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By Robert Aish, Aparajit Pratap (auth.), Lars Hesselgren, Shrikant Sharma, Johannes Wallner, Niccolo Baldassini, Philippe Bompas, Jacques Raynaud (eds.)

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The fact that great circles are geodesic curves of the unit sphere leads to the following initialization procedure: Each vertex "v" of the mesh tp is equipped with a unit vector "a( v)" indicating an asymptotic direction. The latter constitute the vertices of a mesh tp* contained in the unit sphere, which has the same combinatorics as tp. Like above, the unknown strip boundaries are found as level sets of a function f. The 1-1 correspondence between meshes tp, tp* transfers the function f and its level sets to the mesh tp*.

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Figure 11 shows an example where the constant width of strips which was achieved during the initialization phase did not survive the second optimization stage. Our experience shows that the conoidal property (which we consider the most important in the context of this paper) does not seem to be a great restriction - see the comparison provided by Figure 12. Problems arose mostly in enforcing watertightness. We should remark that using a common boundary for adjacent strips will of course overcome that problem, but it will also cost valuable degrees of freedom.

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