A good mesh representation of tridimensional objects is necessary not only to render algorithms but also to support numerical simulations. Objects captured via sensors, e.g., seismic acquisition and laser scanning, have an intrinsic error in its representation of objects. Furthermore, this unprocessed data does not generate a good description of the objects, portraying it inadequately or incorrectly. The existing literature on resampling representations contains various techniques to resolve this problem. In particular, a general approach using triangle mesh has recently gained attention. One benefit of this technique is its mathematical guarantees generating triangles meshes that closely approximate Delaunay triangles. The main drawback to this technique occurs in its application to objects with borders, such as holes or mesh intersections. In this work, we present a new method to re-mesh the object representation taking into account the simplification of the curves that represent the holes. We apply this technique to seismic horizon data.