Three-dimensional curve fitting based on cubic B-spline interpolation curve

Recent advances in curve fitting have led to substantial improvements in Computer Graphics, achieving a resolution of curve simulation in two dimensions. However, previous research on curve fitting was based on traditional parameterization methods, which could only be appropriate for particular situations. Furthermore, previous studies were only used for two dimensions. Thus, this paper introduces a new dynamic parameterization, points selection methods on point cloud and curve fitting algorithms in 3D. The points selection method utilizes the k-d tree and k-nearest neighbor search technique in PCL to rapidly require the data of points on the surface of a body. Based on those data, the proposed dynamic parameterization method provides parameter viable, many of which cannot be calculated accurately with conventional methods. From the parameter viable, interpolation points are generated by the equation of B-spline curve, and then an interpolation curve can be constructed by those interpolation points. Thus, compared to traditional methods, the proposed algorithm overcomes difficulties in providing predicted function expressions of the fitted curve. The three-dimensional curve-fitting can be used for metrology, medical applications and other aspects in life, and its application enable manufactures to minimize the manual labor costs.