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本文探讨了四维空间中正轴测投影的理论和方法。第一部分研究了直角坐标系在三维空间中的正投影。证明了轴测轴是锐角的迹四面体的四条高所确定的四条直线;得出了轴向变形系数的计算公式;证明了N维空间直角坐标系在K维空间中的正投影,其轴向变形系数的平方和等于K。第二部分研究了直角坐标系在二维平面上的正投影。阐明了在四维正轴测投影中,四个轴向变形系数和六个轴间角,可供独立选择的最多只能是四个。得出了轴向变形系数和轴间角的计算公式。
This paper explores the theory and method of orthographic projection in four-dimensional space. In the first part, we study the orthographic projection of Cartesian coordinate system in three-dimensional space. It is proved that the axial line is an acute-angled trace tetrahedron, and the four straight lines are determined. The formulas for calculating the axial deformation coefficient are obtained. The orthogonal projection of the Cartesian coordinate system in K-dimensional space is proved. The square sum of the deformation coefficients is equal to K. The second part studies the orthographic projection of a Cartesian coordinate system in a two-dimensional plane. It is clarified that in the four-dimensional orthographic projection, the four axial deformation coefficients and the six inter-axis angles can be independently selected for a maximum of four. The calculation formulas of axial deformation coefficient and inter-axis angle are obtained.