Abstract: A three-dimensional object is manufactured by forming a series of three-dimensional formed curves of extruded material that together comprise the geometry of the surface of the object. The material is extruded from a nozzle that is positioned by a robotic arm under the control of a robotic controller. A computer that has a definition of the geometric surface generates commands to the robotic controller to cause it to sequentially form the series of formed curves that the computer calculates comprise the surface geometry.