Porous media, heterogeneous materials, and biological tissues are examples of ubiquitous disordered systems, the understanding of which and any physical phenomenon in them entails having an accurate model. We show that a new reconstruction method based on a cross-correlation function and a one-dimensional raster path provides an accurate description of a wide variety of such materials and media. The reconstruction uses a single 2D slice of data to reconstruct an entire 3D medium. Seventeen examples are reconstructed accurately, as indicated by two connectivity functions that we compute for them. The reconstruction method may be used for both unconditioned and conditioned problems, and is highly efficient computationally.