Soft joint shape measurement is challenging because, in most cases, it relies solely on internal sensors. Existing shape estimation methods commonly take measurements at discrete points and utilize curve-fitting schemes, which are inefficient for complex joint shapes that require continuous measurements. Therefore joint shape measurement sensors rely on the fiber Bragg grating (FBG) due to its sensitivity, immunity to electromagnetic interference, and flexibility. Nevertheless, FBG demodulation is still an open research case. Hence, we propose a shape measurement device appropriate for FBG-based continuous measurements that employs a sensor with only three FBGs thrusting inside the soft joint to measure its 3D shape. Moreover, we develop a simple demodulating system exploiting the FBG's filter overlapping properties and design a calibrating process for FBG signals. Soft joint shape measurement experiments highlight our method's effectiveness, providing a relative error within 0.7%. Further tests involving continuum robot measurement reveal that the achieved precision is of the same level as a motion-capturing system.