Apaper reports a method of converting distributed curvature measurements into a three-dimensional shape by combining elastic rod theory and differential geometry to arrive at a three-dimensional solution of the Frenet-Serret formulas. A new method of calculating the shape of a multicore fiber optic cable is presented. The method utilizes discrete strain measurements obtained in each core to create a continuous representation of fiber curvature and torsion. The Frenet-Serret equations are then solved using these representations to obtain fiber shape. Shape measurements were found to have, at most, 7.2% error. The primary source of error is most likely externally induced twisting in the fiber.