Adaptative Cubical Grid for Isosurface Extraction

This work proposes a variation on the Marching Cubes algorithm, where the goal is to represent implicit functions with higher resolution and better graphical quality using the same grid size. The proposed algorithm displaces the vertices of the cubes iteratively until the stop condition is achieved. After each iteration, the difference between the implicit and the explicit representations are reduced, and when the algorithm finishes, the implicit surface representation using the modified cubical grid is more detailed, as the results shall confirm. The proposed algorithm corrects some topological problems that may appear in the discretisation process using