Section: New Results


Participants : Léo Allemand-Giorgis, Georges-Pierre Bonneau [contact] .

In computer visualization we have worked on two topics: topology for visualization and perception for visualization.

In topology for visualization we have worked on scalar field vizualization methods taking into account the topology of the data. In [15] We have derived theoretical results on monotonic interpolation of scalar data. Our method enables to interpolate given topological data such as minima, maxima and saddle points at the corners of a rectangular domain without adding spurious extrema inside the function domain, as illustrated in Figure 7 .

We have collaborated to a state of the art chapter on Uncertain Visualization [16] , in which we described the evaluation of visualization methods based on visual perception.

Furthermore we have worked on two topics related to geometry for visualization. In [6] we introduce a method for interpolating a quad mesh using G1-continuous polynomial surfaces. We plan to use this method in the future for displaying isosurfaces of higher order data. In [12] we have published a method for reconstructing interfaces in highly complex assemblies, as illustrated in Figure 8 . This method has been developed in order to visualize data arising from simulation of complex mechanical assemblies, within the ANR project ROMMA, closed in January 2014.

Figure 7. Local maxima (red), minima (blue), saddles (green) and regular (yellow) vertices are interpolated by a C1 piecewise cubic interpolant. Left: no unwanted local extrema exist in the interior of the cubic patches. Right: partial derivatives too large in size are chosen for the yelllow regular vertices implying that additional unwanted local extrema appear inside the cubic polynomial patches.
Figure 8. Aircraft part for assembling the wings with the body of an aircraft (model courtesy of EADS). (a,b) two views of the components, (c) exploded view, (d) ray casting results, (e) boundary reconstruction, (f) nal interfaces