This paper considers N - 1-dimensional hypersurface fitting based on L 2 distance in N-dimensional input space. The problem is usually reduced to hyperplane fitting in higher dimension. However, because feature mapping is generally a nonlinear mapping, it does not preserve the order of lengthes, and this derives an unacceptable fitting result. To avoid it, JNLPCA is introduced. JNLPCA defines the L 2 distance in the feature space as a weighted L 2 distance to reflect the metric in the input space. In the fitting, random sampling approximation of least k-th power deviation, and least α-percentile of squares are introduced to make estimation robust. The proposed hypersurface fitting method is evaluated by quadratic curve fitting and quadratic curve segments extraction from artificial data and a real image.