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Geometry

Geometry

Chief Scientist

The research of the Geometry Group is focused on algorithms and workflows for creating shape descriptions for efficient design, simulation, analysis and visualization. The work includes applied algebraic geometry, approximation theory, spline technology, big data technology and Cloud computing.

Topics

 

CloudFlow (2013-2017) is an Integrating Project in EUs Factories of the Future PPT in fp7. The focus is Cloud services for manaufacturing and engineering SMEs. SINTEF has the role as techical coordinator. For more information Click here.

Traditional Computer Aided Design Systems target subtractive manufacturing where the material is solid, isotropic and uniform through the volume of the workpieces. Additive Manufacturing (3D Printing) allows varaible material properties, complex inner cavities and anisotropic material. We target a new generation of computer aided technologies for Addive Manufacturing in the H2020 Factories of the Future Research and Innovation CAxMan (2015-2018) coordinated by SINTEF . For more information on CAxMan Click here.

 IQmulus (2012-2016) is an Integrating Project financed by fp7 addressing big GIS data in the framework of Cloud Processing. SINTEF is Coordinator. For more information see: www.iqmulus.eu.

VELaSSCo (2014-2016) is an fp7 STREP. Visualization For Extremely Large-Scale Scientific Computing. Using Cloud Computing and Big Data techniques to investigate and interact with data from extremely large scale simulations. For more information see: http://www.velassco.eu/

Approximation by LR B-spline surfaces

Terrain data can have a very compact representation using LR B-spline surfaces. Large point clouds are approximated using either least squares approximation of LR-MBA (multiresolution B-spline approximation applied to LR B-spline surface). New degrees of freedom are iteratively added to the surface description where the approximation error is too large until some accuracy criteria are met.

TERRIFIC (2012-2014) is a STREP in EU's Factories of the Future initiative in fp7. The objective is to produce tangible evidence of the applicability of Isogeometric representation and analysis by addressing four industrial Use Cases. Click here for Visualization of Isogeometric Analysis of a Model Under External Forces.

For more information see: http://www.terrific-project.eu

Geometry toolkits

Over many years, SINTEF has developed many software libraries for computational geometry as part of research and industrial projects. These libraries are available under the GPL license.
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Locally refined B-splines

The theory of Locally Refined (LR) B-splines offers a framework for local refinements on spline meshes of dimension 2 or higher. LR B-splines have much to contribute for practical deployment of isogeometric analysis in science and industry. Locally Refinable Splines over Box-Partitions published in CAGD click here.

Isogeometric Representation

Isogeometric Analysis aims at an efficient integration of CAD and FEM and uses the spline basis both for geometry description and for finite element analysis. A trivariate block structured spline model is appropriate for representing the geometry corresponding to the analysis at hand.

Exact algebraic methods

With the need for high-quality representations for isogeometric analysis, there is a renewed interest in exact parametrization techniques. We apply results from Laguerre and Isotropic geometry to construct exact rational parametrizations of, in particular, blends between primitive surface elements in Computer Aided Design.

3D Airports for Remotely Operated Towers. SINTEF ICT participates in the SESAR Joint Undertaking, a programme established by the EU to modernize air traffic management system for Europe. Our 3D technologies enhance the experience of air traffic controllers by integrating 3D geometry with 2D video streams.

http://www.sesarju.eu/

Big data

Our focus within the challenges of big data is to establish workflows for processing big point clouds into compact representations suited for advanced processing and visualization. Our approach is to provide hybrid representations that have compact representation of the smooth components of the information (e.g., by LR B-splines) combined with other representation for local features. See the IQmulus and VELaSSCo below for more details

Computational geometry

Computational geometry is the research field that relates to the shape, description, and properties of physical objects. SINTEF Oslo has been a key player in this field for five decades.
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Approximate algebraic geometry

Development of floating point based algorithms for algebraic geometry challenges facilitate industrial use.
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