| determining the volume of a fitted ellipsoid that sticks out the sides of a polyhedron [message #81503] |
Mon, 01 October 2012 09:51  |
Ayla P
Messages: 3
Registered: May 2012
|
Junior Member |
|
|
Hi all,
Here's the basic outline of my problem:
I want to know how different a given polyhedron is in its shape from an ellipsoid of the same volume. To do this, I've started by fitting a polyhedron to my data, then fit an ellipsoid to the polyhedron, and finally re-scaled the fitted ellipsoid to have the same volume as the polyhedron. Now, I want to determine the volume of the ellipsoid that is "sticking out" from the sides of the polyhedron. Hopefully this makes sense...if not, maybe thinking of a 2D diamond surrounded by a circle will help. I'm looking to determine the volume of the curved areas that stick out from the edges of the diamond (except, in reality, I am using a more complex polyhedron and an ellipsoid).
This is where I am stuck. I am thinking there might be some way to use the intersect function in idl to find the surfaces where the polyhedron and the ellipsoid intersect, but I'm not sure how to then get at the remaining volume outside the polyhedron but still inside the ellipsoid. If you have any thoughts on how I might approach the problem, i'd appreciate your insights!
Thanks!
Ayla
|
|
|
|
| Re: determining the volume of a fitted ellipsoid that sticks out the sides of a polyhedron [message #81599 is a reply to message #81503] |
Mon, 01 October 2012 11:43  |
Dick Jackson
Messages: 347
Registered: August 1998
|
Senior Member |
|
|
Hi Ayla,
I don't know of a general polygon mesh intersection routine, but in this case, you may be in luck. The Mesh_Clip() function lets you clip a polyhedral mesh using a plane, and since an ellipsoid is convex, you could trim the polyhedron using the plane of each of the ellipsoid's polygons (need to derive the plane coefficients), giving the intersection of the two volumes. Then your answer (the volume of the curved areas that stick out) is found by subtracting the intersection volume from the original polyhedron's volume.
This might be computationally intensive, depending on how finely you want to define the ellipsoid.
There was some discussion of this kind of this (with an example of using Mesh_Clip) in the following thread:
https://groups.google.com/d/topic/comp.lang.idl-pvwave/iIpdC cPN4YU/discussion
Hope this helps!
Cheers,
-Dick
On Monday, October 1, 2012 9:51:43 AM UTC-7, evi...@gmail.com wrote:
> Hi all,
>
>
>
> Here's the basic outline of my problem:
>
>
>
> I want to know how different a given polyhedron is in its shape from an ellipsoid of the same volume. To do this, I've started by fitting a polyhedron to my data, then fit an ellipsoid to the polyhedron, and finally re-scaled the fitted ellipsoid to have the same volume as the polyhedron. Now, I want to determine the volume of the ellipsoid that is "sticking out" from the sides of the polyhedron. Hopefully this makes sense...if not, maybe thinking of a 2D diamond surrounded by a circle will help. I'm looking to determine the volume of the curved areas that stick out from the edges of the diamond (except, in reality, I am using a more complex polyhedron and an ellipsoid).
>
>
>
> This is where I am stuck. I am thinking there might be some way to use the intersect function in idl to find the surfaces where the polyhedron and the ellipsoid intersect, but I'm not sure how to then get at the remaining volume outside the polyhedron but still inside the ellipsoid. If you have any thoughts on how I might approach the problem, i'd appreciate your insights!
>
>
>
> Thanks!
>
>
>
> Ayla
|
|
|
|
comp.lang.idl-pvwave archive
Members
Search
Help
Login
Home
