We present the results of a new approach to simulating coronal magnetic fields without the constraints inherent to most modeling techniques. Magnetic fields are central to the structure and dynamics of the solar corona, and comprehension of the corona requires an understanding of these fields. Many current simulations make assumptions about the nature of the field, relying on comparisons of force-free (often potential ) field models with optical, EUV, or X-ray observations. We use a novel method that starts with a simple potential field and fits it to a more complicated target field through a series of linear transformations. The matrix transformation that results in the best fit to the target field then provides information on the 3D field configuration and the distribution of currents within that field, with no particular bias toward force-free solutions.