"Freeform shapes represent one of today's important manufacturing challenges. This applies to numerically controlled (NC) machining of parts to be produced in large amounts as well as to outer surfaces and subconstructions for unique designs in modern architecture. However, currently no systematic method exists which could reconcile the competing aims of faithfully reproducing smooth surfaces with their efficient segmentation into easily manufacturable parts. GEMS aims to overcome this challenge by a geometric approach: We consider surfaces generated by the motion of either a milling tool or a profile curve, and investigate their properties and approximation power. Our ultimate goal is to algorithmically determine a segmentation of freeform surfaces into parts exactly manufacturable by a single sweep. This amounts to highly nonlinear optimization with side conditions originating in both geometry and manufacturing and requires a detailed shape analysis. Subsequently these mathematical results have to be expressed in terms of manufacturing processes, such as NC milling, styrofoam cutting, or the building of molds from a sequence of simple curves. Successful completion of this research would mean a very significant contribution to the manufacturing of freeform shapes, and indeed some complex tasks will be made feasible for the first time. We strongly believe that the proposed consortium of five partners has the capacity and knowledge to achieve success: (1) ModuleWorks, a leading provider of CAD/CAM software components (2) TU Wien, a university with deep knowledge in geometry processing and differential geometry (3) Technion, an internationally renowned technical school very successful in computer aided geometric design (4) Evolute, a high tech start up company specializing in geometric computing for architecture and manufacturing (5) ModuleWorks Romania, a ModuleWorks daughter and highly experienced in computational solutions for 5-axis machining."