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Unproject rendering

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I need to render a 360 degrees scene in order to grab the result as a texture that can be mapped on a half sphere ("sky dome"). I would like to render and grab for each planar segment of the target sphere. Such rendering is NOT a standard perspective projection. It would need an unprojection to the target plane. I can unproject each pixel (CPU), but that's not efficient. I wonder if there is some kind of projection matrix that would have made this rendering straight forward so that the result can be applied to the sphere-segment-plane and eventually come right. Maybe a shader? Any other idea? Thanks, Yigal

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