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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.

PROJECTS

Research areas

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.

 

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.

Spline technologies for 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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Software

Expertise