The accurate representation of two-dimensional images in three dimensions has become important for many medical imaging applications and for cardiac magnetic resonance imaging (MRI) in particular. Reconstruction methods applied after data acquisition can produce three-dimensional information from two-dimensional data and make applications such as surgical planning more effective. Current reconstruction techniques usually demand contrast agents, and can suffer due to poor segmentation and sampling constraints that cause surface irregularities and distort dimensions. The novel technique presented here for anatomical modeling uses adaptive control grid interpolation (ACGI) to approximate data not captured by scanning, and a progressive shape-element segmentation technique to complete reconstruction. Quantitative validations conducted on models of pediatric cardiac malformations have confirmed the theoretical advantages of this technique, and that higher quality is achieved than with competing methods based on geometric parameters. Vascular diameters from reconstructions showed errors of less than 1% for a known geometry as compared to over 9% for competing methods. Qualitatively, models produced with the new methodology displayed substantial improvement over alternatives. Approximately 50 rare cardiac structures, including surgically altered Fontan and atypical aortic anatomies, have been reconstructed. All data used to create these reconstructions were acquired using standard pulse sequences and without contrast agents. Benefits of the new technique are particularly evident when complex vascular configurations complicate reconstruction. The proposed methodology enables a powerful tool allowing physicians to analyze and manipulate highly accurate and clearly presented vascular structures in an interactive medium.