Data acquisition and analysis procedures for noncontact atomic force microscopy that allow the recording of dense three-dimensional (3D) surface force and energy fields with atomic resolution are presented. The main obstacles for producing high-quality 3D force maps are long acquisition times that lead to data sets being distorted by drift, and tip changes. Both problems are reduced but not eliminated by low-temperature operation. The procedures presented here employ an image-by-image data acquisition scheme that cuts measurement times by avoiding repeated recording of redundant information, while allowing post-acquisition drift correction. All steps are detailed with the example of measurements performed on highly oriented pyrolytic graphite in ultrahigh vacuum at a temperature of 6 K. The area covered spans several unit cells laterally and vertically from the attractive region to where no force could be measured. The resulting fine data mesh maps piconewton forces with <7 pm lateral and<2 pm vertical resolution. From this 3D data set, two-dimensional cuts along any plane can be plotted. Cuts in a plane parallel to the sample surface show atomic resolution, while cuts along the surface normal visualize how the attractive atomic force fields extend into vacuum. At the same time, maps of the tip-sample potential energy, the lateral tip-sample forces, and the energy dissipated during cantilever oscillation can be produced with identical resolution.