We propose a method to measure the hyperfine vectors between a nitrogen-vacancy (NV) center and an environment of interacting nuclear spins. Our protocol enables the generation of tunable electron-nuclear coupling Hamiltonians while suppressing unwanted inter-nuclear interactions. In this manner, each nucleus can be addressed and controlled individually thereby permitting the reconstruction of the individual hyperfine vectors. With this ability the 3D-structure of spin ensembles and spins in bio-molecules can be identified without the necessity of varying the direction of applied magnetic fields. We demonstrate examples including the complete identification of an interacting spin cluster in diamond and 3D imaging of all the nuclear spins in a bio-molecule of L-malic acid.