Fast RayCasting of volume data []

Direct volume rendering ( visualize the volume data without any prior encoding like polygon extraction) but just the first hit. Surface based rendering.
If a surface point is visible in one projection then it is highly probable that it will remain visible in the next projection.
They can be computed incrementally avoiding full-fledged raycasting.

  
Figure: 2D illustration of an incremental rotation after a full raycasting. At1 has become hidden. At 2 samples have become clustered. At 3 new rays are cast to fill in gaps. A left scan is done at 4 to find new visible surface.

Assume for simplicity:

• The rotation axis is perpendicular to the viewing direction (z axis).
• The rotation axis is parallel to y axes of the volume. Plane xz is projected to a line with constant y in the image plane.
• parallel projection.
• object rotate counterclockwise (Image plane fixed)

First full-fledged raycasting (ray per pixel).
Save in a list all detected surface points. One list for each y sorted in x from left to right.

1. Transform points in the list using a 2D geometric transformation.
2. Remove those points that have become hidden.
3. Detect new surface points by selective raycasting and insert in the list.
4. Resample all surface points.

The surface points became visible and invisible following two rules:

1. Surface points that disappear will project to the left of some new right silhouette edge.
2. Newly visible surface points will appear to the left of some old silhouette.

They don't keep track of the silhouette points.

Step 2 follow rule 1. Points are ``sur-passed''.
Step 3 and 4:

• After the initialization step the list contains uniformly sampled but the rotation transformation yields to non-uniform ( See figure ).
• So they resample rounded to the nearest pixel if more than one per pixel select the nearest. Samples slides too far apart new rays must be cast.
• step 3 and rule 2:
  All the pixels are initialized to B background. The criterion to cast rays in step 3 is : A ray is cast for all contiguous pixels containing B immediately to the left of a resampled and shaded pixel. Stop the scan when a ray does not detect a surface.

This fill the gaps and detecting newly visible points.
PROBLEM: When angle increment is large, background become visible between disjoint objects. The left scan will stop and some surface will go undetected.
SOLUTION: An additional right scan.