Range-Restricted Surface Interpolation Using Rational Bi-Cubic Spline Functions With 12 Parameters

This paper discusses the constraint data interpolation or range restricted interpolation for surface data arranges on rectangular meshes that lie above or below an arbitrary plane and between two arbitrary planes by using partially blended rational bi-cubic spline function with 12 parameters. Common research in range restricted surface interpolation is to construct the constrained surface lie above linear plane. However, in this paper, we consider the constraint surfaces up to degree three (cubic). To construct the constrained surface with shape preserving properties, i.e., the resulting surface will lie below or above single planes or between two respective planes, the data dependent sufficient conditions are derived on four parameters; meanwhile, the remaining eight parameters are free parameters to change the shape of the interpolating surface locally. The proposed scheme is tested with various types of data test, including some well-known functions. From the numerical results, we found that the proposed scheme is easy to use, locally control via free parameters, and require less computation compared with some existing schemes as well as visually pleasant for visualization. Furthermore, based on root mean square error (RMSE) and coefficient of determination (R
²
), the proposed scheme is better than existing scheme with the value of R
²
achieved is in between 0.9701 (97.01%) and 0.9954 (99.54%). This is quite good for range restricted surface data interpolation since we can explain at least 97.01% of the variance in the interpolation by using the proposed scheme. Furthermore, the proposed scheme requires less CPU time (in seconds) compared with the existing scheme.