# Calculating volume of 3D object from its co-ordinates

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 April 16, 2013, 13:22 Calculating volume of 3D object from its co-ordinates #1 New Member   pkumar Join Date: Jun 2010 Posts: 7 Rep Power: 16 Dear Friends, I am working on geometric reconstruction method for volume of fluid method. It is a 3D code. For this i need to evaluate the volume created by intersection of a cell (cube or cuboid) and a plane (may not be aligned with cell faces). I can calculate all the points of the geometry created by the intersection and store in (x,y,z) array but I do not know how to evaluate the volume of the entity. It would be great help if you can suggest me of any existing idea or literature. Sincerely, Purushotam

April 16, 2013, 18:02
#2
Senior Member

Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,793
Rep Power: 71
Quote:
 Originally Posted by purushotam85 Dear Friends, I am working on geometric reconstruction method for volume of fluid method. It is a 3D code. For this i need to evaluate the volume created by intersection of a cell (cube or cuboid) and a plane (may not be aligned with cell faces). I can calculate all the points of the geometry created by the intersection and store in (x,y,z) array but I do not know how to evaluate the volume of the entity. It would be great help if you can suggest me of any existing idea or literature. Sincerely, Purushotam
if you can subdivide your object in tethraedron (Lagrangian simplex) then you can compute volume from the four-node obiect by means of a simple formula you find in books on Finite Element.

 April 16, 2013, 20:29 #3 Senior Member     p ding Join Date: Mar 2009 Posts: 427 Rep Power: 19 The volume of any volume in3D can be calculated with Gauss theorem. int(divergence(xi))dV=int(xc*Sx)dS=sigma (xc*Sx) that means the volume can be calcualted as the sum of (face center x coordinate multiply the surface vector x component) hope this help you.

 April 18, 2013, 07:25 #4 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,163 Blog Entries: 29 Rep Power: 39 Once you have all the points of the surface you can triangulate it and use the following (already discussed by someone above): http://www.public.iastate.edu/~zjw/p...1999-AIAAJ.pdf In general, however, you should check some VOF literature to know if there are some specific issues to consider when applying this with VOF.

 April 18, 2013, 08:14 #5 New Member   tita Join Date: Apr 2013 Posts: 27 Rep Power: 13 hi, do you know how to creat a geometry and could change the length in different conditions.

 April 18, 2013, 11:34 #6 Senior Member   Ahmed Join Date: Mar 2009 Location: NY Posts: 251 Rep Power: 18 Guys It is much more simpler It is the scaler tripple product of your linear algebra text book Good Luck

 Tags intersection, unstructured mesh, volume fraction