This paper studies representation of rigid combination of a directed line and a reference point on it （here referred to as a ＂point-line＂） using dual quatemions. The geometric problem of rational ruled surface des...This paper studies representation of rigid combination of a directed line and a reference point on it （here referred to as a ＂point-line＂） using dual quatemions. The geometric problem of rational ruled surface design is viewed as the kinematic prob- lem of rational point-line motion design. By using the screw theory in kinematics, mappings from the spaces of lines and point-lines in Euclidean three-dimensional space into the hyperplanes in dual quaternion space are constructed, respectively. The problem of rational point-line motion design is then converted to that of projective Bezier or B-spline image curve design in hyperplane of dual quatemions. This kinematic method can unify the geometric design of ruled surfaces and tool path generation for five-axis numerical control （NC） machining.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.50835004 and 51005087)the National Basic Research Program of China(Grant No.2011CB706804)
文摘This paper studies representation of rigid combination of a directed line and a reference point on it （here referred to as a ＂point-line＂） using dual quatemions. The geometric problem of rational ruled surface design is viewed as the kinematic prob- lem of rational point-line motion design. By using the screw theory in kinematics, mappings from the spaces of lines and point-lines in Euclidean three-dimensional space into the hyperplanes in dual quaternion space are constructed, respectively. The problem of rational point-line motion design is then converted to that of projective Bezier or B-spline image curve design in hyperplane of dual quatemions. This kinematic method can unify the geometric design of ruled surfaces and tool path generation for five-axis numerical control （NC） machining.
