A novel direct method for obtaining the orientation-dependent crystal strain field is presented within the framework of finite elements over Rodrigues parameter space. General conditional constraints are established and applied in the context of an optimization problem. A model lattice strain distribution function (LSDF) is obtained via an elasto-viscoplastic polycrystal simulation and used to assess the performance of the method. The validity of representing the inter-granular strains as an LSDF over the orientation space is examined. The strain pole figure inversion method is shown to recover the model LSDF and macrostress to a high degree of accuracy.