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The composite imaging of measured cardiac properties like electrical activation and contractile properties on a reconstructed endocardial surface allows for the diagnosis of cardiac arrhythmia and myocardial infarct. However, it is difficult for an interventionalist to acquire heart surface contacts by navigating a catheter to the desired region of interest under minimal visual aid. This paper discusses a new method for the progressive reconstruction of an endocardial surface during a heart mapping procedure. A generic mesh is first aligned with a set of anchor points to obtain a first approximation of the surface. Subsequent deformations are constrained by the preservation of local surface characteristics and the fidelity of new contact points. The mesh is refined by local subdivision and its geometrical shape is further improved by edge swapping. Compared to prior art, the new method can reconstruct a realistic surface from a set of sparse and random data. It can advantageously provide a smooth reconstruction at initial acquisition and ensure a geometrical consistency between consecutive reconstructions. The accurate reconstruction of a heart chamber provides important visual cues for an interventionalist to decide on the next mapping site, thus constructively influencing the final diagnosis.