ellipsoids intersection volume- how to speed up the code ?

2011 6 22
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I have to determine the intersection volume occupied by ellipsoid in 3D space vs the volume occupied by another ellipsoid at a different orientation. I have created bounding boxes around the ellipsoids for this purpose. However, the usage of below commands makes the code slow.
[x y z]= ellispoid(xc,yc,zc,xr,yr,zr,n)
h=surf(x,y,z)
Any suggestions on how to make the code faster. I dont need the graphical visualisation of the ellipsoidal intersection, so can that be somehow eliminated to make code faster ?

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Patrick Kalita
Patrick Kalita 2011-6-22

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If you don't want to view the ellipsoid, then simply take out the call to surf.

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Sakshi
Sakshi 2011-6-22
But then I need to use the handle graphic, h to perform the rotation. How will I do that if I remove surf command ? Thank you for answering my query.
Patrick Kalita
Patrick Kalita 2011-6-22
I see. Your question didn't mention anything about such a restriction. In the future, you might want to include relevant information like that in your question.
Why don't you just do the rotation yourself? You can define an appropriate rotation matrix (http://en.wikipedia.org/wiki/Rotation_matrix#Rotations_in_three_dimensions), then multiply each (x,y,z) coordinate of the ellipsoid by the rotation matrix to obtain the coordinates of the rotated ellipsoid.
Sakshi
Sakshi 2011-6-22
I am sorry for not clearly mentioning ths rotation aspect in the question. Thanks a lot,the suggestion given by you has reduced the time to a big extent from 70 seconds to 3 seconds. !

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