平行线束法的仿射研究

The Study of the Parallel Lines Method in Affined Coordinate

用 3 个仿射图的投射方向构成 1 个仿射坐标系,同时也构成 1 个三棱锥,在此仿射坐标系中用球面三角重新研究由两个仿射图求第 3 个仿射图的投影作图理论 ——平行线束法。进一步还给出了由两个仿射图得到正投影的条件、由两个正投影得到第 3 个正投影的条件、以及由 V,H 两投影得到指定方向上的正投影的条件,简化了研究过程,得到了更简单的公式。

The projecting directions of three affine pictures form affine coordinate system, and they also form a triangular pyramid at the same time. An axonometric drawing theory to draw an affine picture starting from two given affine picture is studied in affine coordinate system by spherical trigonometry, and three conditions are given out, one is the condition of drawing orthographic projection starting from two given affine picture, the other is the condition of drawing orthographic projection starting from two given orthographic projection, the third is the condition of drawing orthographic projection in the appointed direction from two given vertical and horizontal orthographic projection. Therefore, the process of the study is simplified and the more simple formulas are obtained.