A method is presented for constructing the complete atomic structure of supercoiled DNA starting from a linear description of the double helical pathway. The folding pathway is defined by piecewise B-spline curves and the atoms are initially positioned with respect to the local Frenet trihedra determined by the equations of the curves. The resulting chemical structure is corrected and refined with an energy minimization procedure based on standard potential expressions. The refined molecular structure is then used to study the effects of supercoiling on the local secondary structure of DNA. The minimized structure is found to differ from an isotropic elastic rod model of the double helix, with the base pairs bending in an asymmetric fashion along the supercoiled trajectory. The starting trajectory is chosen so that the refined supercoiled structure is either underwound (10.37 base pairs per turn) or overwound (9.65 base pairs per turn) compared to the standard tenfold B-DNA fiber diffraction model. The underwound supercoil is also lower in energy than the overwound duplex. The variation of base pair sequence in poly(dA).poly(dT).poly(dAT).poly(dTA) and poly(dA5T5).poly(dT5A5) is additionally found to influence the secondary structural features along a given supercoiled pathway. Finally, the detailed features of the refined structures are found to be in agreement with known X-ray crystallographic structures of DNA oligomers.