TY - JOUR

T1 - Triangulation refinement by using edge subdivision

AU - Lebedinskaya, N. A.

AU - Lebedinskii, D. M.

N1 - Funding Information: ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research (projects nos. 07 01 00451 and 07 01 00269).

PY - 2009/6

Y1 - 2009/6

N2 - It is proved that any triangulation of a flat polygonal region can be refined by using repeated subdivisions of an edge so that: (1) the maximum diameter of the triangles would be less than any pre-assigned positive number, and (2) the minimum interior angle of the triangles of the triangulation obtained would be not less than the minimum interior angle of the triangles of the original triangulation divided by 9. The required triangulation refinement is constructed in two steps: first, the triangulation is refined so that the triangles of the triangulation obtained can be combined into pairs, and only boundary triangles may be left unpaired; at this step each triangle is split into at most 4 parts. Then the triangulation obtained is refined once again in order that the diameter of each triangle be less then a prescribed e{open}. At each of the steps, the minimum interior angle of triangles is reduced by at most 3 times. This is guaranteed by the lemma saying that the interior angles of the triangles into which the original triangle is divided by a median are at least as great as one-third of the minimum interior angle of the original triangle.

AB - It is proved that any triangulation of a flat polygonal region can be refined by using repeated subdivisions of an edge so that: (1) the maximum diameter of the triangles would be less than any pre-assigned positive number, and (2) the minimum interior angle of the triangles of the triangulation obtained would be not less than the minimum interior angle of the triangles of the original triangulation divided by 9. The required triangulation refinement is constructed in two steps: first, the triangulation is refined so that the triangles of the triangulation obtained can be combined into pairs, and only boundary triangles may be left unpaired; at this step each triangle is split into at most 4 parts. Then the triangulation obtained is refined once again in order that the diameter of each triangle be less then a prescribed e{open}. At each of the steps, the minimum interior angle of triangles is reduced by at most 3 times. This is guaranteed by the lemma saying that the interior angles of the triangles into which the original triangle is divided by a median are at least as great as one-third of the minimum interior angle of the original triangle.

UR - http://www.scopus.com/inward/record.url?scp=84859702491&partnerID=8YFLogxK

U2 - 10.3103/S1063454109020071

DO - 10.3103/S1063454109020071

M3 - Article

AN - SCOPUS:84859702491

VL - 42

SP - 116

EP - 119

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -