Automated methods implemented in a computer system are provided that allow the translation of geometric shapes from a cutting pattern having a nested configuration to geometric shapes shown in an installed configuration and vice-versa. Methods are also provided that allow modification of cutting patterns based on various modifications applied to the geometric shapes therein. Additionally, certain methods herein allow cutting patterns to be automatically modified to conform to protective films of different sizes. In certain embodiments, methods are provided for optimization of the arrangement of geometric shapes in a nested configuration so as to substantially minimize the surface area occupied by the geometric shapes. Automated pattern manipulation systems implementing one or more of the methods herein are also provided.