The Parametric Blending Interpolation On Triangles

The purpose of this paper is to dosubstantive summary about the main achievements in recent years,and the creative research about the parametric blending interpolation on triangles. At first, mainly introduced the article selected topic background and the production, the development and the application of this theory. We has made the rationalization arrangement to the article structure at the same time.Secondly, we discuss the general theory about the parametric blending interpolation on the triangles. We make concrete analysis with regard to side - side method.From the C⁰ situation, the boolean sum operator was constructed. It was extended to C^N-1 situation through Hermite interpolation primary function. In this process, the compatibility condition was proposed. Namely is the mix-partial derivative of the function to be possible to exchange in the vertex. At the same time the method of removed the compatible conditions was produced. Then the side - vertex method is introduced. Similarly first introduced the C° situation and through Hermite interpolation primary function based on Brown and in the Little skill situation, C¹ interpolation operator is constructed, and in order to avoiding the vertex compatibility , the interpolation operator is constructed. At the same time draws support the Gregory weight function, also structure C¹ interpolation operator.Thirdly, we introduce the application of the general theory about the parametric blending interpolation on triangles. They are polynomial blending interpolation, the triangle which one side is curve, the geometry blending interpolation, and the interior blending interpolation.Then, we take two group points different from with the tradition method. Also therefore obtained the special the blending interpolation operator. Their tensor product and Boolean sum at the certain side on has the interpolation nature in the triangle.All the traditional theory is based on curved surface function defined on the triangles. Finally, We extend BBG to practical. Namely in curved surface function unknown, merely in the known triangle boundary curve function as well as in the boundary guide curve function situation. We produce the new the blending interpolation surface. At the same time, we propose the information compatibility condition of the blending interpolation.