Abstract: A method and system for rendering the quaternion shape and orientation of a three-dimensional structure. The proposed system and method keeps track of twist/roll angles and updates its effect on pitch and yaw orientations. The system relies on a single or multi-core optical fiber or multi-fiber bundle containing fiber Bragg grating sensors (FBGs) arrayed in rosettes at 45° deltas and spaced at uniform intervals along the entire length of the structure to be monitored. A tunable laser is used to interrogate the sensors using optical frequency domain reflectometry (OFDR), which detects shifts in the wavelength reflected by the sensors in response to strain on the fibers. Each sensor is continuously queried by software which determines the strain magnitude (?L/L) for each fiber at a given triplet. Given these measured strain values, the software implements a novel quaternion approach to rendering the 3D shape of the fiber including twist.