By focusing on the properties used to measure map projections and utilizing them to manipulate map projection parameters, we have developed a new interface for manipulating such map projections. With our interface, a user can create his or her own map projections by manipulating the weight of each property via sliders. Specifically, we employ equidistancy, equiareality, and conformality as property elements and allow the user to balance these property elements according to their perceived levels of importance. Additionally, along with this interface, we also have developed a technique for reducing the number of projection parameters by assuming that latitude lines are horizontal and that longitude widths are identical in each latitude, which improves execution speed. Furthermore, as an additional interface, we have implemented a method for creating interrupted maps. This allows users to make interruptions on a map easily by clicking the interruption panel. Our system also provides a new manipulation method with which the user can traverse a number of existing cylindrical projections, such as those created with the Mercator and Lambert cylindrical projection methods.