After introducing the theories parabola （FDP）, half-wave-length length, offset and the maximum of acceleration （LCA）, the SI curve, and geometric features of four familiar transition curves （cubic parabola （CP）...After introducing the theories parabola （FDP）, half-wave-length length, offset and the maximum of acceleration （LCA）, the SI curve, and geometric features of four familiar transition curves （cubic parabola （CP）, fifth degree sinusoidal （HS） and sinusoidal （SI）） , these curves are compared under identical conditions of the first derivative of curvature. In terms of the roll acceleration （RA） and the lateral change of in theory, is superior to other transition curves.展开更多
Metaball-based constraint deformation technique is used to change the definition of r, the straight-line distance from a space point to a constraint center in the original calculation of the potential function. By rep...Metaball-based constraint deformation technique is used to change the definition of r, the straight-line distance from a space point to a constraint center in the original calculation of the potential function. By replacing the parameter of the pararnetrized surface w with the straight-line distance r, a method of building transition surfaces according to cormected boundary curves and skeleton curves is proposed. The method has no restrictions on boundary curves that control the space shapes of transition surfaces or on types of skeleton curves, thus transition surfaces, which reach C^1 continuity and are more abundant in shapes and natural, can be obtained.展开更多
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
We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the ...We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bezier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples This method has the following three advantages： （1） the pattern is unified; （2） the parameter able to adjust the shape of the transition curve is available; （3） the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement.展开更多
基金The National Natural Science Foundation of China(No.50878134)the Natural Science Foundation of Hebei Province(No.E2006000394)the Natural Science Foundation of Hebei Education Department(No.2006142)
文摘After introducing the theories parabola （FDP）, half-wave-length length, offset and the maximum of acceleration （LCA）, the SI curve, and geometric features of four familiar transition curves （cubic parabola （CP）, fifth degree sinusoidal （HS） and sinusoidal （SI）） , these curves are compared under identical conditions of the first derivative of curvature. In terms of the roll acceleration （RA） and the lateral change of in theory, is superior to other transition curves.
基金This project is supported by National Hi-tech Research and DevelopmentProgram of China (863 Program, No.2004AA84ts03) and Provincial Scienceand Technology Committee of Zhejiang, China (No.2004C31018).
文摘Metaball-based constraint deformation technique is used to change the definition of r, the straight-line distance from a space point to a constraint center in the original calculation of the potential function. By replacing the parameter of the pararnetrized surface w with the straight-line distance r, a method of building transition surfaces according to cormected boundary curves and skeleton curves is proposed. The method has no restrictions on boundary curves that control the space shapes of transition surfaces or on types of skeleton curves, thus transition surfaces, which reach C^1 continuity and are more abundant in shapes and natural, can be obtained.
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.
基金supported by the National Natural Science Foundation ofChina (No. 60673031)the National Basic Research Program(973) of China (No. 2004CB719400)
文摘We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bezier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples This method has the following three advantages： （1） the pattern is unified; （2） the parameter able to adjust the shape of the transition curve is available; （3） the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement.
