[vtkusers] Quantifying the Intersection of two Volumes

[David E. Jones]

Erik Sobel wrote:

> Does anyone have an example of how to measure the volume produced by the
> intersection (overlap) of two volumes?
>
> Thanks,
> Erik
> ----------------------------------------------------------------------------------------------------------
> Erik Sobel
> esobel at alphatech.com
> ----------------------------------------------------------------------------------------------------------
>
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I assume that you have only a polygonal surface to define the volumes.

1) If both volumes are convex you can actually calculate the surface defining
     the intersection using vtkHull (I think it's vtkHull).  vtkMassProperties
     will calculate the volume for you.

2) For non-convex (or convex) volumes, the best approach to calculating the
    volume of the intersection is to calculate the polygonal boundaries of the
    intersections of the volumes with a set of planes and use the areas of the
     polygons to integrate in 3D.

    The intersection of the polygons in a plane is equivalent to the scan-conversion
     algorithm for rendering polygons.  (The is some code in Graphics Gems
     which does this.) A really cool way to do it would be to draw the polygons
     into an offscreen buffer using transparency using certain colors for the
     polygonal interiors.  The numbers of pixels with the appropriate blended color
     measures the area of the intersection.

     You don't really need to integrate.  Just count the pixels in one of the
      volumes and in the intesection in a series of planes.  The ratio of these
      pixel counts is a number < 1 which can the multiplied by the original
      volume to get the intersection volume.

      I yield to other people with another approach which is plausible.
      I have dealt with related problems and don't know of a better way
      to do this.

Dav



--
David E Jones
Du Pont Central Research
Experimental Station, Bldg 320
Wilmington, DE 19880-0320


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