CUBIC SPLINE INTERPOLATION TO APPROXIMATE SEA DEPTH BETWEEN TELUK SUAK AND LEMUKUTAN ISLAND

Abstract

Interpolation is a technique that determines the value of a function at a point located between several known data points. Various interpolation methods include polynomial interpolation, Lagrange interpolation, Newton interpolation, and spline interpolation. Cubic spline interpolation aims to produce accurate approximations characterized by minimal oscillations in the resulting curve. This research uses the cubic spline interpolation method to estimate the sea depth in the waters between Teluk Suak and Pulau Lemukutan. The sea depth measurements are conducted to acquire information regarding the underwater topography. We collected data points using remote sensing techniques through Google Earth Pro. These points are selected based on the sea depth profile considerations, including steep areas and points of depth variation to maintain the seabed conditions within the interpolation curve, with a total of 31 data points. Subsequently, we subjected these data points to the conditions necessary for cubic spline interpolation, resulting in a system of 120 linear equations. After solving this system of linear equations, we obtained cubic spline interpolation polynomials for each subinterval and then estimated the sea depth at other points. Based on the cubic spline interpolation results, we achieved a Mean Average Percentage Error (MAPE) of 1.58%, indicating a highly accurate interpolation outcome.