In order to realize the 3D measurement and reconstruction for a curved shape

a quasi-distributed measuring system based on curvature fiber optic sensors is presented and its algorithms such as the layout of sensors

measurements of curvature and torsion angles

and 3D reconstruction methods are investigated. Firstly

a number of looped fiber optic sensors are arranged on the two symmetrical surfaces of a flexible tape

and a quasi-distributed measuring system is established to measure bend and torsion deformations simultaneously using linear superposition theorem. Based on the bend and torsion data provided by curvature fiber optic sensors

a moving coordinate system is established by the curve tangent and curvature using a differential geometry method and the osculating plane is determined by a torsion angle in the moving coordinate system. Then

the curve bending is calculated and the recursion of coordinate system is analyzed in the osculating plane. The correlative formulas are deduced and the method is validated by examples.Finally

the quasi-distributed measuring system is used to reconstruct the curve of a simply supported beam with a length of 500 mm. Results show that when 20 points are inserted between two measured points

the maximum deviation of reconstructed curve is 1.1 mm

which means the measurement system and the reconstruction method can reconstruct 3D shapes precisely.