CT colonography (CTC) is a new technology, which permits endoscopic-like evaluation of the mucosal surface. Recently, an electrical field based approach was developed to unravel the colon in spiral CT image volumes, that is to digitally straighten then flatten the colon using curved cross-sections. In this paper, we report (1) an exact and computation- intensive algorithm for straightening the colon using curved cross-sections, and (2) an approximate but computationally efficient straightening algorithm. In the direct straightening algorithm, each curved cross-section of the colon is defined by electrical force lines due to charges distributed along the colon path, and constructed by directly tracing the force lines. In the fast straightening algorithm, only representative force lines are traced that originate equiangularly from the current colon path position, while other force lines are interpolated from the traced force lines. The experiments are performed with both phantom and patient data. It is demonstrated that straightening the colon with curved cross-sections facilitates visualization and analysis, has potential for use in CTC; and the speed of the interpolation based straightening algorithm is practically acceptable, which is about 40 times faster than that of the direct algorithm.