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