Convex hull property is an important characteristic of designing control points of Bezier curves, which can be used for obstacle avoidance in path generating. η³-splines belong to a kind of 7^th degree G³ polynomial curves that interpolate the boundary conditions of position, tangent, curvature and curvature derivative. In this research, the derivation of equivalence bijective transformation from simplified η³-splines to 7^th degree Bezier curves is presented to take advantage of these two kinds of curves. Therefore, the manipulation of simplified η³-splines becomes more intuitive, and the design of Bezier curves to satisfy boundary conditions on the curvature and curvature derivative is computationally simpler. In addition, the transformation allows a clear geometric interpretation of the η parameter in terms of the control points. We propose the usage of this transformation as a basis for a path design procedure with an illustration of vehicle entering into roundabout.