Finding the origin of an arrythmia

A medical apparatus, comprising:

• a probe, configured to be inserted into a chamber of a heart of a human subject, and to generate location signals indicative of location coordinates of a distal end of the probe, and comprising at least two pairs of electrodes at the distal end, which are configured to acquire from positions on a surface of the chamber respective electrical signals in response to a conduction wave traversing the surface;
• a display;
• and
• a processor, configured to:
• process the location signals to generate and present on the display a three-dimensional (3D) representation of the surface,
• derive respective local activation times (LATs) from the respective electrical signals at the positions on the surface,
• calculate a first time difference between the respective LATs at a first pair of the positions on the surface and a second time difference between the respective LATs at a second pair of the positions on the surface,
• calculate first and second LAT-derived distances as respective products of the first time difference and the second time difference with a conduction velocity of the conduction wave,
• identify an origin of an arrhythmia at a location on the surface such that a first difference in distances over the surface from the location to the first pair of the positions is equal to the first LAT-derived distance, and a second difference in distances over the surface from the location to the second pair of the positions is equal to the second LAT-derived distance, and
• mark the identified origin on the representation of the surface on the display,
• wherein the processor is configured to generate a mesh from the location coordinates, and wherein the distances over the surface comprise shortest distances measured along edges of the mesh,
• wherein the mesh comprises a triangular mesh,
• wherein the processor covers the triangular mesh to form a smooth continuous 3D surface, wherein the processor displays a graphic representation of the smooth 3D surface on the display, wherein the processor specifies equally spaced sample points on the triangular mesh, wherein the processor uses the sample points to perform discrete calculations on the continuous 3D surface.