基于斜投影变换研究画法几何中相贯线图解

Graphically illustrate lines of intersection in descriptive geometry based on oblique projection shifting

在画法几何中,相贯线普遍被认为是难点。在求其投影时往往用辅助面法,通过2组截交线的交点求出相贯线上的点。由于相贯线本身形状复杂,所以作图更显繁锁。通过平面立体与平面立体相交,曲面立体与曲面立体相交的实例,重点研究画法几何中相对难度大、作图繁杂的相贯线的图解方法,给出三棱锥K-DEF与三棱柱的相贯线、斜置椭圆柱面与环面的相贯线。实践证明,只要根据作图需要选择投影面和投射方向,使其处于有利解题的位置,再利用斜投影法只需一次变换即可求得相贯线。该方法能够将工程图学中用正投影方法多次投影变换才能解决的图示、图解问题仅做一次投影变换解决,相对其他方法灵活、简单。

In descriptive geometry, the issue of intersection lines is commonly regarded difficult. When the projections of intersection lines are tried to gain, the approach of auxiliary surface is always applied--using intersections points Of two sets of lines of section to get the points on lines of intersection. Because of the complexity of lines of intersection, illustrating them seems more cumbersome. Through examples of intersections among plane bodies and intersections among curved surface bodies, this article primarily focuses on the approach that can graphically illustrate the relatively difficult and complicated lines of intersection and provides the lines of intersection between triangular prism K-DEF and triangular pyramid and the lines of intersection between oblique elliptic cylindrical surface and ring surface. It is true that as long as choosing projecting planes and directions is according to graphs and putting them on the positions that are advantageous to solving the problems, then applying one oblique projection shift can obtain the lines of intersections, which is comparatively flexible and simple. Only applying one shift, this method can solve the problems on graphical representation, comparing to that Orthographic Projection Method has to adopt many times of projection shifting to figure out.