Abstract: This paper presents a method for the 3D model reconstruction of the endoscope's body to meet the need of endoscopic inspection. First, the paper introduces the moving coordinate system based on the curve tangent vector and the curvature component vectors. Next, the total curvature vector is composed and the osculating plane determined in the moving coordinate system. The curve bending is then calculated and the recursion analysis made on the osculating plane. Finally, the correlative formulas are deduced and the method is validated by examples.

Key words: endoscopy, model reconstruction, curvature, 3D curve fitting