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Defining an arbitrary region

  1. Jan 11, 2010 #1
    For some reason I can't seem to think of a simple solution to defining an arbitrary region. I would like to do this so that I can then apply various operations to certain regions. The value of the region is irrelavent, so long as it is constant, it is it's location that I am interested in.

    Is there something equivalent to defining points, [tex]\delta(\vec{r}-\vec{r_i})[/tex], which defines an entire region?

    Can I simply define some region with, [tex]\int_Vd^3r'\delta(\vec{r}-\vec{r} ')[/tex] ?

    How would I explicitly define the complimentary region of space such that their union defines all of space?

    Would it be better to approach this using some sort of distribution?
     
  2. jcsd
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