By using the geometric constraints on the control polygon of a Pythagorean hodo- graph （PH） quartic curve, we propose a sufficient condition for this curve to have monotone curvature and provide the detailed proof. ...By using the geometric constraints on the control polygon of a Pythagorean hodo- graph （PH） quartic curve, we propose a sufficient condition for this curve to have monotone curvature and provide the detailed proof. Based on the results, we discuss the construction of spiral PH quartic curves between two given points and formulate the transition curve of a G2 contact between two circles with one circle inside another circle. In particular, we deduce an attainable range of the distance between the centers of the two circles and summarize the algorithm for implementation. Compared with the construction of a PH quintic curve, the complexity of the solution of the equation for obtaining the transition curves is reduced.展开更多
In this paper, a new method for blending two canal surfaces is proposed. Theblending surface is itself a generalized canal surface, the spine curve of which is a PH(Pythagorean-Hodograph) curve. The blending surface p...In this paper, a new method for blending two canal surfaces is proposed. Theblending surface is itself a generalized canal surface, the spine curve of which is a PH(Pythagorean-Hodograph) curve. The blending surface possesses an attractive property - itsrepresentation is rational. The method is extensible to blend general surfaces as long as theblending boundaries are well-defined.展开更多
基金Supported by the National Natural Science Foundation of China(61272300)
文摘By using the geometric constraints on the control polygon of a Pythagorean hodo- graph （PH） quartic curve, we propose a sufficient condition for this curve to have monotone curvature and provide the detailed proof. Based on the results, we discuss the construction of spiral PH quartic curves between two given points and formulate the transition curve of a G2 contact between two circles with one circle inside another circle. In particular, we deduce an attainable range of the distance between the centers of the two circles and summarize the algorithm for implementation. Compared with the construction of a PH quintic curve, the complexity of the solution of the equation for obtaining the transition curves is reduced.
文摘In this paper, a new method for blending two canal surfaces is proposed. Theblending surface is itself a generalized canal surface, the spine curve of which is a PH(Pythagorean-Hodograph) curve. The blending surface possesses an attractive property - itsrepresentation is rational. The method is extensible to blend general surfaces as long as theblending boundaries are well-defined.
