射影线束形成的二阶曲线及其退化形式

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。

The curve of second order formed by projective line pencils and their degenerate types

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.