3D Geometric Constraint Solution Based on Spherical Geometry

The paper studies the application of spherical geometry to the field of 3D geometric constraint solution and presents a geometric constraint solution method,called spherical solution method.The method is based on decoupling the constraints into postural constraints and positional constraints,and the postural constraint solution is emphasized as once the postural constraints are solved,the positional ones can be solved easily.The method maps the vectors representing the postures of rigid bodies to the points on spherical plane,and maps postural constraints to the distances between the points. Via spherical geometry,the method can infer efficiently and intuitively the analytical solution of postural constraints in most cases.For the other cases,the postural constraints can be solved by a mixed algorithm of numerical solution method and spherical solution method.