# Continuing triangulated surface with positive normals

Let $S$ is a triangulated surface in 3D space, $S_{xy}$ is its projection to $xy$-plane, $B_{xy}$ is a bounding box of $S_{xy}$. All triangles of $S$ have the following property: their normals point to the positive octant of the space, i.e., $N_x>0$, $N_y>0$, $N_z>0$.

The problem: to construct an algorithm, continuing $S$ to a new triangulated surface $\hat S$, by adding new triangles at the border, with the same property for normals, until projection will reach the bounding box: $\hat S _{xy} =B_{xy}$.