Random spherically-constrained (RSC) reconstruction is a new form of single particle reconstruction (SPR) using cryo-EM images of membrane proteins embedded in spherical lipid vesicles to generate a 3D protein structure. The method has many advantages over conventional SPR, including a more native environment for protein particles and an initial estimate of the particle's angular orientation. These advances allow us to determine structures of membrane proteins such as ion channels and derive more reliable structure estimates. We present an algorithm that relates conventional SPR to the RSC model, and generally, to projection images of particles embedded with an axis parallel to the local normal of a general 2D manifold. We illustrate the performance of this algorithm in the spherical system using synthetic data.