Point Toolpath-Mesh Intersection

Figure 1 depicts intersections of a point toolpath with a finite element, $E$. The toolpath is defined by the path connecting points $(X_1,X_2,X_3,\mathrm{...},X_n)$ at times $(t_1,t_2,t_3,\mathrm{...},t_n)$. It is assumed that the tool travels at a constant velocity over a segment connecting two successive points in the path. The first field defined in the event series represents a state of the tool, such as the laser power. The field defined for a point $X_n$ remains constant over the segment connecting $X_n$ and $X_{n+1}$. All path segments where the tool is in the "on" state are required to be perpendicular to the global $z_g$-direction. For a given element, the toolpath-mesh intersection module computes the number of intersections of the toolpath, the coordinates of the start and end points ($\xi$_s and $\xi$_e, respectively, expressed in the element reference coordinate system), and the start and end times (t_s and t_e, respectively) for each intersection.

Figure 1. Point toolpath-mesh intersection.