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As you can see, the texture starts off pretty much unchanged on the right side. As the stereogram progresses from left to right, however, the cumulative depth displacements make the texture pretty warped. To minimize this warping, I changed the order in which I generated the corresponding points. Instead, I started in the middle of the image and worked to the right side. Then I went from the middle to the left, sampling the depths and projecting to points into the already generated right hand side to find the correct color. This method forces the texture to be unwarped in the center, and the cumulative displacements can only be half as much before, as you can see on the following image:
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