry. 70(3), 1059–1089.
Brunck, Florestan R. “Iterated Medial Triangle Subdivision in Surfaces of Constant Curvature.” Discrete and Computational Geometry, vol. 70, no. 3, Springer Nature, 2023, pp. 1059–89, doi:10.1007/s00454-023-00500-5.
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