A method and apparatus for displaying arbitrary cross-sectional views of a three-dimensional body from a regular array of values of at least one physical property in the interior of the body includes making physical property measurements with such systems as computerized tomographic x-ray systems, or magnetic resonance imaging systems. Cut planes are defined by the user as displacement from, and rotations from, an arbitrary coordinate origin in the data space. An initial plane of pixel positions of arbitrary density is displaced and rotated to correspond to the cut plane. The values for the physical property at the pixel positions are interpolated from the surrounding measurements of actual values. Cross-sectional images are thereby supplied interactively in real time to support, for example, ongoing surgical procedures.