曲面法线平行于投影面时曲面曲线与投影曲率半径间的关系

“画法微分几何”的主要内容之一是研究曲线以及曲线投影的曲率。迄今为止,曲面曲线在投影中的曲率一般需借助于曲线的密切平面方能求出,从而使利用曲率圆简化绘制曲线的作用受到了限制。本文推导了一个公式,可以不借助密切平面而直接求出曲线投影的曲率,解决了在此之前难以解决的作图问题。

The Relation between the Curvatures of a Surface Curve and Its Image when the Surface Normal is Parallel to the Projection Plane

According to the methods generally used, to construct an image of a space curve accurately, many images of points must be constructed. If tangents of curve at some points can be constructed, the images of points can be reduced. Furthermore, if curvature circles at some points on the image curve can be constructed, less images of points are needed to construct the image of a space curve. The constructive differential geometry is a new subject being developed recently, and one of its major contents is the research on curvature of a curve and its image. Up to now, the curvature of the image: of the curve on a curved surface can be obtained only by using the osculating plane of the curve. But it is difficult to gain the osculating plane of a space curve, so the method to construct a space curve by using its curvature circle is restricted, with which the curvature of the image of a curve can be gained directly without using osculating plane, so some constructive problems unresolved before can be resolved.