Stewart, Sandy 443-6113

10-02-1996, 12:08 AM

Dear Fellow Biomechanicians,

Can anyone help with this problem? I need to calculate

the surface area of an ellipsoid whose defining equation is:

2 2 2

X Y Z

---- + ---- + ---- = 1

2 2 2

a b c

I need the solution for the case where a, b, and c are all

different, and for the special case where b = c. I also need to

be able to calculate the surface area for a sector of an

ellipsoid (i.e., a hemi-ellipsoid or less, but symmetric about

one of the axes).

I have seen a paper where both of these solutions are given

(and they are complex), yet when I try to derive them myself, I

get different answers, even when using a symbolic algebra

program. I would appreciate seeing a total derivation.

In my first try, I got the area equal to:

4 2 2 2

--- * pi * (a + b + c )

3

This seems intuitively obvious (i.e., if a = b = c you get

the correct equation for the surface area of a sphere) but

apparently is NOT correct. I found my error that led to this

solution, but still have had little luck getting the correct

answer.

I would appreciate any input into this problem. I will

post all replies at a future date.

Thanking you in advance,

--Sandy Stewart

Research Biomedical Engineer,

CDRH, Food & Drug Administration

sxs@fdadr.cdrh.fda.gov

Can anyone help with this problem? I need to calculate

the surface area of an ellipsoid whose defining equation is:

2 2 2

X Y Z

---- + ---- + ---- = 1

2 2 2

a b c

I need the solution for the case where a, b, and c are all

different, and for the special case where b = c. I also need to

be able to calculate the surface area for a sector of an

ellipsoid (i.e., a hemi-ellipsoid or less, but symmetric about

one of the axes).

I have seen a paper where both of these solutions are given

(and they are complex), yet when I try to derive them myself, I

get different answers, even when using a symbolic algebra

program. I would appreciate seeing a total derivation.

In my first try, I got the area equal to:

4 2 2 2

--- * pi * (a + b + c )

3

This seems intuitively obvious (i.e., if a = b = c you get

the correct equation for the surface area of a sphere) but

apparently is NOT correct. I found my error that led to this

solution, but still have had little luck getting the correct

answer.

I would appreciate any input into this problem. I will

post all replies at a future date.

Thanking you in advance,

--Sandy Stewart

Research Biomedical Engineer,

CDRH, Food & Drug Administration

sxs@fdadr.cdrh.fda.gov