A computational method is described for mapping the volume within the DNA double helix accessible to the groove-binding antibiotic netropsin. Topological critical point analysis is used to locate maxima in electron density maps reconstructed from crystallographically determined atomic coordinates. The peaks obtained in this way are represented as ellipsoids with axes related to local curvature of the electron density function. Combining the ellipsoids produces a single electron density function which can be probed to estimate effective volumes of the interacting species. Close complementarity between host and ligand in this example shows the method to give a good representation of the electron density function at various resolutions. At the atomic level, the ellipsoid method gives results which are in close agreement with those from the conventional spherical van der Waals approach.