A mathematical definition of bilateral symmetry in point cloud is proposed after a profound study of the principle of symmetry, and an iterative closest point (ICP) based symmetry plane extraction method is presented.

Presents a symmetry plane reconstruction method based on measured data points, because the majority of parts had been designed with symmetry geometric relationship; after the symmetry plane had been recovered and one with symmetry featuress has been modeled, other symmetry features can be reconstructed by mirror operation.

Rigid body trajectory model of rolling missiles with plane-symmetry;

In according with the basic theory of exterior ballistics and in allusion to the theoretic need of research of key technology of simulative cruise missile,the paper brings forward the requirement of motion equation of plane-symmetry shell.

By means of discussing plane symmetry that relates to point, curved surface and curve in a three-dimensional space, this paper gives a method to study point?curved surface?plane symmetric point on a curve?symmetric curved surface and symmetric curve equation.

By way of the study, we may also judge whether a plane is a symmetric plane of a space curved surface and curve.