Resumen: This chapter describes a surface reconstruction method that mixes interpolating and approximating features and its implementation in graphics hardware. Hybrid methods are useful in areas such sculpting, medicine, and cultural heritage, where details must be preserved. Such cases may also contain noise (due to sampling inaccuracies) or duplicated points (in the case of the scan is done from multiple points of view), where hybrid methods provide an interesting solution. The proposed method makes use of a point projection operator to create a regular distributed and noise free set of points, which is reconstructed using local Delaunay triangulations. Both points projection and triangulation methods are studied in its basic serial version, but aiming to design parallel versions (more specifically GPU implementations) that increase their performance. The adaptations required for the parallel reconstruction are discussed, and several implementation details are given.