Thank you for the reply. Let me use two quotes from the MACET paper (Edge Transformations for Improving Mesh Quality of Marching Cubes), in the context of isosurface extraction.
"For each configuration, the set of active edges, i.e., edges where the function f has different signs at the endpoints, independently determines both the geometry and topology of the mesh. The topology is determined by the configuration of active edges for each cell. The geometry is determined by the location of the isovalue along each active edge. This independence leaves room to change the geometry of the mesh while keeping the topology intact. Our modification to MC explores this independence. Some edge transformations do not change the underlying topology: <<they only change the geometry of the isosurface.>>"
"In this work, we use a cubic spline interpolation to reconstruct the derivatives of the scalar field. <<We also use the corresponding cubic spline to reconstruct the scalar field itself>> at the sampling grid vertices. This means there might be more than one root in active edges. However, since the topology has already been determined by the lookup into the MC tables and the intersection calculation returns only one vertex, this presents no practical problems."
I want to leverage this independence of topology/geometry and get the geometry using cubic splines, in order to extract isolines from a volume dataset (a slice of it sor instace); preferably, using the teem library as cited in the paper. Do you have any pointers on how to proceed?