Metal artifacts are a well-known problem in computed tomography - particularly in interventional imaging where surgical tools and hardware are often found in the field-of-view. An increasing number of interventional imaging systems are capable of non-circular orbits providing one potential avenue to avoid metal artifacts entirely by careful design of the orbital trajectory. In this work, we propose a general design methodology to find complete data solution by applying Tuy’s condition for data completeness. That is, because metal implants effectively cause missing data in projections, we propose to find orbital designs that will not have missing data based on arbitrary placement of metal within the imaging field-of-view. We present the design process for these missing-data-free orbits and evaluate the orbital designs in simulation experiments. The resulting orbits are highly robust to metal objects and show greatly improved visualization of features that are ordinarily obscured.