Cubic B-Spline Curve Interpolation with Arbitrary Derivatives on its Data Points

B-Spline is an approximating curve, its shape is determined by the control points but it also has parametric nature. To interpolate data points, various works have been done by the previous researcher in B-Spline parameterization. The proposed study is the extension in the B-spline interpolation technique using arbitrary end derivatives. In this paper, we present a new way for interpolating cubic B-Spline curve by taking first and second derivative at endpoints and only first derivative at inner points. An algorithm is presented for interpolating data points. The algorithm computes knot values for parameterization methods. These knot values are used in constructing a matrix of B-Spline basis function and derivative of the basis function. Then, we solved it for unknown control points by using the LU decomposition method, such that the curve will pass through the original data points. For interpolation, the parameterization method used in this paper is exponential parameterization. The main advantage of this concept of derivatives is that we can generate different shapes of curves by setting different direction at all points. As an application, our method is applied in a curve reconstruction on road map with data points and driving directions.