【摘要】 论文用图示法首次系统表达了在二射影平面场中,存在3种形式的射影对应线束。这些对应线束形成二阶曲线时有一定的变化规律。其中底都为非固有点的二线束形成双曲线;底为固有点和非固有点的二线束形成抛物线;底都为固有点的二线束,只要旋转其中之一就可以分别形成双曲线、抛物线和椭圆。这些结论为我们实现二阶曲线之间的转换奠定了理论基础。更多还原

【Abstract】 The paper uses,for the first time,the graphic method to systematically express the existence of three forms of line pencils in the projective plane.The line pencils show a certain pattern in the formation of second-order curve: the two pencils of lines with infinite points as the base form a hyperbola;the two pencils of lines with both finite and infinite points as the base form a parabola;the two pencils of lines with both finite points as the base form a hyperbola,a parabola or an ellipse upon rotating any one of them.These conclusions lay a theoretical foundation for the realization of the transition between the second-order curve.更多还原