Ideal particle accumulation on an arbitrary visibility polyline, in which all segments have a negative y-intereepts, is studied in this paper. Particles are assumed to be emitted from a fixed point location at the same emission velocity onto the surface of the ground. Since particles acted on by gravity travel in space via parabolic trajectories, by grouping parabolas, the accumulation of particles on curves approximated by polylines can be deduced. Analytical equations, namely the accumulation density functions, are used to represent particle accumulation on such curves. As many practical surfaces are generated by sweeping curve around cither a point, a line, or another curve, this simulated accumulation of materials on surfaces can be applied in many application areas, including agricultural spraying irrigation, seeding, chemical vapor deposition, and spray painting.
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