Research On B(?)zier Curve And Surface With Multiple Shape Parameters

The expansion of Bezier curve with shape parameter is studied in this paper. A new extension method of the quartic Bezier and n degree Bezier is proposed on the original basis.In the first chapter, we introduce the research background and content about the Computer Aided Geometric Design.In the second chapter, we give the definition and the properties of the Bezier curve and surface. The expansion of the quartic Bezier and n degree Bezier with a shape parameter are recommended.In the third chapter, a new extension of the quartic Bezier curve with a shape pa-rameter is provided by adding shape parameters.In the fourth chapter, we use the same method of adding shape parameters, then exploit de Casteljau recursive method to get a new extension of n degree Bezier.In the end, we summarize the full text and point out the existing problems of Bezier curve and the future research directions.