From: spellucci@mathematik.tu-darmstadt.de (Peter Spellucci)
Subject: Re: integration/interpolation on a sphere
Date: 23 Feb 1999 10:29:12 GMT
Newsgroups: sci.math.num-analysis
To: jordi romeu <romeu@voltor.upc.es>

In article <36D1ADE6.7768@voltor.upc.es>,
 jordi romeu <romeu@voltor.upc.es> writes:
|> hello,
|> 
|> could anybody help me with
|> good references or tips on the problem
|> of efficient integration and interpolation on
|> the surface of a sphere?
|> thanks in advance,
|> alex heldring
|> (please reply to heldring@voltor.upc.es)
may be the following sources are of help:
1)
  AUTHOR = {R. Pfeifle and H.-P. Seidel},
  TITLE = {Spherical Triangular {B-splines} with Application to Data Fitting},
  BOOKTITLE = {Proceedings of EUROGRAPHICS '95},
  YEAR = {1995},
  ORGANIZATION = {Eurographics Association},
  PUBLISHER = {Blackwell}
2)
http://www.iinet.com.au/~watson/modemap.html

It does the Delaunay/Voronoi/Natural_Neighbour_Circle diagrams on
a sphere with interpolated contours of radial density.
3)
        spheres/index.html


4)
fft:
There's a collection of such routines written in Fortran 77, available
from  NCAR under the name spherepack. Try

  http://www.scd.ucar.edu/softlib/mathlib.html

peter
==============================================================================

From: heldring@voltor.upc.es (Alex Heldring)
Subject: Re: integral over sphere
Date: Mon, 15 Mar 1999 12:29:56 GMT
Newsgroups: sci.math.num-analysis

On Mon, 15 Mar 1999 11:50:33 +0100, Antoni Zochowski
<zochowsk@ibspan.waw.pl> wrote:

>Could someone direct me to a reference about a scheme
>of numerical integration over the sphere ? Does a better
>solution then parametrization and Gauss quadrature exist ?
>Thank you in advance
>
>zochowsk@ibspan.waw.pl

here s a reference: A.D. Mc Laren,"Optimal numerical integration on a
sphere," Mathematics on Computation, 17 pp 361-383, 1963 
it's quite complicated though. i didn t try to use it, and stuck with
Gauss-Legendre in theta-direction and uniform summation in
phi-direction. if you find out more i d be happy to hear about it.
what is your application?

Alex Heldring (heldring@voltor.upc.es)