A system for updating a mesh following an ablation procedure, the mesh representing an electroanatomical map of a surface of a heart and comprising a plurality of vertices, the system comprising: an electrical interface; a display; and a processor, 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 an intrabody catheter, the signals indicating an electrical property of each of a plurality of locations on the surface of the heart in the region of the ablated tissue; and to update the mesh as the processor identifies the heart's electrical properties from the received signals, by, for each particular location of the locations: identifying a closest one of the sample points, which corresponds to a location that is closest to the particular location, relative to other ones of the sample points, subsequently, identifying, in a portion of the mesh in which the closest one of the sample points is located, a closest point, which corresponds to a location on the portion of the mesh that is closest to the particular location; wherein the portion of the mesh consists of a tile in which the closest sample point is located, and a plurality of neighboring tiles that surround the tile in which the closest sample point is located, and subsequently, associating the closest point with the electrical property of the particular location and retiling the mesh to incorporate the closest point; and to render the updated mesh on the display. an electrical interface; a display; and a processor, 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 an intrabody catheter, the signals indicating an electrical property of each of a plurality of locations on the surface of the heart in the region of the ablated tissue; and to update the mesh as the processor identifies the heart's electrical properties from the received signals, by, for each particular location of the locations: identifying a closest one of the sample points, which corresponds to a location that is closest to the particular location, relative to other ones of the sample points, subsequently, identifying, in a portion of the mesh in which the closest one of the sample points is located, a closest point, which corresponds to a location on the portion of the mesh that is closest to the particular location; wherein the portion of the mesh consists of a tile in which the closest sample point is located, and a plurality of neighboring tiles that surround the tile in which the closest sample point is located, and subsequently, associating the closest point with the electrical property of the particular location and retiling the mesh to incorporate the closest point; and to render the updated mesh on the display. 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 an intrabody catheter, the signals indicating an electrical property of each of a plurality of locations on the surface of the heart in the region of the ablated tissue; and to update the mesh as the processor identifies the heart's electrical properties from the received signals, by, for each particular location of the locations: identifying a closest one of the sample points, which corresponds to a location that is closest to the particular location, relative to other ones of the sample points, subsequently, identifying, in a portion of the mesh in which the closest one of the sample points is located, a closest point, which corresponds to a location on the portion of the mesh that is closest to the particular location; wherein the portion of the mesh consists of a tile in which the closest sample point is located, and a plurality of neighboring tiles that surround the tile in which the closest sample point is located, and subsequently, associating the closest point with the electrical property of the particular location and retiling the mesh to incorporate the closest point; and identifying a closest one of the sample points, which corresponds to a location that is closest to the particular location, relative to other ones of the sample points, subsequently, identifying, in a portion of the mesh in which the closest one of the sample points is located, a closest point, which corresponds to a location on the portion of the mesh that is closest to the particular location; wherein the portion of the mesh consists of a tile in which the closest sample point is located, and a plurality of neighboring tiles that surround the tile in which the closest sample point is located, and subsequently, associating the closest point with the electrical property of the particular location and retiling the mesh to incorporate the closest point; and to render the updated mesh on the display.