The construction of a GC1 cubicinterpolatiing curve that lies on the same side of a given straight line as the data points is studied. The main task is to choose appropriate approaches to modify tangent vectors at the data points for the desired curve. Three types of approches for changing the magnitudes of the tangent vectors are presented.The first-type approach modifies the tanggent vectors by applying a constraint to the curve segment. The second one does thework by optimization techniques. The thired one is a modification of the existing method. Three critera are prsented to compare the three types of approaches with the existing method. the experiments that test the effectiveess of the approaches are included.