Adjusting Shape of NURBS Curve by Cross Product of Tangent Vectors

A new method for adjusting the shape of NURBS curve is presented.The new method defines the objective function by the integral of the squared cross product of the two tangent vectors of the original and new curves.By minimizing the objective function,the new method makes the deviation of the new curve with the original be one least,which makes the new curve have the shape suggested by the original curve while satisfying the conditions required by the modification.The examples for comparing the shapes and errors of the curves by the new method are included.