1. A method of designing a part having a portion conforming to a companion structure having a known topology, the method comprising: electronically accessing a reference geometry representing the topology; electronically accessing a source polygonal data model, wherein the source polygonal data model comprises a plurality of source vertices; generating modification vectors based on data generated by subdividing the source polygonal data model; modifying position characteristics of one or more of the source vertices, wherein the position characteristics are modified based on the modification vectors, wherein the source vertices are modified so that after the source polygonal data model is subdivided, vertices in the subdivided polygonal data model corresponding with the modified source vertices conform to the reference geometry; after modifying the source vertices, subdividing the source polygonal data model having the modified source vertices to generate the designed part, wherein subdividing the source polygonal data model causes vertices in the designed part to be positioned such that the designed part is spaced apart from the reference geometry by less than a maximum threshold at least partly because of the modified position of the modified source vertices; and displaying a representation of the designed part.