The present invention is directed to a high density mapping catheter including a number of shape memory electrode fibers and associated methods of construction and operation. The invention ensures good electrical contact between a large number of mapping electrodes and cardiac tissue in relation to a number of cardiac tissue approach angles, including head-on approaches. In addition, the invention allows for a reduced range of deflection angles in relation to deployment and retraction of the electrode fibers, thereby reducing resistance to retraction and reducing stress on the fibers and associated concerns regarding patient safety. The catheter of the present invention allows for rapid acquisition of a large amount of mapping data and allows for a variety of different geometries in relation to sweeping of the catheter across the cardiac tissue.