旋转游戏
几何画板及绘图内容加载中,请稍等……
这个范例展示了旋转变换的动态效果。它涉及几何变换中的旋转概念。通过使用GeoGebra命令Sequence, Zip, Prism, Rotate等,可以创建旋转的立体图形。适合初中及以上学生学习几何变换和立体几何。
GeoGebra 命令及参数
Sequence(k, k, -4, 3) → Ln, {-4, -3, -2, -1, 0, 1, 2, 3}Zip("prism" + (Text[k]), k, Lm) → LnamePrism(Polygon[(4, -4, -4), (4, 4, -4), 4, xOyPlane], 1) → prism1, A, edge1, edge2, edge3, edge4, edgeAB, edgeBC, edgeCD, edgeAD, B, C, D, face1, face3, face4, face2, faceABCDPrism(Polygon[(4, -4, -3), (4, 4, -3), 4, xOyPlane], 1) → prism2, E, edge5, edge6, edge7, edge8, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, face5, face7, face8, face6, faceEFGHPrism(Polygon[(4, -4, -2), (4, 4, -2), 4, xOyPlane], 1) → prism3, I, edge9, edge10, edge11, edge12, edgeIJ, edgeJK, edgeKL, edgeIL, J, K, L, face9, face11, face12, face10, faceIJKLPrism(Polygon[(4, -4, -1), (4, 4, -1), 4, xOyPlane], 1) → prism4, M, edge13, edge14, edge15, edge16, edgeMN, edgeNO, edgeOP, edgeMP, N, O, P, face13, face15, face16, face14, faceMNOPPrism(Polygon[(4, -4, 0), (4, 4, 0), 4, xOyPlane], 1) → prism5, Q, edge17, edge18, edge19, edge20, edge41, edge42, edge43, edge44, R, S, T, face17, face18, face19, face20, face35Prism(Polygon[(4, -4, 1), (4, 4, 1), 4, xOyPlane], 1) → prism6, U, edge21, edge22, edge23, edge24, edgeUV, edgeVW, edgeWZ, edgeUZ, V, W, Z, face21, face23, face24, face22, faceUVWZPrism(Polygon[(4, -4, 2), (4, 4, 2), 4, xOyPlane], 1) → prism7, A_1, edge25, edge26, edge27, edge28, edge29, edge31, edge32, edge30, B_1, C_1, D_1, face25, face27, face28, face26, face29Prism(Polygon[(4, -4, 3), (4, 4, 3), 4, xOyPlane], 1) → prism8, E_1, edge33, edge34, edge35, edge36, edge37, edge39, edge40, edge38, F_1, G_1, H_1, face30, face32, face33, face31, face34Rotate(prism1, (F1(t) * π), zAxis) → P1Rotate(prism2, (F2(t) * π), zAxis) → P2Rotate(prism3, (F3(t) * π), zAxis) → P3Rotate(prism4, (F4(t) * π), zAxis) → P4Rotate(prism5, (F5(t) * π), zAxis) → P5Rotate(prism6, (F6(t) * π), zAxis) → P6Rotate(prism7, (F7(t) * π), zAxis) → P7Rotate(prism8, (F8(t) * π), zAxis) → P8
AI 绘图提示语参考
绘制一个以 xOy 平面为基底的3D旋转体阵列:先在平面上取一条矩形轮廓在不同 z 高度处生成多层同型棱柱(底边用点(4,-4,-k)与(4,4,-k)确定,层对应 k 从-4 到3),每层为竖直棱柱并可见其侧棱与上下面。然后围绕 z 轴将每一层棱柱做旋转变换,令旋转角随参数变化为若干不同的分段函数倍数(可理解为以 π 为单位随时间变化),最终呈现多段相互旋转的棱柱形态。
以上提示语为根据原始绘图命令整理而来,仅供参考。