| Analysis capabilities are tightly integrated within many CAD systems, enabling seamless analysis of components' behavior without physical testing or prototyping. This seamless integration yields the notion of fully-augmented geometric models---models of shapes and their physics. While such integration is routine and expected with CAD models, analysis is not so routine with an increasingly important class of geometric representations arising froth laser surface scanning, computed tomography, and other modern acquisition technologies.;Meshfree analysis with distances promises analysis directly from geometry without an expensive and error-prone sequence of conversions. Previous work on meshfree analysis incorporated geometry into the solution as an implicit representation constructed using analytic primitives combined using R-functions. The resulting global function possessed "distance-like" properties at the domain boundary; however, the theory underlying the method actually places minimal requirements on the properties of the implicit representation.;The natural "distance-like" behavior of Euclidean distance, combined with the minimal requirements placed on the implicit representations for meshfree analysis, suggest that Euclidean distance would be a, good starting point for constructing such functions. This thesis demonstrates that meshfree analysis can be carried out from implicit representations constructed using samples of distance taken in the vicinity of the domain. The initial brute-force demonstration uses fitting to construct the implicit representation from samples of Euclidean distance taken at random. This fitting process is computationally intensive, requiring the assembly and solution of a global linear system. Meshfree analysis leaves sufficient freedom to use Euclidean distance directly for analysis if means can be found to evaluate, differentiate, and integrate it at any point within the domain. These operations are shown to be efficiently performed from samples of Euclidean distance taken on a regular grid and extended among the samples using local kernel interpolation or approximation. By sampling distance, analysis is based on a property intrinsic to the geometry and a frequent intermediate representation in reverse engineering algorithms. The result is automated analysis of artifacts, both designed and acquired. |
