*** 9660504 Waupotitsch This Small Business Innovation Research Phase I project will develop proof-of-concept geometric mathematical software tools to allow for the incremental reconstruction and control of surfaces and volumes generated from arbitrary point set data. The tools will incorporate novel methods for geometric modeling based on a combination of concepts from combinatorial topology and computational geometry. Current methods of surface reconstruction have found limited use due to a number of factors, including slow data processing, the introduction of approximation errors, and the requirement that data sets be well behaved. If successful, this project will result in the development of an elegant and compact solution to automatic surface and volume reconstruction and model simplification which is free of these limitations. The ability to accurately and automatically reconstruct or model the surface and volume of objects defined by an unstructured set of points has the potential to fundamentally impact a number of major economic sectors including the CAD/CAM, animation, and biological and medical modeling industries .***
