Simple comparisons of of nodal based vs Voxel (cell-based) would be:
  • plume vs. plume_cell
  • indicator_geology Smooth vs. Block (this is truly analogous since Block probabilities are kriged to the cells and Smooth is kriged to the nodes).
To appreciate the difference resulting from a plume operation, you merely need to “visualize” what is happening within a single EVS hexahedron (8 node) cell.  It helps if you grab a rectangular cardboard box (kleenex or amazon) and consider some cases by marking it up with colored markers.
  • Values are computed at all 8 nodes.  
    • Though a cell has 8 nodes, except at model faces, edges and corners, each node is shared with 7 other cells.
    • For a typical 100 x 100 x 100 node grid, there will be 99 x 99 x 99 cells.
      • For the above grid there are ~3% more nodes than cells.  
  • When a plume is computed for Do > Tn (Data is greater than Threshold-n), a complex process ensues:
    • All cells where all of the cell’s nodes are < Tn are removed.
    • All cells where all of the cell’s nodes are > Tn remain.
    • For cells where some nodes > Tn and some are < Tn
      • All cell edges where the two edge nodes are < Tn are removed.
      • All cell edges where the two edge nodes are > Tn remain.
      • All cell edges where one edge node is < Tn and the other is > Tn are split.  
        • For the small domain of a single cell, linear interpolation across any edge to determine the location of the split is very accurate (sub-percentile) as compared with kriging values along the edge.  
        • At the split location a new node is created.
        • The edge node < Tn is removed.
      • The complexity of the subdivided cell can vary dramatically depending on the number of remaining nodes.
        • The minimum number of remaining nodes is 4 and the maximum is 16! (yes, much greater than what you start with).
        • New cells are created using the remaining and created (from splits) nodes.
        • There are 256 cases of how new cells are created from all permutations of which nodes remain.
          • All possible volumetric cell types can result from the subdivision, but all higher order cells can be cleanly subdivided into tetrahedrons.
            • This is why a hexahedral grid becomes Tetrahedrons after subsetting operations. 
          • The reason there are so many cases is that we take extreme care to eliminate internal volume faces that do not have a matching face to ensure that transparency of volumetric plumes is correct and lacks unwanted internal faces.
      • The accuracy of the splitting is the reason why nodal representations are far superior to cell-based representations.
        • Since splitting occurs along all three dimensions (x-y-z), and is sub-percentile accurate, the cell subdivision is at-least as good as a cell-based grid whose resolution is 100 times greater in X, Y & Z directions. 
        • NOTE: The reason why I insist that grids should have at least two cells between any samples that exhibit a high gradient is to enforce and maintain the subdivision accuracy.
We do not want to imply that cell based representations are  useless nor potentially amazing for certain applications.  However, the superiority of nodal based models vs. cell-based models is difficult to dispute.