Abstract discussed structure, the nature of the algorithm and four spline EB, EB discussed CMM four fitting detection data spline surfaces, the use of fast iterative algorithm establishes the error measured contour surface parts Evaluation model. And gives an application example. In complex mechanical parts (such as camber indexing cams), molds, etc., with complex 3D space surface parts manufacturing, measurement and CAD modeling, it is often necessary to describe and control the 3D space surface to generate graphics on a computer screen or Meet the needs of NC machining, or fit the measured data to a spline surface (curve) to meet the needs of error assessment. The four EB spline curves and surfaces discussed in this paper greatly improve the fitting degree of curves and surfaces by introducing tunable parameters with obvious geometrical significance. 1 four EB splines 1.1 four EB spline curves P i (t)= G i (t)+k F i (t) Introducing the k value can be adjusted by changing the shape of the curve so that the difference from the feature polygon can be large or small. When k=0, P i (t)= G i (t), the fourth EB spline curve is the basic curve, which becomes the interpolation curve of the feature vertices. The starting and ending points of the basic curve segment pass through the corresponding feature polygon vertices r i+1 , r i+2 ; if the two control vertices r 0 and r n+1 are broadened in some way, the curve { G i can be made (t)} passes all given vertices r 1 ,r 2 ,...,r n . If the n given points are the type points on a curve, the curve is the interpolation curve of the n type points [1] . 1.2 four EB spline surfaces Next page
Keywords CMM error evaluation spline EB
The quadratic EB spline curve P i (t) is prepared from the basic curve G i (t) via the blending curve F i (t). which is
(0 ≤ t ≤ 1; i = 1, 2..., n-3) (1)
The vector equation for the four-time EB spline curve is 
The four-time EB spline surface can be regarded as the direct product of the EB spline curves in the U and V directions. Given m × n spatial position vectors r i,j (i=1,2,...,n;j=1,2,...,m) construct a surface whose vector equation is 
