Another method is to use ListContourPlot3D to our use to create some polygons, and use these polygons to plot our ListSliceContourplot3D:

n=5;
pts=Table[x^2+y^2+z^2-1,{x,Subdivide[-2,2,n]},{y,Subdivide[-2,2,n]},{z,Subdivide[-2,2,n]}];
surf=Table[x^3+y^2-z^2,{x,Subdivide[-2,2,n]},{y,Subdivide[-2,2,n]},{z,Subdivide[-2,2,n]}];
lcp=ListContourPlot3D[surf,DataRange->{{-2,2},{-2,2},{-2,2}},Contours->{0},Mesh->None,BoundaryStyle->None];

gc=FirstCase[lcp,GraphicsComplex[__],{},\[Infinity]];
gc[[2]]=Cases[gc[[2]],Polygon[_],\[Infinity]];
gc=Drop[gc,-1];
pols=Normal[gc];

Graphics3D[pols]

ListSliceContourPlot3D[pts,pols,DataRange->{{-2,2},{-2,2},{-2,2}},Contours->{0},BoundaryStyle->None,ContourShading->None]

Thanks Sander for your reply. I am not really sure that I understood what you mean. I am still interested in finding a fast way of plotting these intersection lines, since my method crashes most of the time. Would you mind to write the analogous function 'person' for me, please?

Danica

Sorry Jason I cannot publish my matrices as they are the result of my research. I could send them to you in private though.

Is there any way for you to post the data (save as a "*.m" file and upload to gist.github.com) so that we could give it a try?

Perhaps try to use SliceContourPlot3D (version 10.2 and up), with the second argument being based on an interpolation function? I have not tried it, but might work.. Surface-surface intersection is not that easy to do 'out of the box' I think...