摘要
通过对回转抛物面与圆柱面相交的研究，得出交线的水平投影曲线——为四次代数曲线——Perseus座曲线的结论。其形状特征及其变化规律取决于参数和之值。研究得出它具有三种基本形式：①当时，为不共焦点的Booth双纽线族；②当时，为共焦点的卡西尼卵形线族；③当时，为其特殊情况伯努利双纽线。从而得出了交线的水平投影曲线——Perseus曲线的全部形状特征及其整个变化规律。
Through studying the intersection of paraboloid of revolution and cylinder, the author concluded that the horizontal projection of the intersecting lines—, is the famous Four-order algebra curve-Perseus curve. The character of shape and the changing law of curve depend on the value of the parameter , and . The three basic forms of the curve are as follows: ① when , the horizontal projection curve of the intersection curve is the Booth lemniscate family which isn't confocal. ② when , the horizontal projection curve of the intersection curve is the Cassini oval family which is confocal. ③ when ， , the horizontal projection curve of the intersection curve is the special Bernoulli lemniscate. Then the whole changing law and character of shape of the horizontal projection of the intersection curve -Perseus curve is obtained.
出处
《工程图学学报》
CSCD
2000年第3期139-146,共8页
Journal of Engineering Graphics
基金
湖南省教委资助
