Described embodiments include a system for updating a mesh, which includes a plurality of vertices, representing a surface of a heart. The system includes an electrical interface and a processor. The processor is configured to define a plurality of sample points on the mesh, such that a density of the sample points is greater than a density of the vertices, to receive, via the electrical interface, a plurality of signals from a catheter, the signals indicating an electrical property of each of a plurality of locations on the surface, and to update the mesh in accordance with the electrical property, by, for each of the locations, identifying a closest sample point to the location, subsequently, identifying, in a portion of the mesh in which the closest sample point is located, a closest point to the location, and, subsequently, associating the closest point with the electrical property of the location.