螺旋面及其CAD

为简化旋转楼梯的设计、图示、施工及剖面形状，对螺旋面的形成进行了分析，建立了螺旋面的数学模型。由于螺旋面为直纹曲面，因此可用它的一组素线表示，用极坐标的形式写出内外两条螺旋线的方程，求出任一素线的方程，并通过投影变换求得素线上两端点的坐标矩阵，进而设计出螺旋面的CAD系统，并将其应用于实践，为设计优化决策提供有力的证据

Helicoid and CAD

To simplified the designing, diagram presentation, construction and profile of helicoidal stair, the formation of helicoid is analyzed, and it′s mathematical model is studied. Being formed by linear-grain curved surface, helicoid can be expressed by a group of simple-lines. Writing two equations of inside and outside of the helicoid, getting any one of simple-line′s equation and from which getting th e coordinations of two end points by projection transformation, the CAD syste m of helicoid is achieved. It has been applied into the practice successfully.