The problem of designing smoothly rounded corners with planar polynomial Pythagorean-hodograph (PH) curves is addressed. A $G^1$ corner can be uniquely specified as a single PH cubic segment. Similarly, a $G^2$ corner can be uniquely specified with a single PH quintic segment. To obtain $G^2$ corners incorporating shape freedoms that permit a fine tuning of a curvature profile, PH curves of degree 7 are required. As an alternative, a $G^2$ corner construction based upon splicing together two PH cuintic segments is proposed. The corner shapes constructed through these schemes can excel computational advantages of PH curves. Those ensure them many possible applications in different fields of science: industry, robotics, 3D printing etc. In this work a mechanical engineering application in connection to furniture industry is presented.
|
