轴测投影基本定理的佐证

Proof of Fundamental Theorem of Axonometric Projection

该文运用轴测投影的基本原理及据此建立的轴测投影变换的通用矩阵为工具，根据矩阵比较法，两矩阵相等其对应元素相等的代数关系，确定轴测投影变换矩阵中的各个参数。文中以尺度单位四面体为例，对其作用轴测投影变换矩阵而得到一个完全四角形，这个完全四角形即为尺度单位四面体的轴测投影，并用形数结合的方法证明了波尔凯－许华兹定理。

In this paper, the basic principles of axonometric projection are used to set up a common transformation matrix of axonometric projection. According to matrix matching method, if two matrixes are equal, their corresponding elements are equal respectively. This method is used to determine parameters of axonometric projective transformation matrix. When an axonometric projective transformation matrix is applied to scale tetrahedron, the scale tetrahedron can be transformed into a pure quadrangle. The quadrangle is axonometic projection of scale tetrahedron. So this paper applied the method to combine geometry with mathematics, to prove the Pohlke Schwarz theorem. It provided an example of using computer and mathematics to study graphic theory.