A method of reconstructing a shape of a volume of a part of a subject based on intrabody measurements of a plurality of crossing electromagnetic fields established within the volume, the method including:receiving, by computer circuitry, measurements of the crossing electromagnetic fields carried out using at least one sensor carried on an intrabody probe, the measuring being carried out with the probe at multiple locations in the volume, to provide a set of measurement samples, each taken at a location；generating, by computer circuitry and based on said measurement samples, a transformation that transforms measurement samples to geometric positions；transforming, using said generated transformation fewer than half of the measurements in said set of measurement samples into a set of geometric positions； andreconstructing the shape of said volume from said set of geometric positions.
