In order to derive models that realistically describe the dynamics of photons around black holes, the use of a geodesic integrator is required. Using such an integrator, we may track null geodesics in curved spacetimes surrounding black holes. Since the binary black hole solution to the Einstein equations is not analytic, one requires the use of computationally intensive 3 + 1 numerical relativity. Instead, we consider a different route, by defining a novel metric, created from analytic space-like hyper-surfaces. With this in hand, applying a ray-tracing algorithm requires minimal computational resources. Critically, we present a preliminary step to finding black hole shadows for general binaries.