Spline Interpolation Based On Cubic Bézier Curve

Bézier curve is one of the most basic modeling tools in CAD / CAM systems.Bézier curve inherits many good properties as it uses a special class of polynomial basis functions.But it is difficult for assembling of segments of Bézier curves, especially with G 2continuity conditions. This problem can be solved by rational Bézier spline curves. On the other hand, Bézier curve can only approach quadratic curves with similar methods. But trigonometric Bézier curve can represent conic curve precisely and represent some remarkable transcendental curves precisely.After briefly reviewing the basic concept and properties of Bézier curve, the paper summarise the concept and properties of rational Bézier curve,and analysis G 2 continuity conditions for assembling of two cubic rational Bézier spline curves. By analyzing the characters of Bézier curves, we construct trigonometric polynomial curves in the space of trigonometric functions , which called trigonometric Bézier curves. And combining interpolation algorithm of cubic spline, the paper gives the method of constructing spline curves by cubic trigonometric Bézier basis function.