The approximate implicitization developed by partner SINTEF is aimed at the challenges of singular and near singular intersection, and uses the full polynomial Bernstein basis (over a simplex). The use of a sparse basis, both in the case of the Bernstein basis and when extending the approach to multivariate tensor product representations, will allow for flexible modelling of the properties of the approximate (piecewise) algebraic surface.
There also exist methods for predicting the support of the implicit equation by exploiting, at the same time, the structure and the sparseness of the parametric expressions. This approach can be enhanced by recent advances in the theory of tropical geometry and the related algorithms. Such methods reduce the problem of implicitization to a question in linear algebra. This project aims at juxtaposing the numerical implicitization with support prediction methods. It will examine to what extent sparseness and structure can guide or enhance the approximation procedure with respect to specific applications.
For more details contact: Ioannis Emiris
Published June 20, 2008