For reconstructing a freeform feature from point cloud, a deformation-based method is proposed in this paper. The freeform feature consists of a secondary surface and a blending surface. The secondary surface plays a ...For reconstructing a freeform feature from point cloud, a deformation-based method is proposed in this paper. The freeform feature consists of a secondary surface and a blending surface. The secondary surface plays a role in substituting a local region of a given primary surface. The blending surface acts as a bridge to smoothly connect the unchanged region of the primary surface with the secondary surface. The secondary surface is generated by surface deformation subjected to line constraints, i.e., character lines and limiting lines, not designed by conventional methods. The lines are used to represent the underlying informa-tion of the freeform feature in point cloud, where the character lines depict the feature’s shape, and the limiting lines determine its location and orientation. The configuration of the character lines and the extraction of the limiting lines are discussed in detail. The blending surface is designed by the traditional modeling method, whose intrinsic parameters are recovered from point cloud through a series of steps, namely, point cloud slicing, circle fitting and regression analysis. The proposed method is used not only to effectively and efficiently reconstruct the freeform feature, but also to modify it by manipulating the line constraints. Typical examples are given to verify our method.展开更多
The existence and uniqueness of limit cycle for the E 1 3 type of cubic systems with two integral straight lines has been studied in this paper. It is found that the system has no limit cycle when the two int...The existence and uniqueness of limit cycle for the E 1 3 type of cubic systems with two integral straight lines has been studied in this paper. It is found that the system has no limit cycle when the two integral straight lines intersect each other; it has a unique limit cycle when the two integral straight lines are paralleled. The sufficient and necessary conditions are also given to guarantee the existence of the unique limit cycle.展开更多
基金the National Natural Science Foundation of China (No. 50575098)China Postdoctoral Science Foundation
文摘For reconstructing a freeform feature from point cloud, a deformation-based method is proposed in this paper. The freeform feature consists of a secondary surface and a blending surface. The secondary surface plays a role in substituting a local region of a given primary surface. The blending surface acts as a bridge to smoothly connect the unchanged region of the primary surface with the secondary surface. The secondary surface is generated by surface deformation subjected to line constraints, i.e., character lines and limiting lines, not designed by conventional methods. The lines are used to represent the underlying informa-tion of the freeform feature in point cloud, where the character lines depict the feature’s shape, and the limiting lines determine its location and orientation. The configuration of the character lines and the extraction of the limiting lines are discussed in detail. The blending surface is designed by the traditional modeling method, whose intrinsic parameters are recovered from point cloud through a series of steps, namely, point cloud slicing, circle fitting and regression analysis. The proposed method is used not only to effectively and efficiently reconstruct the freeform feature, but also to modify it by manipulating the line constraints. Typical examples are given to verify our method.
文摘The existence and uniqueness of limit cycle for the E 1 3 type of cubic systems with two integral straight lines has been studied in this paper. It is found that the system has no limit cycle when the two integral straight lines intersect each other; it has a unique limit cycle when the two integral straight lines are paralleled. The sufficient and necessary conditions are also given to guarantee the existence of the unique limit cycle.
