This Small Business Innovation Research Phase I project involves the development of Proof-of-Concept geometric mathematical software tools for the incremental reconstruction and control of high quality surfaces and volumes generated from point cloud data. This new incremental technique will make it possible to process the millions of points that come from today's laser and optical scanners. The tools will incorporate novel methods for geometric modeling based on a combination of concepts from discrete geometry and topology and from combinatorial and numerical algorithms. The proposed software tools will address two crucial needs in surface reconstruction: the need to deal with large point clouds automatically and efficiently, and the need to create high quality surfaces from large point clouds satisfying certain tolerance conditions. Raindrop Geomagic, Inc. will rely on its proven mathematical technology to implement a proposed solution that is more general, more efficient, and more rational than any of the previous approaches to the problem. The ability to accurately and automatically reconstruct or model the surface and volume of an object defined by a large, unstructured set of points has the potential to fundamentally impact a number of major economic sectors including the CAD/CAM, animation, and medical modeling industries.
