Martedi 19 Dicembre, alle ore 14.30 presso la sala conferenze dell'IMATI-CNR di Genova, il

Dr. Hamish Carr, Senior Lecturer all'Università di Leeds, UK,

terrà un seminario dal titolo:

Fiber Surfaces, Jacobi Sets and Reeb Spaces.

 


Abstract:

Classic techniques from scientific visualisation such as isosurfaces and direct volume rendering are used for scalar fields (i.e. functions in space with univariate output).  For bivariate and higher functions, rather fewer techniques exist, except in the special case of vector fields. We have recently defined the analogue for isosurfaces in bivariate fields, which we call fiber surfaces. These generalise isosurfaces by taking the inverse image of a curve in the function's range - i.e. a loop on a (continuous) scatterplot.  This provides a rigorous and easy to compute geometric surface that can be used to capture regions of interest in the data interactively. Since fiber surfaces are based on marching cubes, many techniques can be carried over, such as acceleration structures, but detailed geometric interpolation is considerably more difficult. We therefore show how to extract fiber surfaces for marching cubes cases and for tetrahedral meshes, and illustrate how ray-tracing can also capture fiber surfaces for trilinear interpolants. Finally, as the data scales, tools such as topological analysis become significant in visualisation. We therefore also show how to generalise contour tree/Reeb graph analysis to bivariate functions with a correct and efficient algorithm for extracting the Reeb space. Finally, we show how the Reeb space can be used to support interactive scatterplot peeling for efficient visualisation of smaller features that would otherwise be hidden by occlusion.