达利风格巨型半正多面体
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所属专题
geometriadinamica.es
①本范例演示了基于达利艺术风格的几何图形构造,通过半正多面体展示立体几何与变换的融合;②涉及核心概念包括向量、棱锥、相似变换、曲面、数列与级数;③构造过程中运用了Line(线)、OrthogonalLine(垂线)、Point(点)、Dilate(缩放)、Circle(圆)、Intersect(交点)、Polygon(多边形)、Segment(线段)、CircumcircleArc(圆心角)等GeoGebra命令与对象;④适合高中及以上学生及数学爱好者用于立体几何、变换与参数化学习。
GeoGebra 命令及参数
Line(H1, H2) → aLine(A, a) → bOrthogonalLine(A, a) → cPoint(b) → BDilate(B, pr, A) → DilCircle(A, Dil) → dIntersect(d, c) → D5, COrthogonalLine(C, c) → eOrthogonalLine(B, b) → fIntersect(f, e) → DPolygon(A, B, D, C) → P, a_1, b_1, d_1, c_1Circle(C, D) → pOrthogonalLine(A_1, c_1) → nIntersect(b_1, n) → ESegment(A_1, E) → qCircle(A_1, E) → rPoint(r) → FCircumcircleArc(C, F, E) → sPolygon(A_1, E, D, C) → poly1, a_2, e_1, d_2, c_2Circle(E, B) → tOrthogonalLine(A_2, a_1) → a1Intersect(a1, a_1) → GCircle(A_2, E) → c1Point(c1) → HCircumcircleArc(E, H, G) → d1Polygon(G, B, E, A_2) → poly2, g_1, b_2, e_2, a_3Circle(G, A) → e1OrthogonalLine(A_3, c_1) → b1Intersect(c_1, b1) → ICircle(A_3, G) → f1Point(f1) → JCircumcircleArc(G, J, I) → g1Polygon(A_3, G, A, I) → poly3, a_4, g_2, a_5, i_1Circle(I, A_1) → h1Circle(A_4, I) → k1Point(k1) → MOrthogonalLine(A_4, g_2) → i1Circle(A_4, I) → p1Intersect(p1, i1) → K, LPoint(p1) → NCircumcircleArc(I, N, K) → q1Polygon(I, A_1, K, A_4) → poly4, i_2, a_6, k_1, a_7Circle(K, A_2) → r1OrthogonalLine(A_5, a_5) → j1Intersect(a_3, j1) → OPoint(P) → RCircle(A_5, K) → s1Point(s1) → QCircumcircleArc(K, Q, O) → t1Polygon(A_5, K, A_2, O) → poly5, a_8, k_2, a_9, oCircle(A_3, O) → c2OrthogonalLine(A_6, e_2) → l1Intersect(o, l1) → SCircle(S, O) → d2Point(d2) → TCircumcircleArc(O, T, A_6) → e2Polygon(A_6, S, O, A_3) → poly6, a_{10}, s_1, o_1, a_{11}Intersect(d_1, a1) → UPolygon(A, A_1, A_2, G) → poly7, a_{12}, a_{13}, a_{14}, g_3Polygon(A_2, U, D, E) → poly8, a_{15}, u_1, d_3, e_3Segment(A, D) → m1
AI 绘图提示语参考
画一个受达利风格启发的空间几何构图:以给定的两条直线作为基准并在交点处生成一组点,然后做一次以某点为中心的放大得到新点,再以该点为圆心画圆并与前述正交直线相交得到若干关键点。连接这些点形成多边形面片,并分别以圆与若干点的两点圆心关系构造出多个圆弧,圆弧端点取自相交得到的点。再用若干垂线在不同构造点上寻找交点,继续生成补充多边形与圆弧,整体呈现由一组相交圆、垂线与面片组合的立体感几何图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。