4.1 Initialization

Dependent on the number of dimensions, the initial boundary is usually given as an oriented line segmentation or an oriented triangulation, respectively. The orientation of a line segment or a triangle is defined in this work as shown in Figure 4.1. The normal vector always points to the positive region of the LS function. Without loss of generality, grid point coordinates are assumed to be equal to their indices ${\vec{p}}$ . As a consequence, the grid spacing is unity ( ${\Delta x}=1$ ).

Figure 4.1: The orientation of the normal vector ${{\vec{n}}}$ on a line segment and on a triangle as defined in this work with respect to the order of nodes ${{\vec{x}}_i}$ .