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Segment composition

  Usually the angle between the left and right rays tex2html_wrap_inline1674 is small ( tex2html_wrap_inline1718 degree is recommended). As a result series of sampling points along a single left-ray could be reprojected onto the same right-eye pixel.

Assuming that a sampling point tex2html_wrap_inline1650 is projected to tex2html_wrap_inline1662 of the left-image and tex2html_wrap_inline1664 of the right image and the distance between the left and the right center of projection is e. If we assign

displaymath1698

then for a left ray, cast from tex2html_wrap_inline1662 , c is a constant, and

displaymath1699

Assume that

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then for all sampling points on the ray in the interval

displaymath1701

we have

displaymath1702

figure448

Thus, instead of reprojecting the sampling points on the ray one by one segments of the ray with lenght tex2html_wrap_inline1732 can be reproject and composite the color and opacity of the segments onto a pixel on the right image:

Suppose that tex2html_wrap_inline1378 is the opacity, tex2html_wrap_inline1736 the translucency, the accumulated color and translucency tex2html_wrap_inline1738 and tex2html_wrap_inline1740 resp. at the entry point of a certain segment. ( tex2html_wrap_inline1742 and tex2html_wrap_inline1744 resp. at the exit point). The translucency tex2html_wrap_inline1746 and the color tex2html_wrap_inline1748 of this segment can be calculated as

displaymath1703

displaymath1704

and the composition on the reprojected pixel is

displaymath1705

displaymath1706

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.

figure484



Lukas Mroz
Tue Feb 9 12:46:24 MET 1999