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| Curves on surfaces can be very useful to visualize surface features at low graphical and memory cost. Curves on surfaces are also used for surface segmentation with possible applications to visualization, reconstruction and parameterization of complex surfaces. In this paper an algorithm for building smooth polygonal lines on triangulated 2D-manifold polygonal meshes is introduced. The algorithm combines geometrical optimization with topological operations on PLs in order to iteratively smooth an initial crude PL interpolating a user-defined set of triangles. One key feature of this algorithm is that it relies solely on the geometry of the surface and the polygonal line. Another key feature is that during the smoothing the polygonal lines always stay on the surface. |
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