Optimization by hierachical spatial enumeration

Given a voxel dataset like in with .

1. Data structure

   Voxels are treated as points and are the vertices of cells filling the space between voxels. Cells in this dataset are indexed by a a level number m = 0,...,M and a vektor . The value contained in a cell i ion level m is denoted . The size of cells on level m is defined to be times the spacing between voxels.
   The pyramid is constructed as follows:

   • if all its eight vovels lying on the vertices have opacity equal to zero.
   • if all eight cells on level m-1 that form its octants are zero.
   • otherwise its value is one.
2. Optimized algorithm

   For each ray

   • compute the cell which is hit by the ray at top level 0
   • if advance along the ray to the next cell on the same level
   • if the parent of the new cell differs from the parent of the old cell, move up to the parent of the new cell.
   • if the parent does contain zero advance on its level, otherwise go back to the childs level.
   • if one of the cells is one, draw samples (???) at evenly spaced locations along that portion of the ray falling within the cell, resample the data at these sample locations and composite the resulting color and opacity into the color and opacity of the ray.
   This opimization allows to advance very fast cross empty areas.