1. A system for generating a multi-dimensional surface model of a geometric structure, the system comprising: a device comprising at least one sensor configured to collect a set of location data points corresponding to respective locations on or enclosed by a surface of the geometric structure; and a computer-based model construction system coupled to the device and configured to: generate a working volume based on the set of location data points; calculate a dilated field for the working volume; define a dilated surface based on the dilated field; calculate an eroded field for the working volume based on the dilated surface; and define an eroded surface based on the eroded field.