Construction of polynomial blending curves and surfaces

As the traditional blending curve has difficulty for computing its derivative and integral, this paper presents a new presentation for polynomial blending curve and surface. If the curve or surface to be blended is polynomial, the blending curve or surface is also the polynomial. This blending formula can be extended for the blending curve and surface with any parametric continuity C⁽ⁿ⁾ and geometric continuity G⁽ⁿ⁾. After obtaining a family of blending curves and surfaces, we construct a new energy smoothing equation for determining the parameters to get the desirable blending curve and surface. Experimental results show that the new blending method is stable and effective.