Cosmetic Spray Robot: Surface-Normal Deposition

Robotic cosmetics application — spray tanning, aerosol foundation, protective coatings — depends on keeping an applicator nozzle perpendicular to a curved surface while sweeping a raster path that leaves no gaps and no over-thick streaks. This simulator builds a doubly-curved bust as a true surface of revolution, derives the outward normal analytically at every point, and drives a 3-DOF robot arm (rotary base plus an analytic 2-link inverse-kinematics solve) to keep the nozzle normal-aligned along a boustrophedon toolpath. A Gaussian spray-cone model with inverse-square standoff falloff deposits coating thickness in real time, so speed, standoff, line pitch and flow rate each visibly trade off against coverage uniformity and build time — exactly the parameters a real coating-robot programmer has to tune.