1. A system for generating a patch surface model of a heart, the system comprising: a computer-based model construction system configured to be coupled to a catheter including a distal end configured to be navigated through a vein and into the heart of a patient, the catheter comprising a sensor disposed at the distal end and configured to contact a surface of the heart and determine a set of original location data points corresponding to respective locations on the surface of the heart, the computer-based model construction system further configured to receive the set of original location data points, the computer-based model construction system further configured to: generate a reference surface based on the acquired original location data points; subdivide the reference surface into a plurality of triangles; project at least some of the original location data points onto a respective nearest point on the subdivided reference surface; compute a function that morphs the projected location data points towards the original location data points to generate a patch surface model; define a bounding box and erode away a portion of the plurality of triangles that do not contain projected original location data points from edges of the bounding box to determine a boundary for the patch surface model; and generate the patch surface model for display on a display system.