A system for generating a multi-dimensional voxel based 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 (46, 702) 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 (46, 702); calculate a dilated field for the working volume; define a dilated surface including vertices based on the dilated field; calculate an eroded field for the working volume based on the dilated surface; and define an eroded surface as the multi-dimensional surface model based on the eroded field such that the eroded surface is defined within the dilated surface, wherein to calculate a dilated field, the computer-based model construction system is configured to calculate a dilated field value D for each location in the working volume, and wherein the dilated field value D is the distance between the location and the closest location data point (46, 702), wherein to define a dilated surface, the computer-based model construction system is configured to define the dilated surface such that each vertex on the dilated surface has a dilated field value D equal to a first predetermined value α and vertices are interpolated between voxel centers to lie exactly on the dilated surface, wherein to calculate an eroded field, the computer-based model construction system is configured to calculate an eroded field value E for each location in the working volume, and wherein the eroded field value E is the distance between the location and the closest point on the dilated surface, and wherein to define an eroded surface, the computer-based model construction system is configured to define the eroded surface such that each vertex on the eroded surface has an eroded field value E equal to the difference between the first predetermined value α and a second predetermined value k, wherein the amount of fine detail in the surface is controlled by the predetermined value α and k controls a minimum radius of curves in the surface. a device comprising at least one sensor configured to collect a set of location data points (46, 702) 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 (46, 702); calculate a dilated field for the working volume; define a dilated surface including vertices based on the dilated field; calculate an eroded field for the working volume based on the dilated surface; and define an eroded surface as the multi-dimensional surface model based on the eroded field such that the eroded surface is defined within the dilated surface, generate a working volume based on the set of location data points (46, 702); calculate a dilated field for the working volume; define a dilated surface including vertices based on the dilated field; calculate an eroded field for the working volume based on the dilated surface; and define an eroded surface as the multi-dimensional surface model based on the eroded field such that the eroded surface is defined within the dilated surface, wherein to calculate a dilated field, the computer-based model construction system is configured to calculate a dilated field value D for each location in the working volume, and wherein the dilated field value D is the distance between the location and the closest location data point (46, 702), wherein to define a dilated surface, the computer-based model construction system is configured to define the dilated surface such that each vertex on the dilated surface has a dilated field value D equal to a first predetermined value α and vertices are interpolated between voxel centers to lie exactly on the dilated surface, wherein to calculate an eroded field, the computer-based model construction system is configured to calculate an eroded field value E for each location in the working volume, and wherein the eroded field value E is the distance between the location and the closest point on the dilated surface, and wherein to define an eroded surface, the computer-based model construction system is configured to define the eroded surface such that each vertex on the eroded surface has an eroded field value E equal to the difference between the first predetermined value α and a second predetermined value k, wherein the amount of fine detail in the surface is controlled by the predetermined value α and k controls a minimum radius of curves in the surface.