An example method includes storing invasive position data representing different positions of one or more sensors in a given coordinate system within a volume defined by an electromagnetic field and storing non-invasive position data representing different positions of a plurality of control points in the given coordinate system determined from a position of one or more sensors. The method also includes computing internal geometry data based on the invasive position data, the internal geometry data representing a three-dimensional anatomical surface within a patient's body. The method also includes computing electrode geometry data based on the non-invasive position data, the electrode geometry data representing a location of each of a plurality of electrodes on an outer surface of the patient's body. Electrical activity sensed by the plurality of electrodes can be reconstructed onto an anatomical envelope within the patient's body.