摘要
本文在叠置场上研究平面三次和四次代数曲线的射影构成。提出在射影坐标系里二次线束单参数方程的表示法,并证明它的充分性和必要性。进而证明三个定理:①一次线束和其射影对应的二次线束,所对应直线交点的轨迹为三次平面曲线;②射影三线场对应直线交点构成平面三次曲线;③两成射影对应的二次线束,其对应直线交点的轨迹是四次平面曲线。且写出了上述定理的对偶定理,并在微机APPLE-Ⅱ上作出部分图形。
In this paper three theorems of projective geometry are given out and proved.They are ①cubic plane curve constituted with projective pencil of lines and line eonic;②cubic plane curveconstituted with three projective fields of lines;③ quartic curve constituted with two projectiveline conics.The dual theorems of them are also given.
出处
《图学学报》
CSCD
1991年第1期54-62,共9页
Journal of Graphics