纸艺八面体折纸动画
几何画板及绘图内容加载中,请稍等……
本范例演示了来自《Action Modular Origami》一书的纸艺八面体折纸过程。核心数学概念包括几何作图和变换。使用了Point, Intersect, Line, Polygon, Dilate, Plane, Mirror, OrthogonalLine, Sequence, Vector, Translate, Rotate等GeoGebra命令。适合用于几何学教学,特别是立体几何和几何作图的教学。
GeoGebra 命令及参数
Point(zAxis) → APoint(yAxis) → BPoint(xAxis) → CPoint(yAxis) → DPoint(xAxis) → EPoint(zAxis) → FIntersect(zAxis, xOyPlane) → OLine(O, Z) → aPolygon(B, C, D, E) → poly1, b, c, d, ePolygon(B, F, D, A) → poly2, b_1, f, d_1, a_1Polygon(E, F, C, A) → poly3, e_1, f_1, c_1, a_2Dilate(A, scalefactor, O) → A'Dilate(B, scalefactor, O) → B'Dilate(C, scalefactor, O) → C'Dilate(D, scalefactor, O) → D'Dilate(E, scalefactor, O) → E'Dilate(F, scalefactor, O) → F'Plane(F', C', D') → gMirror(O, g) → O'Line(E, C) → hLine(B, D) → iOrthogonalLine(C', h, xOyPlane) → jIntersect(j, b) → GIntersect(j, c) → HOrthogonalLine(G, i, xOyPlane) → kIntersect(i, yAxis) → IIntersect(i, yAxis) → JIntersect(k, i) → KPolygon(O, C', H, C, G, K) → poly10, o, c'_2, h_1, c_2, g_1, k_1Mirror(G, i) → G'Polygon(B, G, K, O, E', G') → poly11, b_2, g_2, k_2, o_1, e', g'Sequence(Rotate[poly10, (n * 180°), O], n, 0, 2) → ListPolyXY1Sequence(Rotate[poly11, (n * 180°), O], n, 0, 2) → ListPolyXY2Vector((0, 0, 0), (0, 0, sep)) → uTranslate(ListPolyXY1, u) → ListPolyXY1'_1Translate(ListPolyXY2, u) → ListPolyXY2'_1Rotate(ListPolyXY1'_1, 180°, h) → ListPolyXY1'Rotate(ListPolyXY2'_1, 180°, h) → ListPolyXY2'Translate({ListPolyXY1, ListPolyXY1'}, Vector[(0, 0, 0), (0, 0, 0)]) → ListPoly1Translate({ListPolyXY2, ListPolyXY2'}, Vector[(0, 0, 0), (0, 0, 0)]) → ListPoly2Line(O, F) → mRotate(ListPoly1, 120°, a) → ListPoly1'Rotate(ListPoly2, 120°, a) → ListPoly2'Rotate(ListPoly1', 120°, a) → ListPoly1''Rotate(ListPoly2', 120°, a) → ListPoly2''Line(O, F) → lRotate({ListPoly1'', ListPoly2'}, α, l) → list2Rotate({ListPoly1', ListPoly2}, α, l) → list1Rotate({ListPoly1, ListPoly2''}, α, l) → list0
AI 绘图提示语参考
绘制一个由六个顶点构成的正八面体骨架,其中三个顶点分别位于三条坐标轴的正半轴,另三个位于负半轴。以原点为中心,将各顶点按比例缩放,形成内部缩小的八面体。连接内外对应顶点,构造出多个三角形和四边形面片,并沿坐标轴旋转复制,形成对称的折叠结构。最后,将整体绕一条竖直轴旋转一定角度,并沿该轴平移,展示八面体的折叠动画效果。
以上提示语为根据原始绘图命令整理而来,仅供参考。