In article <1993Apr12.221942.6...@magnus.acs.ohio-state.edu>, tab...@magnus.acs.ohio-state.edu (Troy A Baer) writes:

Hi Troy,

|> I'm trying to generate contour plots of Mach number and pressure

|> distribution around an airfoil. The problem is that the grid at which

|> the points are defined is not rectangular.

|>

|> Does anyone know of either A) a PC based program that will do this (at

|> this point, it doesn't matter if it's PD, shareware, or commercial), or

|> B) an algorithm that will do this and can be implemented in Fortran 77

|> with GKS?

I had a similar problem last year. At the time, I was asked, but "forgot" :{

to post any useful references. Most were in fact posted to the newsgroup,

but here goes (LONG).

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For general reference, I am aware of

Burrough P.A. "Principles of Geographical Information Systems

for Land Resources Assessment", Clarendon Press,Oxford(1986)

Clarke K.C. "Analytical and Computer Cartography",

Prentice-Hall (1990).

Len.Ma...@mel.dit.csiro.au | Manager, User Support |

CSIRO Division of Information Technology | CSIRO Supercomputing Facility|

723 Swanston Street, Carlton | Tel: +61 3 282 2622 |

VIC 3053, Australia | Fax: +61 3 282 2600 |

Here are some better references to "how to do it" from the replies

I received then:

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From: Markku_Peltoni...@hut.fi

Subject: Gridding algorithms - expreriences

Here is some information about gridding algorithms. Background for this is

a M.Sc. thesis made here in 1985 by Tuire Valli. She is currently working

at the Geological Survey of Finland, Espoo, Finland. Her results are

shortly and partly summarised as follows.

1. Kriging methods are theoretically superior, but working with real

aeromagnetic data gave disappointing results: the method is extremely

laborous and slow for big amounts of data and requires two phases: first,

estimation of the semivariogram from the input data, and second, estimation

of the grid values. If the input data has regional trends, the

semivariogram must be computed separately for each sub-area, which alone

makes the idea impractical. The sw code used was from Uniras company

(Denmark) and, to put it mildly, had some plenty of bugs (e.g. the trend

option didn't work at all).

2. If you have possibility to include gradient information of the data into

the interpolation algorithm, then the outcome will be much improved. This

is the case for our aeromagnetic data and hence, an interpolation method

which utilizes both the field and the derivative values (F, dF/dx and dF/dy

for every obsevation point) gave the best results for our real-life data.

The method is advantageous as the trends are automatically taken into

account through the derivative information. As far as I know, the method

has not yet been properly documented in English; the best source would be

the thesis. The method has been under development at the Geol Survey of

Finland since mid-70's, first by Mr. Juha Korhonen, geophysicist at the

GSF.

3. By far the best results for synthetic test data were reached using the

smoothing spline -technique, developed at the Univ of Wisconsin-Madison,

Dept of Statistics since mid-70's. The idea is to take care of the errors

of your original data by allowing a user-selectable amount of smoothing to

be done before the application of the splines. The method works fine, but

the software would need upgrading and further testing for our own needs.

That was the reason to use synthetic and not the real data for testing. It

was Tuire's (and my as well) idea to continue work on this after her

graduation, but not much has been been accomplished since.

The run times for 10,000 points of input data were:

Kriging 30 minutes CPU-time on VAX-785;

gradient interpolation about 1.6 minutes on the same computer, and

smoothing spline about 3 minutes on VAX-8600.

References (only to get you started if you find these relevant)

Clarc,I., 1979: Practical Geostatistics. Applied Sci Publ Ltd, England.

Haas & Viallix, 1976: Krigeage applied to geophysics. Geophysical

Prospecting Vol 24 pp 49-69.

Journel & Huijbregts, 1978: Mining Geostatistics. Academic Press, London.

Reinsch, C.H., 1967: Smoothing by spline functions. Numerische Mathematik

Vol 10 pp 177-183

Reinsch, C.H., 1970: Smoothing by spline functions II. Numerische

Mathematik Vol 16 pp 451-454.

Valli, T., 1985: Estimation of magnetic field between flight lines. M.Sc.

thesis, Helsinki Univ of Technology, Lab of Engineering Geology and

Geophysics, Espoo, Finland. 76 p + app (in Finnish).

Wabha, G., 1979: How to smooth curves and surfaces with splines and

cross-validation. Tech Rep No 555, Univ of Wisconsin-Madison, Dept of

Statistics.

Wendelberger, J.G., 1981: The computation of Laplacian Smoothing Splines

with Examples. Tech Rep No 648, Univ of Wisconsin-Madison, Dept of

Statistics.

Good Luck!

Markku Peltoniemi

Helsinki Univ of Technology

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From: ch...@mqatmos.cic.mq.edu.au (Chris Skelly)

Subject: gridding

offhand I can recommend two good reference books, none specific

to your problem although they might touch on them somewhat,

Ripley, Brian 1981, Spatial Statistics (or something very close

to this)

Cressie, Noel, 1991, Statistics for spatial data analysis

(again I'm not positive about the title, but I know its

Wiley and Sons)

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From: w...@ux6.lbl.gov (Wes Bethel)

Subject: Gridding

>Help! Does anyone know of a good gridding program on the network (ie.

>anonamous ftp'able). Or is there a gridder burried in Khoros somewhere?

I have written several gridding modules for AVS. These are available

via anon ftp from avs.ncsc.org. The module names are "bivar", "trivar",

"scat 2d" and "scat 3d". The four modules may be classified as

performing either 2 or 3 variable gridding (surfaces or volumes), and as

distance-based or function-based. Each has its strengths and weaknesses.

These modules have been used a lot here to do exactly the type of work

you indicate you need to do.

You are certainly welcome to ftp these and hack them into Khoros.

Another option is to poke around at netlib (net...@ornl.gov). The

function-based numerical code that I use was obtained from netlib and

ported into AVS. You may find other stuff there that you like.

A final option is to wait for yet another user-supplied toolbox which will

accompany Khoros 2 and the geometry functionality.

The algorithms which will be available in K2 will do the

numerical-based gridding for two- and three-variable

functions as well as weighted-averages of nearby points,

also for two- and three-variable datasets.

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From: ow...@attmail.com

Subject: Gridding algorithms

It would be interested for you to contact Oleg Musin in Moscow, Russia.

His group developed software, including a few approaches, for

calculating on regular x,y grid z-values. They told me that this is

most powerfull package for this kind of tasks. You can contact them

by e-mail. Their address is

internet!relcom.kiae.su!uucp!ecosoft.npimsu.msk.su!musin and fax

(095) 939-4407.

Michail Bogdanov

Oklahoma City, USA attmail.com!owusa

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In article <1992Jun24.005928.23...@uniwa.uwa.edu.au>, wat...@maths.uwa.oz.au (David Watson) writes:

|> Briggs, I.C., 1974, Machine contouring using minimum curvature:

|> Geophysics, v.39, no.1, p. 39-48.

|>

|> The methods described in this paper and over 500 other contouring

|> articles are discussed in "CONTOURING: A guide to the analysis and

|> display of spatial data", by David F Watson.(Pergamon Press 1992).

|> It surveys, and categorizes, all (I think) published methods of

|> interpolation and surface fitting, and includes code for 18

|> interpolation methods.

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\centerline{\bf SELECTED REFERENCES TO CONTOURING LITERATURE}

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{\sevenrm

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\frenchspacing

Akima, H., 1978, A method of bivariate interpolation and smooth surface fitting for irregularly distributed data points, ACM Trans.\ Math.\ Software, 4(2), \hbox{148--159.}

\noindent

\hangindent=2pc

\hangafter=1

Bourke, P.D., 1987, A contouring subroutine, Byte, 12, \hbox{143--150.}

\noindent

\hangindent=2pc

\hangafter=1

Cayley, A., 1859, On contour and slope lines, Philosophical Magazine, 18, \hbox{264--268.}

\noindent

\hangindent=2pc

\hangafter=1

Foley, T.A., 1984, Three-stage interpolation to scattered data, Rocky Mountain J.\ Math., 14(1),

\hbox{141--149.}

\noindent

\hangindent=2pc

\hangafter=1

Panofsky, H.A., 1949, Objective weather-map analysis, J.\ Meteorology, 6, \hbox{386--392.}

\noindent

\hangindent=2pc

\hangafter=1

Sawkar, D.G., Shevare, G.R., and Koruthu, S.P., 1987, Contour plotting for scattered data, Computers \& Graphics, 11(2), \hbox{101--104.}

\noindent

\hangindent=2pc

\hangafter=1

Sibson, R., 1981, A brief description of natural neighbour interpolation, {\sevenit in} Interpreting multivariate data, {\sevenit ed}.\ V.\ Barnett, John Wiley, \hbox{21--36.}

\noindent

\hangindent=2pc

\hangafter=1

Simons, S.L.Jr., 1983, Make fast and simple plots on a microcomputer, Byte, 8, \hbox{487--492.}

\noindent

\hangindent=2pc

\hangafter=1

Watson, D.F., 1982, ACORD---Automatic contouring of raw data, Computers \& Geosciences, 8(1), \hbox{97--101.}

\noindent

\hangindent=2pc

\hangafter=1

Watson, D.F., 1985, Natural neighbour sorting, The Australian Computer J., 17(4), \hbox{189--193.}

\noindent
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