Assuming that a sampling point is projected to
of the left-image and of the right image
and the distance between the left and the right center of projection is
e. If we assign
then for a left ray, cast from , c is a constant, and
Assume that
then for all sampling points on the ray in the interval
we have
Thus, instead of reprojecting the sampling points on the ray one by one segments of the ray with lenght can be reproject and composite the color and opacity of the segments onto a pixel on the right image:
Suppose that is the opacity, the translucency, the accumulated color and translucency and resp. at the entry point of a certain segment. ( and resp. at the exit point). The translucency and the color of this segment can be calculated as
and the composition on the reprojected pixel is
Solution of the early ray termination problem:
The left ray is not terminated if a certain treshold is reached: the sampling within the current segment is terminated then we jump to the entry point of the next segment which corresponds to the next right eye pixel and reproject the sapmling points inside that segment. The same process is applied to all segments that correspond to non-opaque pixels in the right eye image. But the sampling points behind left ray termination are reprojected one by one.