Lonni J Friedman

02-01-1997, 05:54 AM

Virgil,

Please DO NOT attach files to emails that are not asked for. It is

both rude and destructive to send people files through email that they did

not request. What you should have done is asked all those interested to

email you with a request for the file. Not everyone is interested in the

derivation, and not everyone wants random files from being sent to them.

This kind of abuse could just as easily be mailicious if some destructive

individual decides to email a 50MB file to a mailing list.

I do not mean to flame, just to warn you.

-Lonni Friedman

At 08:45 PM 2/1/97 +0100, you wrote:

>This is a follow-up to a previously posted message by Dr. Sandy

>Stewart on the surface area of an ellipsoid. This was a very

>interesting posting since what would intutively seem to be a

>rather simple problem (since an ellipsoid is such a simple

>object) was not simple at all.

>

>The attached file (a 2-page PDF document) gives a short derivation

>of the definite integral for the surface area of an ellipsoid.

>You will need Reader 3.0 to display/print it which is free and can be

>downloaded from http://www.adobe.com/. This definite integral can

>be used to obtain the surface area of a general (triaxial) ellipsoid:

>

> 2 2 2

> x + y + z

> --- --- --- = 1

> 2 2 2

> a b c

>

>for any a,b,c > 0. The actual numerical integration is easily

>accomplished in Mathematica with the precision of the

>estimated area chosen by the user.

>

>Also, it may be reassuring to know that the last symbolic

>formula given (surface area of an asymmetric ellipsoid) in

>Dr. Stewart's summary is quite likely correct -- at least I

>was able to find the same equation. However, two warnings in

>using this equation: 1) it can be numerically unstable when

>the semi-axes (a,b,c) or close (in value) even if a > b > c,

>2) the elliptic integrals given in some references can have

>opposite ordering to those shown in the symbolic equation. Also,

>it is interesting that after extensive testing of the numercial

>evaluation of the definite integral and direct evaluation of

>the symbolic equation it seems that the numerical evaluation

>is more accurate!

>--

>

>************************************************** *********

>V. P. Stokes *

>BMC, Neuroscience *

>Karolinska Institute Quality Has No Fear *

>Box 5626 of Time *

>S-114 86 Stockholm *

>SWEDEN *

>************************************************** *********

>

>Attachment Converted: D:\TEMP\Ellip01.pdf

>

When you ply the Net, is the experience you're looking for

like watching TV, or is it like reading?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Lonni J Friedman

Brother in the Epsilon Zeta chapter of Alpha Phi Omega

friedl@rpi.edu OR beemer@hal.stu.rpi.edu

http://www.rpi.edu/~friedl/

Biomedical Engineering (BME)

Rensselaer Polytechnic Institute

Class of '98

Please DO NOT attach files to emails that are not asked for. It is

both rude and destructive to send people files through email that they did

not request. What you should have done is asked all those interested to

email you with a request for the file. Not everyone is interested in the

derivation, and not everyone wants random files from being sent to them.

This kind of abuse could just as easily be mailicious if some destructive

individual decides to email a 50MB file to a mailing list.

I do not mean to flame, just to warn you.

-Lonni Friedman

At 08:45 PM 2/1/97 +0100, you wrote:

>This is a follow-up to a previously posted message by Dr. Sandy

>Stewart on the surface area of an ellipsoid. This was a very

>interesting posting since what would intutively seem to be a

>rather simple problem (since an ellipsoid is such a simple

>object) was not simple at all.

>

>The attached file (a 2-page PDF document) gives a short derivation

>of the definite integral for the surface area of an ellipsoid.

>You will need Reader 3.0 to display/print it which is free and can be

>downloaded from http://www.adobe.com/. This definite integral can

>be used to obtain the surface area of a general (triaxial) ellipsoid:

>

> 2 2 2

> x + y + z

> --- --- --- = 1

> 2 2 2

> a b c

>

>for any a,b,c > 0. The actual numerical integration is easily

>accomplished in Mathematica with the precision of the

>estimated area chosen by the user.

>

>Also, it may be reassuring to know that the last symbolic

>formula given (surface area of an asymmetric ellipsoid) in

>Dr. Stewart's summary is quite likely correct -- at least I

>was able to find the same equation. However, two warnings in

>using this equation: 1) it can be numerically unstable when

>the semi-axes (a,b,c) or close (in value) even if a > b > c,

>2) the elliptic integrals given in some references can have

>opposite ordering to those shown in the symbolic equation. Also,

>it is interesting that after extensive testing of the numercial

>evaluation of the definite integral and direct evaluation of

>the symbolic equation it seems that the numerical evaluation

>is more accurate!

>--

>

>************************************************** *********

>V. P. Stokes *

>BMC, Neuroscience *

>Karolinska Institute Quality Has No Fear *

>Box 5626 of Time *

>S-114 86 Stockholm *

>SWEDEN *

>************************************************** *********

>

>Attachment Converted: D:\TEMP\Ellip01.pdf

>

When you ply the Net, is the experience you're looking for

like watching TV, or is it like reading?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Lonni J Friedman

Brother in the Epsilon Zeta chapter of Alpha Phi Omega

friedl@rpi.edu OR beemer@hal.stu.rpi.edu

http://www.rpi.edu/~friedl/

Biomedical Engineering (BME)

Rensselaer Polytechnic Institute

Class of '98