| Title:
|
Stereology of dihedral angles (English) |
| Author:
|
Horálek, Vratislav |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
45 |
| Issue:
|
6 |
| Year:
|
2000 |
| Pages:
|
411-417 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper presents a short survey of stereological problems concerning dihedral angles, their solutions and applications, and introduces a graph for determining the distribution functions of planar angles under the hypothesis that dihedral angles in $\mathbb{R}^3$ are of the same size and create a random field. (English) |
| Keyword:
|
dihedral angles |
| Keyword:
|
distribution function |
| Keyword:
|
graph theory |
| Keyword:
|
stereology |
| MSC:
|
52A22 |
| MSC:
|
60D05 |
| idZBL:
|
Zbl 1002.60003 |
| idMR:
|
MR1800962 |
| DOI:
|
10.1023/A:1022329432636 |
| . |
| Date available:
|
2009-09-22T18:04:56Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134449 |
| . |
| Reference:
|
[1] K. A. Brakke: Variances of dihedral angle estimations.Metallography 20 (1987), 491–493. 10.1016/0026-0800(87)90022-X |
| Reference:
|
[2] J. P. Butler, J. A. Reeds: Stereology of dihedral angles. Part I: First two moments.SIAM J. Appl. Math. 94 (1987), 670–677. MR 0889646 |
| Reference:
|
[3] J. P. Butler, S. Suzuki, E. H. Oldmixon, F. G. Hoppin: A theory of diffuse light scattering by lungs.J. Appl. Physiol. 58 (1985), 89–96. 10.1152/jappl.1985.58.1.89 |
| Reference:
|
[4] B. C. Carlson: Computing elliptic integrals by duplication.Num. Math. 33 (1979), 1–16. Zbl 0438.65029, MR 0545738, 10.1007/BF01396491 |
| Reference:
|
[5] B. C. Carlson, E. M. Notis: Algorithms for incomplete elliptic integrals.ACM Trans. Math. Software 7 (1981), 398–403. 10.1145/355958.355970 |
| Reference:
|
[6] R. T. DeHoff: Estimation of dihedral angles from stereological counting measurements.Metallography 19 (1986), 209–217. 10.1016/0026-0800(86)90036-4 |
| Reference:
|
[7] A. V. Duvaljan: Approximate determination of the angle variance in alloys.Zavodskaja laboratorija 8 (1971), 939–941. (Russian) |
| Reference:
|
[8] D. Harker, E. R. Parker: Grain shape and grain growth.Trans. Am. Soc. Metals 34 (1945), 156–201. |
| Reference:
|
[9] V. Horálek: A note to dihedral angles and their stereology.In: Geometrical Problems of Image Processing (U. Eckhardt, A. Hübler, W. Nagel, G. Werner, eds.). Research in Informatics, Vol 4, Akademie-Verlag, Berlin, 1991, pp. 159–164. MR 1111700 |
| Reference:
|
[10] R. E. Miles: Dihedral angle distributions.Acta Stereologica 6 (1987), 19–24. Zbl 0617.60012 |
| Reference:
|
[11] J. A. Reeds, J. P. Butler: Stereology of dihedral angles. Part II. Distribution function.SIAM J. Appl. Math. 47 (1987), 678–688. MR 0889647, 10.1137/0147046 |
| Reference:
|
[12] O. K. Riegger, L. H. van Vlack: Dihedral angle measurement.Trans. Met. Soc. AIME 218 (1960), 933–935. |
| Reference:
|
[13] J. Rys, A. Kasperczyk: Heterogeneity of the single-phase polycrystalline structure due to dihedral angles.Metalurgia i odlewnictvo 7 (1981), 473–489. |
| Reference:
|
[14] A. Schwandtke: Distributional analysis of dihedral angles in single-phase polycrystalline structure.Metalurgia i odlewnictvo 7 (1985), 171–182. |
| Reference:
|
[15] S. Suzuki, J. P. Butler, E. H. Oldmixon, F. G. Hoppin: Light scattering by lungs correlates with stereologic measurements.J. Appl. Physiol. 58 (1985), 97–104. 10.1152/jappl.1985.58.1.97 |
| . |
