Using a combination of self-consistent and test-particle techniques, Identikit 1 (ascl:1011.001) provided a way to vary the initial geometry of a galactic collision and instantly visualize the outcome. Identikit 2 uses the same techniques to define a mapping from the current morphology and kinematics of a tidal encounter back to the initial conditions. By requiring that various regions along a tidal feature all originate from a single disc with a unique orientation, this mapping can be used to derive the initial collision geometry. In addition, Identikit 2 offers a robust way to measure how well a particular model reproduces the morphology and kinematics of a pair of interacting galaxies. A set of eight self-consistent simulations is used to demonstrate the algorithm's ability to search a ten-dimensional parameter space and find near-optimal matches; all eight systems are successfully reconstructed.