Method for Determining the Regularity of Bézier Curves

The regularity of Bezier curve is determined by its control points.Perfect situation is that we can determine the regularity of Bezier curve according to the geometry relation of control points.In this paper,we get geometry relation between the points of Bezier curves by its derivative curves which is not equal to zero during the interval 0 and 1,we only need to know the opposite location of control points or compute the slopes of bordered lines,then we can determine the regularity of Bezier curve quickly.There is no need to determine whether the origin is on the derivative curve.Some numerical examples are given..