| There has been tremendous growth of 3D content through the use of computers. Within the past decade, the capability to acquire, display and modify complex geometry on machines which formerly would have cost orders of magnitude more has been developed. As these technologies continue to develop, demand for larger and more complex 3D models will inevitably increase. This thesis provides solutions in three areas involved in the creation of 3D content to meet this demand: acquisition, surface representation, and reconstruction.;The first part of this thesis provides a method for improving the resolution of surfaces captured by scanners by combining many very similar scans. This idea is based on an application of the 2D image processing technique known as super resolution. The input lower-resolution scans are each randomly shifted, so that each one contributes with slightly different information to the final model.;In order to efficiently display, process, and edit massive 3D models, significant effort has been devoted to point-set surfaces, which define a 2D surface implied by a point cloud. However, most of these representations have been originally defined algorithmically as the output of a particular meshless construction, which, unfortunately, does not reveal much about the properties of these surfaces. The second part of this thesis provides an explicit definition by generalizing these point-set representations to what is known as extremal surfaces. This generalization simplifies the constructions of other variants and allows for the comparison and visualization of properties of point-set surface models to be easily made.;In some situations, the distribution of the sample points is entirely under the control of the application which upsamples, downsamples, and smooths the distribution as necessary. The third part of this thesis presents a simple and completely local surface reconstruction algorithm for input point distributions that are locally uniform. The locality of the computation lets us handle large point sets using parallel and out-of-core methods. The algorithm can be implemented robustly, with floating-point arithmetic. The simplicity, efficiency, and numerical stability of this algorithm is demonstrated with an out-of-core and parallel implementation, using graphics hardware. |
