1. A computer-implemented method for performing an electronic database search to identify previously designed components that are geometrically similar or identical to a source component, the method comprising: transforming a three-dimensional model of the source component into a coded representation of the geometry of the source component, wherein the transformation is performed using a defined field generating condition that would generate a field of a defined type in a region of space, and wherein the transformation is performed using a physical property of the source component as an input to a mathematical framework based on a field theory for the defined type of field, and wherein the mathematical framework yields one or more values that describe the field generated in the region of space; accessing an electronic database repository having stored therein multiple coded representations that each represent the geometry of a different previously designed component, each coded representation having been previously generated by transforming a three-dimensional model of the previously designed component into a coded representation of the geometry of the previously designed component using the same transformation used in transforming the three-dimensional model of the source component into the coded representation of the geometry of the source component; comparing the coded representation of the geometry of the source component to at least one of the stored multiple coded representations that each represent the geometry of a different previously designed component, to identify at least one previously designed component that is geometrically similar or identical to the source component; and generating a search result that identifies at least one of the previously designed components that are identified in the comparison to be geometrically similar or identical to the source product.