Surface Interpolation from Cross Sections

An essential technique of visualizing the inner structure of a body is tomography. Tomographic methods represent the body by a sequence of cross sectional slices. For the observer, however, it is often rather difficult to imagine the true three-dimensional shape from the slices. For this reason, numerous methods for reconstructing a three-dimensional representation from a given stack of slices were suggested in the past. We give a unifying survey of such methods and sketch several new approaches not published yet. The emphasis is on techniques which can be also applied to larger distances between the cross sections and in the case of distorted slices. The methods usually yield a surface representation which can be used beyond visualization for purposes of geometric modeling, simulation, and manufacturing.