Robot Arm Painting: Toolpath-Driven Brushstroke Generator (2D)

This top-down 2D companion to the 3D SCARA painting-robot simulator solves the same closed-form two-link inverse-kinematics problem, computed independently every frame: pick a generative toolpath (a rose curve, a Lissajous figure, or an expanding spiral) and the arm's shoulder and elbow angles are derived geometrically to keep the brush exactly on that curve, depositing instanced paint dabs whose spacing and hue track the tool's real angular speed. A fixed-size ring buffer holds the dabs so the canvas coverage caps out realistically instead of growing without bound, and you can drag to pan or scroll to zoom the view while the arm keeps painting. Live readouts track both joint angles, instantaneous tool speed, and how much of the canvas has been painted.