Nonobtuse mesh: Difference between revisions
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| title = Linear-size nonobtuse triangulation of polygons |
| title = Linear-size nonobtuse triangulation of polygons |
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| volume = 14 |
| volume = 14 |
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| year = 1995}}</ref> These nonobtuse triangulations can be further refined to produce acute triangulations with <math>O(n)</math> triangles.<ref>{{citation |
| year = 1995| doi-access = free |
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}}</ref> These nonobtuse triangulations can be further refined to produce acute triangulations with <math>O(n)</math> triangles.<ref>{{citation |
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| last = Maehara | first = H. |
| last = Maehara | first = H. |
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| doi = 10.1006/eujc.2001.0531 |
| doi = 10.1006/eujc.2001.0531 |
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| title = Acute triangulations of polygons |
| title = Acute triangulations of polygons |
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| volume = 23 |
| volume = 23 |
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| year = 2002}}</ref><ref>{{citation |
| year = 2002| doi-access = free |
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}}</ref><ref>{{citation |
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| last = Yuan | first = Liping |
| last = Yuan | first = Liping |
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| doi = 10.1007/s00454-005-1188-9 |
| doi = 10.1007/s00454-005-1188-9 |
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| volume = 34 |
| volume = 34 |
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| year = 2005| s2cid = 26601451 |
| year = 2005| s2cid = 26601451 |
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| doi-access = free |
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Latest revision as of 20:06, 28 January 2023
In computer graphics, a nonobtuse triangle mesh is a polygon mesh composed of a set of triangles in which no angle is obtuse, i.e. greater than 90°. If each (triangle) face angle is strictly less than 90°, then the triangle mesh is said to be acute. Every polygon with sides has a nonobtuse triangulation with triangles (expressed in big O notation), allowing some triangle vertices to be added to the sides and interior of the polygon.[1] These nonobtuse triangulations can be further refined to produce acute triangulations with triangles.[2][3]
Nonobtuse meshes avoid certain problems of nonconvergence or of convergence to the wrong numerical solution as demonstrated by the Schwarz lantern.[1] The immediate benefits of a nonobtuse or acute mesh include more efficient and more accurate geodesic computation using fast marching, and guaranteed validity for planar mesh embeddings via discrete harmonic maps.
References
[edit]- ^ a b Bern, M.; Mitchell, S.; Ruppert, J. (1995), "Linear-size nonobtuse triangulation of polygons", Discrete & Computational Geometry, 14 (4): 411–428, doi:10.1007/BF02570715, MR 1360945
- ^ Maehara, H. (2002), "Acute triangulations of polygons", European Journal of Combinatorics, 23 (1): 45–55, doi:10.1006/eujc.2001.0531, MR 1878775
- ^ Yuan, Liping (2005), "Acute triangulations of polygons", Discrete & Computational Geometry, 34 (4): 697–706, doi:10.1007/s00454-005-1188-9, MR 2173934, S2CID 26601451