One of the major performance gains in volume rendering can be achieved by efficiently skipping data which is classified as transparent. In particular, it is important to begin sampling at positions close to the data of interest, i.e., the non-transparent data. This is particularly true for medical datasets, as the data of interest is usually surrounded by large amounts of empty space (air). The idea is to find, for every ray, a position close to its intersection point with the visible volume, thus, we refer to this search as entry point determination. The advantage of entry point determination is that it does not require additional overhead during the actual raycasting process, but still allows to skip a high percentage of empty space. The entry points are determined in the ray setup phase and the rays are initialized to start processing at the calculated entry position. The basic goal of entry point determination is to establish a buffer, the entry point buffer, which stores the position of the first intersection with the visible volume for each ray.
As blocks are the basic processing entities of our algorithm, the first step is to find all blocks which do not contribute to the visible volume using the current classification, i.e., all blocks that only contain data values which are classified as transparent. It is important that the classification of a whole block can be calculated efficiently to allow interactive transfer function modification. We store the minimum and maximum value of the samples contained in a block and use a summed area table of the opacity transfer function to determine the visibility of the block. We then perform a projection of each non-transparent block onto the image plane with hidden surface removal to find the first intersection point of each ray with the visible volume. The goal is to establish an entry point buffer of the same size as the image plane, which contains the depth value for each ray's intersection point with the visible volume. For parallel projection, this step can be simplified. As all blocks have exactly the same shape, it is sufficient to generate one template by rasterizing the block under the current viewing transformation. Projection is performed by translating the template by a vector
which corresponds to the block's position in three-dimensional space in viewing coordinates. Thus, 
and 
specify the position of the block on the image plane (and therefore the location where the template has to be written into the entry point buffer) and 
is added to the depth values of the template. The Z-buffer algorithm is used to ensure correct visibility. In ray setup, the depth values stored in the entry point buffer are used to initialize the ray positions.
The disadvantage of this approach is that it requires an addition and a depth test at every pixel of the template for each block. This can be greatly reduced by choosing an alternative method. The blocks are projected in back-to-front order. The back-to-front order can be easily established by traversing the generated block lists in reverse order. For each block the Z-value of the generic template is written into the entry point buffer together with a unique index of the block. After the projection has been performed, the entry point buffer contains the indices and relative depth values of the entry points for each ray. In ray setup, the block index is used to find the translation vector 
for the block and is added to the relative depth value stored in the buffer to find the entry point of the ray. The addition only has to be performed for every ray that actually intersects the visible volume.
We further extended this approach to determine the entry points in a finer resolution than block granularity. We replaced the minimum and maximum values stored for every block by a min-max octree. Its root node stores the minimum and maximum values of all samples contained in the block. Each additional level contains the minimum and maximum value for smaller regions, resulting in a more detailed description of parameter variations inside the block. Every time the classification changes, the summed area table is recursively evaluated for each octree node and the classification information is stored as linearized octree bit encoding using hierarchy compression.
The projection algorithm was modified as follows. Instead of one block template there is now a template for every octree level. The projection of one block is performed by recursively traversing the hierarchical classification information in back-to-front order and projecting the appropriate templates for each level, if the corresponding octree node is non-transparent. In addition to the block index, the entry point buffer now also stores an index for the corresponding octree node. In ray setup, the depth value in the entry point buffer is translated by the component of the translation vector plus the sum of the relative offsets of the node in the octree. The relative translational offsets for the octree nodes can be pre-computed and stored in a lookup table.