Constrained for G1 cubic trigonometric spline curve interpolation

Abstract

This paper presented the G1 cubic trigonometric spline function with three shape parameters that generate a constrained curve that interpolates 2D data. The purpose of this research is to ensure the generated curve passes through all data point yet satisfied the three cases of line constraints given. The three cases are: the data must lie above line Li the data must lie below line Li and lastly, the data must lie between two lines Li,1 and Li,2. A simpler theorem is implemented involving the roles of shape parameters. Two of the shape parameters are set free, while another parameter is fixed to fulfil all the three cases stated. The results show that a smooth curve of the G1 cubic trigonometric spline function can be produced within the constrained line by using the theorem developed while the hereditary shape of the data is preserved. Numerical examples are illustrated and discussed.