This paper proposes a near-central camera model and its solution approach. 'Near-central' refers to cases in which the rays do not converge to a point and do not have severely arbitrary directions (non-central cases). Conventional calibration methods are difficult to apply in such cases. Although the generalized camera model can be applied, dense observation points are required for accurate calibration. Moreover, this approach is computationally expensive in the iterative projection framework. We developed a noniterative ray correction method based on sparse observation points to address this problem. First, we established a smoothed three-dimensional (3D) residual framework using a backbone to avoid using the iterative framework. Second, we interpolated the residual by applying local inverse distance weighting on the nearest neighbor of a given point. Specifically, we prevented excessive computation and the deterioration in accuracy that may occur in inverse projection through the 3D smoothed residual vectors. Moreover, the 3D vectors can represent the ray directions more accurately than the 2D entities. Synthetic experiments show that the proposed method can achieve prompt and accurate calibration. The depth error is reduced by approximately 63% in the bumpy shield dataset, and the proposed approach is noted to be two digits faster than the iterative methods.