Infinite Line Toolpath-Mesh Intersection

Figure 1 depicts intersections of an infinite line toolpath with a finite element, $E$. The toolpath is defined by an infinite line attached to a reference point that is moving along the path connecting points $(X_1,X_2,X_3,\mathrm{...},X_n)$ such that the reference point is at $X_i$ at time $t_i$. It is assumed that the tool travels at a constant velocity over a segment connecting two successive points in the path, and the infinite line remains perpendicular to the segment. The first field defined in the event series represents a state of the tool, such as the "on/off" state of a recoater roller. The field defined for a point $X_n$ remains constant over the segment connecting $X_n$ and $X_{n+1}$. All path segments when the tool is in the "on" state must be perpendicular to the global z_g-direction. For a given element, the toolpath-mesh intersection module computes the number of intersections, $m$, of the toolpath and the volume fraction, $v_f$, for each intersection. The volume fraction is equal to the ratio of the partial volume of the element below the z-plane defined by the motion of the infinite line following the path to the total volume of the element. The module also computes the area, A; the coordinate $X^a$ with respect to the element reference coordinate system of the center of intersection of the z-plane and the element; as well as the area fractions, $a_f^i$, below the z-plane for all sides (i = 1 to the number of side facets of the element) for each intersection.

Figure 1. Infinite line toolpath-mesh intersection.