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As much as i understand. Geodesic line of curvature is a line on the surface such that the projection on the tangent plane of it's curvature vector is 0 at every point. The lines of curavture are lines such that their tangent direction is coincident with one of the principal direction on the surface at every point. But I can't see the difference between them. Can anyone make it clear for me?

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    wow, that was clear. Thanks a lot. Stupid me2012-06-20

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