Algorithms for complex shapes

PERSON IN CHARGE: Emiris Ioannis
FUNDED BY: European Comission
START DATE: 01/02/2005
END DATE: 31/01/2008
The project aims at advancing the state of the art in computing with complex shapes, starting with curves in the plane and surfaces in three-dimentional space, and including piecewise smooth surfaces, surfaces with singularities, as well as manifolds of codimension larger than one in moderately high dimension. Increasingly demanding applications require efficient and robust algorithms for complex shapes. Topics that arise and that we address are shape approximation (including meshing and simplification), shape learning (including reconstruction and feauture extraction), as well as robust modelling (including boolean operations). Our work on these topics will be closely intertwined with basic research on shape representations. A unique and ambitious feature of our approach is the quaranteed quality of all data structures and algorithms we plan to develop. through certified topology and numerics, we will be able to prove that the output is topologically and numerically consistent, according to prespecified criteria. A software prototype, dealing with a restricted class of complex shapes, will demonstrate the feaibility of our techniques in practice.
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