||Due to its complex geometry, the basal ring is often omitted when putting different heart geometries into correspondence. In this paper, we present the first results on a new mapping of the left ventricle basal rings onto a normalized coordinate system using a fold-over free approach to the solution to the Laplacian. To guarantee correspondences between different basal rings, we imposed some internal constrained positions at anatomical landmarks in the normalized coordinate system. To prevent internal fold-overs, constraints are handled by cutting the volume into regions defined by anatomical features and mapping each piece of the volume separately. Initial results presented in this paper indicate that our method is able to handle internal constrains without introducing fold-overs and thus guarantees one-to-one mappings between different basal ring geometries.