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The Gauss map on the right shows the overlay of a feature pair FV, where the intersection can be easily missed if this pair is projected onto a plane. There is definitely a chance I misunderstand how the projection works. Otherwise I have to workaround without the projection.
After some web searching, I learned that I was using orthographic projection, while I should use is gnomonic projection. The advantage for gnomonic projection is that the great circles will always be mapped to straight lines.
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