1. A method of measuring and displaying electrical surface potentials on a surface of a heart, the method comprising the steps of: providing a display, a processor, and an input device; providing a vascular probe comprising (a) a position sensor configured to generate electrical signals indicative of a position coordinate of a distal end of the probe, and further comprising (b) an electrode at the distal end of the probe which is configured to measure an electrical potential of the surface of the heart at the position coordinate; contacting the surface of the heart with the probe at a plurality of points; the processor receiving the electrical signals from the probe and determining both the position coordinate of the distal end of the probe, and the electrical potential measurement of the surface of the heart at the position coordinate, for each of the plurality of points; (i) using the processor, producing an initial map of the surface of the heart using all of the plurality of points, said map which includes all of the points on the heart contacted by the probe being at a first spatial density; (ii) displaying the initial map comprising all of the points on said display at the first spatial density, including by depicting the electrical potential measurement of the surface of the heart on the display for each of the respective points; (iii) after the initial map is produced, and using the input device: receiving operator input including selecting at least a first sub-region, a second sub-region, and optionally additional sub-regions, the sub-regions each corresponding to different respective areas of the initial map as shown on the display; (iv) after the initial map is produced, and using the input device: receiving further operator input comprising a first sub-region density, a second sub-region density, and optionally additional sub-region densities, said sub-region densities each being map point densities which are lower than said first spatial density; (v) after receiving said operator input, generating a diluted map using the processor and displaying the diluted map on the display, wherein when the diluted map is displayed: the first sub-region is displayed at the first sub-region density, comprising displaying only a subset of the points on the corresponding areas of heart surface which were contacted by the probe and which were displayed in the corresponding portion of the initial map; the second sub-region is displayed at the second sub-region density, comprising displaying only a subset of the points on the corresponding areas of heart surface which were contacted by the probe and which were displayed in the corresponding portion of the initial map; areas which were part of the initial map but which do not fall within any sub-region identified by the operator at step (iii) are displayed at the first spatial density; and the diluted map comprises a single continuous image of at least part of the heart on the display, where different areas of said single continuous image are simultaneously displayed at the first sub-region density, the second sub-region density, and the first spatial density.