Reconstruction of the initial curve from a two-dimensional shape for the B-spline curve fitting

Curve reconstruction is a significant challenge in computer-aided geometric design, computational atomic and molecular physics, engineering design, virtual reality and data visualization. This study discusses a method of producing B-spline parametric curve from the large number of data points. The introduced scheme includes three major parts for curve reconstruction: (1) formulation of the B-spline curve fitting as a nonlinear least squares optimization problem, (2) construction of the precise initial B-spline curve using properly determined control points, and (3) usage of the diagonal approximation BFGS method to identify the location parameters and the control points simultaneously. The modeling examples demonstrate that the suggested techniques are successful and can therefore significantly reduce fitting error by adjusting the number and location of control points.