1. A method for modeling geometrically complex objects comprising the steps of: obtaining voxel-based image data of a three-dimensional region wherein the image data includes an image of a first three-dimensional object, and storing the voxel-based image data on a computer; segmenting the voxel-based image data, the segmentation output comprising a grid of points and a first set of signed distance values comprising a signed distance value for each point on the grid of points, wherein the magnitude of the signed distance value for each point represents the shortest distance from the point to a surface of a representation of the first three-dimensional object; using wavelets to interpolate the signed distance values between points on the grid of points and to generate a function-based representation of the first three-dimensional object; obtaining a second set of signed distance values on the grid of points, wherein the second set of signed distance values represent a second three-dimensional object; manipulating the first and second sets of signed distance values to perform a computer-aided design operation; and storing the second set of signed distance values and at least one of: (i) the first set of signed distance values, and (ii) the function-based representation of the first three-dimensional object, onto a non-transitory computer-readable medium; wherein the computer-aided design operation is selected from the set comprising complement, intersection, union, and difference.