This Small Business Innovation Research Phase I project from Raindrop Geomagic, Inc. will explore the automatic creation of non-uniform rational B-spline (NURBS) surfaces from both 3D point sets and polygonal surfaces representing 3D models. NURBS surfaces are the preferred representation in the design phase because they allow easy and intuitive manual manipulation through control points; yet using current methods, the task of constructing NURBS surfaces has been both laborious and time-consuming for designers. Raindrop Geomagic seeks to investigate and prototype several methods from the theoretical community and compare their performance and feasibility. Automatically creating NURBS surfaces is one of the hardest unsolved problems in the computer-aided design industry, and a general solution may not be found in the short term. In Phase I, Raindrop Geomagic will prototype different geometric methods for this problem in the context of selected markets where data classification is not completely general. This work will provide the project team with a gain insight necessary to the achievement of defining an implementation path for a product for automated conversion in the next phase of the research. The resulting software, when fully developed, will fill an urgent need in the computer-aided design industry: to freely convert from polygonal surfaces (used for analysis and rendering) to NURBS-based surfaces (used for conceptual design and styling). Both computer-aided design/computer aided manufacturing (CAD/CAM) users and animators have a strong need for software tools that can help speed up their production schedules and reduce their costs.