射影线束形成的抛物线与椭圆抛物面的相似断层表示

图学学报

射影线束形成的抛物线与椭圆抛物面的相似断层表示

出版日期:2013-10-31 发布日期:2015-06-19

The Similar Cutting Layers of Parabola and Elliptic Paraboloid Formed by two Projective Line Pencil

Online:2013-10-31 Published:2015-06-19

摘要/Abstract

摘要： 利用图示法，说明了二射影对应线束形成抛物线时，线束中的特殊线影响
了抛物线的形状。如果任意五边形的顶点在一条抛物线上，由相似五边形的顶点确定的另一
条抛物线与其“相似”。我们可以用一系列平行的截平面来表示椭圆抛物面，这些平行的截
平面上抛物线相似，称为相似断层表示法。这种表示法为我们实现用计算机绘制三维椭圆抛
物面奠定了理论基础。

关键词: 射影线束, 相似抛物线, 椭圆抛物面, 断层法

Abstract: With drawing, a changing parabold is formed by the two projective line pencils
formed. If the five vertexes of a pentagon are on a parabold, another parabold formed by a similar
pentagon is similar to this one. In order to draw elliptic parabolaid using computer, a series of
parallel cutting planes can be used which are similar parabolds to show the curves. This is referred
to as cutting layers method.

Key words: projective line pencils, similar parabold, elliptic paraboloid, cutting layer
method

刘阜平，丁勇. 射影线束形成的抛物线与椭圆抛物面的相似断层表示[J]. 图学学报.

Liu Fuping, Ding Yong. The Similar Cutting Layers of Parabola and Elliptic Paraboloid Formed by two Projective Line Pencil[J]. Journal of Graphics.