UNIFORMITY DEGREE OF SOME SPHERICAL GRIDS USED IN MAGNETIC RESONANCE POWDER SIMULATIONS

Cora CRĂCIUN

Authors

Cora CRĂCIUN Babeş-Bolyai University, Faculty of Physics, Cluj-Napoca, Romania. Corresponding author e-mail: cora.craciun@phys.ubbcluj.ro

Keywords:

spherical grid, uniformity degree, Voronoi cell.

Abstract

This paper compares the uniformity degree of nine spherical grids used in magnetic resonance powder simulations. The comparison is based on known mesh quality measures, which depend on the grid points and the generated Voronoi regions on the unit sphere. According to computations, the distributions of the grids' geometric properties characterise better the grids' quality then the global uniformity metrics.

Author Biography

Cora CRĂCIUN, Babeş-Bolyai University, Faculty of Physics, Cluj-Napoca, Romania. Corresponding author e-mail: cora.craciun@phys.ubbcluj.ro

Babeş-Bolyai University, Faculty of Physics, 1 Kogălniceanu str., 400084 Cluj-Napoca, Romania.

Corresponding author e-mail: cora.craciun@phys.ubbcluj.ro

References

S. Stoll, Ph.D. Thesis, ETH Zurich, Switzerland, 2003.

A. Ponti, J. Magn. Reson., 138, 288 (1999).

M. Bak, N.C. Nielsen, J. Magn. Reson., 125, 181 (1997).

C. Crăciun, J. Magn. Reson., 245, 63 (2014).

H. Nguyen, J. Burkardt, M. Gunzburger, L. Ju, Y. Saka, Comput. Geom., 42, 1 (2009).

J. Burkardt, M. Gunzburger, J. Peterson, R. Brannon, Technical Report: SAND2002-0099, Sandia National Laboratories, February 2002.

M.J. Nilges, Ph.D. Thesis, University of Illinois, Urbana, Illinois, 1979.

V.I. Lebedev, Comput. Math. Math. Phys., 15, 44 (1975).

V.I. Lebedev, Comput. Math. Math. Phys., 16, 10 (1976).

V.I. Lebedev, Siberian Math. J., 18, 99 (1977).

V.I. Lebedev, A.L. Skorokhodov, Russ. Acad. Sci. Dokl. Math., 45, 587 (1992).

V.I. Lebedev, Russ. Acad. Sci. Dokl. Math., 50, 283 (1995).

V.I. Lebedev, D.N. Laikov, Russ. Acad. Sci. Dokl. Math., 59, 477 (1999).

M.J. Mombourquette, J.A. Weil, J. Magn. Reson., 99, 37 (1992).

R. Swinbank, R.J. Purser, Quart. J. Roy. Meteorol. Soc., 132, 1769 (2006).

S.K. Zaremba, Ann. Mat. Pura Appl., 73, 293 (1966).

H. Conroy, J. Chem. Phys., 47, 5307 (1967).

V.B. Cheng, H.H. Suzukawa Jr., M. Wolfsberg, J. Chem. Phys., 59, 3992 (1973).

D.W. Alderman, M.S. Solum, D.M. Grant, J. Chem. Phys., 84, 3717 (1986).

D. Wang, G.R. Hanson, J. Magn. Reson. A, 117, 1 (1995).

S. Stoll, A. Schweiger, J. Magn. Reson. 178, 42 (2006).

R.J. Renka, ACM Trans. Math. Softw., 23, 416 (1997).

http://people.sc.fsu.edu/~jburkardt/f_src/f_src.html

J. Arvo, in: S.G. Mair, R. Cook (Eds.), Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’95), ACM, New York, pp. 437-438 (1995).

J. Arvo, Stratified sampling of 2-manifolds, in: SIGGRAPH 2001 Course Notes, vol. 29 (2001).

http://www.gnu.org/software/octave/

M. Matsumoto, T. Nishimura, ACM Trans. Model. Comput. Simulat., 8, 3 (1998).

http://www.r-project.org/