In the realms of computer-aided geometric design, density function estimation, and related applications, constructing an interpolated spline curve that meets specific conditions for a given histogram poses a significant challenge. This paper addresses this challenge by proposing a novel \(C^1\) strictly monotone histogram interpolating spline curve. The spline is meticulously constructed to preserve the sign of its first derivative across the entire interval, thereby ensuring strict monotonicity. Under certain boundary conditions, this \(C^1\) continuous strictly monotone histogram interpolating spline curve is both existent and unique for any strictly monotone histogram. We present a solution system for the specific form of the interpolation spline using Levenberg-Marquardt algorithm. The effectiveness and robustness of our proposed spline curve are validated through five numerical examples, illustrating the spline’s behavior under diverse boundary conditions.
