Fiber optic shape sensing uses embedded sensors to measure the full 3D shape of a flexible surgical device along its entire length in real time. By sensing the device itself from the inside, it provides continuous awareness of how the device bends, twists, and turns as it moves. Fiber Bragg Grating (FBG) sensors inscribed in multi-core optical fibers have been democratized over the years and nowadays offer a compact and robust platform for shape reconstruction. In this work, we propose a novel, computationally efficient method for determining the 3D tip position of a bent. Fiber optic shape sensing has an outstanding capability to sense curvature and shape in 2D and 3D. In cooperation with our spin-off company Fionec GmbH.