Geometry

Geomtry is the branch of mathematics that investigates relationships, properties and measurement of volumes, surfaces, curves and angles. The science that treats properties and relationships, the science that treats spatial relations. Geometry is a basic tool for describing and understanding natural and human made objects. Computer based geometric models can both describe such physical object as well as non-existent virtual objects. Such virtual objects play a central role in Computer Aided Design, Animation movies and computer games. The computer models are an important tool for understanding the structures and properties of both real and virtual objects. Geometry is classical branch of mathematics, however, rapidly evolving. The increased computational power and graphics capacity of standard computers is a driving force in this rapid evolution.

The SINTEF activities within geometry combines theory and experience from spline technology, applied algebraic geometry and numeric methods with requirements from industry and society based on what is computational feasible on commodity and emerging hardware technologies.  

Mathematics for CAD/CAM-systems, with a special focus on surface intersection, has been central in the activity for more than two decades, and still plays a central role within the research, especially with relation to CAD-type intersection algorithms.  The intersection technology for NURBS-type surfaces in the CoCreate systems for PCT is developed at SINTEF.

During the last years new intersection technology has been developed in the EU-sponsored GAIA II project. This technology addresses singular and near singular intersections of CAD-surfaces and CAD-surface self-intersection. The development was done in close cooperation with think3. A new software tool is made available under the GNU GPL-license .

Another new development is acceleration of intersection algorithms by using the computational power of programmable graphics cards (GPUs) (Patent PCT/NO05/00453: Apparatus and method for determining intersections). This development is done in our GPGPU-project. This approach will significantly increase the speed CAD-intersections calculation that guarantees the quality of the intersections calculated. We expect at least a 10x performance increase for singular and near singular intersection situations.  Use of these tools for determining the semantics of CAD-type surfaces are investigated in the EU-sponsored AIM@SHAPE NoE.