Current reconstruction methodologies for atom probe tomography (APT) contain serious geometric artifacts that are difficult to address due to their reliance on empirical factors to generate a reconstructed volume. To overcome this limitation, a reconstruction technique is demonstrated where the analyzed volume is instead defined by the specimen geometry and crystal structure as determined by transmission electron microscopy (TEM) and diffraction acquired before and after APT analysis. APT data are reconstructed using a bottom-up approach, where the post-APT TEM image is used to define the substrate upon which APT detection events are placed. Transmission electron diffraction enables the quantification of the relationship between atomic positions and the evaporated specimen volume. Using an example dataset of ZnMgO:Ga grown epitaxially on c-plane sapphire, a volume is reconstructed that has the correct geometry and atomic spacings in 3D. APT data are thus reconstructed in 3D without using empirical parameters for the reverse projection reconstruction algorithm.