Accurate delineation of the volumetric motion of Left- Ventricle (LV) of the heart from magnetic resonance imaging is an important area of research. We have built a system that takes tagged short-axis (SA) and long-axis (LA) image sequences as input, fits a 3D B-spline solid model to the LV of the heart by matching 3 sequences of solid knot planes to 3 sequences of tag planes, and volumetrically tracks the LV deformations. The formulation described in this article is more efficient than our previously proposed B-spline solid work. The advantage of the B-spline solid is that each LV myocardial point is uniquely indexed by a solid point, simplifying displacement reconstruction. The output of the system is a 3D solid that accurately captures the volumetric LV motion and provides a 3D motion field. The concept of registering and fitting the solid's knot planes to the LV tag planes is novel. In order to outline the myocardium from the solid, two B-spline surface models are used to fit the endocardial and epicardial walls. The generated motion fields follow the ground-truth motion fields closely.