Constructing a Constrained C1 Continuous Planar Interpolated Spline Curve

The problem of constructing a smooth C¹ continuous planar interpolated spline curve has attracted the attention of many people working in the area of CAD/CAM and its applications such as robotics. In the present paper we propose a method for constructing a C¹ continuous planar interpolated spline using rational quadratic Bezier curve that falls within a closed boundary of straight line segments, which is most frequently used in computer graphics and geometric modelling. The rational quadratic curves are used by CAGD scientists since they do not require complex computations as other higher degree curves do. However, in practice it is desirable to approximate conic sections which cannot be represented by simple Bezier curve. Besides this, we have also presented the some useful properties of the rational quadratic Bezier curve.