Abstract: Disclosed herein are systems and methods for three-dimensional (3D) printing and scanning (or rapid prototyping). For example, presented herein are 3D printing and scanning systems and methods to create a 3D replica of a 3D object on a build surface. Movements and/or controls of the system are generally based on polar coordinates relative to a center of a build surface. System components may generally include: (1) a rotatable build surface; (2) a media extruder positioned over the build surface; (3) a heating element to melt media as it is drawn into the extruder; (4) an extruder positioning system coupled to the extruder and configured to move the extruder over the build surface based on polar coordinates relative to a center of the build surface; and (5) an optical scanning system for scanning of a 3D object to obtain a plurality of two-dimensional (2D) images of the 3D object.