It shows a new three-dimensional reconstruction technique is presented, for the creation of surfaces from two overlapping polygons with different depths, based on the problem addressed by Gill Barequet and Amir Waxman. The presented reconstruction takes two polygons with three-dimensional spatial positions, superimposes on the two-dimensional plane, performs an arbitrary local triangulation, generates each vertex and faces, and returns the triangulation to the three-dimensional plane. This technique assumes high speed by avoiding interpolation processes and assumes an O (n) complexity. All the algorithms made use the same data structures, the same coding and all the programs were coded in the ANSI C language. For their correct implementation the following hardware configurations were used; Computer CPU using 5th generation Intel Core i7 processor Core i7-5775C 4-Core 3.3GHz; Core i7-5775C 4-Core 3.3GHz with three NVIDIA 9800 GTS cards interconnected with an SLI bus and an Adapteva Epiphany-V64 embedded system. The range of applications where this algorithm can be used is very diverse, including areas such as visual computing, video games, generation of geographic surfaces, geosciences and spatial processes. Keywords: Graphic computation, fast triangulation, 3D reconstruction, triangulation by interpolation