A Note on Variable Upper Limit Integral of Bezier Curve

摘要

The integral of degree n Bezier curve in parameter interval [0,1] is (p_0+p_1+...+p_0) + 1, but the variable upper limit integral of that curve is a parameter curve about t in [0,1], through a preassigned point, it could be constructed as a degree n +1 Bezier curve by the method given in this paper. Since the arbitrariness of the preassigned point, the number of integral curve is infinite, after defining an equivalent relation R, the set of all the degree n+1 Bezier curves: S~(n+1) could be divided into different equivalent classes, thus a one-to-one correspondence could be built between B~n (the set of all the degree n Bezier curves) and quotient set B~(n+1)/R.