We address the synthesis of controllers for large groups of robots and sensors, tackling the specific problem of controlling a swarm of robots to generate patterns specified by implicit functions of the form s(x, y) = 0. We derive decentralized controllers that allow the robots to converge to a given curve S and spread along this curve. We consider implicit functions that are weighted sums of radial basis functions created by interpolating from a set of constraint points, which give us a high degree of control over the desired 2D curves. We describe the generation of simple plans for swarms of robots using these functions and illustrate.