deletions | additions       diff --git a/Sampling Spatial.tex b/Sampling Spatial.tex  index 5ee3dfb..42ba1bd 100644  --- a/Sampling Spatial.tex  +++ b/Sampling Spatial.tex 
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Two classifications of sampling patterns exist in the spatial domain: gridded and non-gridded.(Figure qq) Gridded sampling corresponds to information that is evenly spaced within the sample volume. Voxel, or 3-D pixel, based information is a gridded dataset because of this criteria; it is assumed that the voxel is the probe volume of the model. Non-gridded data is extracted from a sample volume of finite dimensions wherein x can take any value within the range. Models such as Atom Probe Microscopy [ref] and Molecular Dynamics [ref] will often exhibit non-gridded, or point cloud, sampling characteristics. The probe volume associated with point cloud datasets will relate to the resolution precision of the model from which the information is generated.   In prior work and this paper, indicator functions provide the basis to partition the spatial domain into non-overlapping, evenly spaced, cuboidal volumes [ref]; an investigation of other basis functions are currently underway (e.g. wavelets). Equation xx ~\ref{test}  defines the basis for the spatial domain as $\chi_{s}(x)$. $s$ is an index to a unique cuboidal volume $\omega_{s}$ in the spatial domain with the properties \begin{equation} \begin{equation}\label{test}  \omega_{s} \cap \omega_{t} =   \begin{cases}   \omega_{s}, & \mbox{if } s\mbox{ =t}