滚动桥梁
几何画板及绘图内容加载中,请稍等……
这个范例演示了一个桥梁的滚动过程。它涉及几何变换和轨迹的概念。通过使用GeoGebra命令如Rotate、Intersect、Polygon等,可以动态展示桥梁的滚动路径。适合高中几何和解析几何课程。
GeoGebra 命令及参数
Point(xAxis) → APoint(xAxis) → BLine(B, yAxis) → kLine(A, k) → lRotate(B, (-α), l) → B'Line(B', l) → mRotate(A, α, m) → A'Line(A', m) → nRotate(B', α, n) → B''Line(B'', n) → pRotate(A', α, p) → A''Line(A'', p) → qRotate(B'', α, q) → B'''Line(B''', q) → rRotate(A'', α, r) → A'''Line(A''', r) → sRotate(B''', α, s) → EIntersect(k, g) → CIntersect(l, g) → DIntersect(m, g) → FIntersect(n, g) → GIntersect(p, q) → HIntersect(r, g) → IIntersect(p, g) → JIntersect(q, g) → KIntersect(s, g) → LLine(E, s) → hIntersect(h, g) → MPolygon(C, B, A, D) → q1, c, b, a, dPolygon(D, F, B', A) → q2, d_1, f_1, b', a_1Polygon(F, G, A', B') → q3, f_2, g_1, a', iPolygon(G, J, B'', A') → q4, g_2, j, b'', tPolygon(J, K, A'', B'') → q5, j_1, k_1, a'', ePolygon(K, I, B''', A'') → q6, k_2, i_1, b''', h_1Polygon(I, L, A''', B''') → q7, i_2, l_1, a''', m_1Polygon(L, M, E, A''') → q8, l_2, m_2, e_1, n_1Rotate(A, 67.5°, k) → A'_{1}Rotate(B, -67.5°, l) → B'_{1}Ray(A, B'_{1}) → q_1Rotate(B', 65°, l) → B''_{1}Ray(A, B''_{1}) → s_1Rotate(A, 67.5°, m) → A'_{2}Ray(B', A'_{2}) → t_1Rotate(A', -67.5°, m) → A''_{1}Rotate(A', -67.5°, m) → A''_{2}Rotate(B', 67.5°, n) → B''_{2}Rotate(B'', -67.5°, n) → B'''_{1}Ray(B', A''_{2}) → b_1Ray(A', B''_{2}) → c_1Ray(A', B'''_{1}) → h_2Rotate(A', 67.5°, p) → A''_{3}Ray(B'', A''_{3}) → j_2Rotate(A'', -67.5°, p) → A'''_{1}Rotate(B''', -67.5°, q) → RRotate(A''', -67.5°, r) → SRotate(E, -67.5°, s) → E'Ray(B'', A'''_{1}) → n_2Ray(A'', R) → q_2Ray(B''', S) → s_2Ray(A''', E') → a_2Rotate(B'', 67.5°, q) → B'''_{2}Ray(A'', B'''_{2}) → r_1Rotate(A'', 67.5°, r) → A'''_{2}Ray(B''', A'''_{2}) → p_2Rotate(B''', 67.5°, s) → ORay(A''', O) → r_2Rotate(A''', 67.5°, h) → PRay(E, P) → t_2Ray(B, A'_{1}) → p_1Sphere(B, sradius) → oIntersect(p_1, o) → N,Sphere(A, sradius) → uIntersect(q_1, u) → Q,Intersect(s_1, u) → T,Sphere(B', sradius) → vSphere(A', sradius) → wSphere(B'', sradius) → o_1Sphere(A'', sradius) → u_1Sphere(B''', sradius) → v_1Sphere(A''', sradius) → w_1Sphere(E, sradius) → b_2Intersect(t_1, v) → U,Intersect(b_1, v) → V,Intersect(c_1, w) → W,Intersect(h_2, w) → Z,Intersect(j_2, o_1) → A_1,Intersect(n_2, o_1) → B_1,Intersect(r_1, u_1) → C_1,Intersect(q_2, u_1) → D_1,Intersect(p_2, v_1) → E_1,Intersect(s_2, v_1) → F_1,Intersect(r_2, w_1) → G_1,Intersect(a_2, w_1) → H_1,Intersect(t_2, b_2) → I_1,Midpoint(H_1, G_1) → J_1Midpoint(F_1, E_1) → K_1Midpoint(D_1, C_1) → L_1Midpoint(B_1, A_1) → M_1Midpoint(Z, W) → N_1Midpoint(V, U) → O_1Midpoint(T, Q) → P_1Segment(I_1, E) → j_3Ray(A, P_1) → c_2Ray(A', N_1) → e_2Ray(B'', M_1) → f_3Ray(A'', L_1) → g_3Ray(B''', K_1) → h_3Ray(A''', J_1) → i_3Ray(B', O_1) → d_2Sphere(P_1, adjustment) → o_2Intersect(c_2, o_2) → Q_1, R_1Sphere(O_1, adjustment) → u_2Sphere(N_1, adjustment) → v_2Sphere(M_1, adjustment) → w_2Sphere(L_1, adjustment) → a_3Sphere(K_1, adjustment) → b_3Sphere(J_1, adjustment) → c_3Intersect(d_2, u_2) → S_1, T_1Intersect(e_2, v_2) → U_1, V_1Intersect(f_3, w_2) → W_1, Z_1Intersect(g_3, a_3) → A_2, B_2Intersect(h_3, b_3) → C_2, D_2Intersect(i_3, c_3) → E_2, F_2Segment(R_1, Q) → k_3Segment(R_1, T) → l_3Segment(T_1, U) → m_3Segment(T_1, V) → n_3Segment(V_1, W) → p_3Segment(V_1, Z) → q_3Segment(Z_1, A_1) → r_3Segment(Z_1, B_1) → s_3Segment(B_2, C_1) → t_3Segment(B_2, D_1) → d_3Segment(D_2, E_1) → e_3Segment(D_2, F_1) → f_4Segment(F_2, G_1) → g_4Segment(F_2, H_1) → h_4Segment(N, Q) → i_4Segment(T, U) → j_4Segment(V, W) → k_4Segment(Z, A_1) → l_4Segment(B_1, C_1) → m_4Segment(D_1, E_1) → n_4Segment(F_1, G_1) → p_4Segment(H_1, I_1) → q_4Segment(H_1, A''') → r_4Segment(G_1, A''') → s_4Segment(F_1, B''') → t_4Segment(B''', E_1) → a_4Segment(D_1, A'') → b_4Segment(A'', C_1) → c_4Segment(B_1, B'') → d_4Segment(B'', A_1) → e_4Segment(Z, A') → f_5Segment(A', W) → g_5Segment(V, B') → h_5Segment(B', U) → i_5Segment(T, A) → j_5Segment(A, Q) → k_5Segment(N, B) → l_5Segment(F_2, A''') → m_5Segment(D_2, B''') → n_5Segment(B_2, A'') → p_5Segment(Z_1, B'') → q_5Segment(V_1, A') → r_5Segment(T_1, B') → s_5Segment(R_1, A) → t_5Ray(B, N) → b_5Line(C, B) → c_5Line(B, N) → a_5Sphere(N, adjustment) → o_3Intersect(a_5, o_3) → G_2, H_2Segment(B, H_2) → d_5Ray(E, I_1) → e_5Sphere(I_1, adjustment) → u_3Intersect(e_5, u_3) → I_2, J_2Segment(J_2, E) → f_6Segment(R_1, A) → g_6Mirror(J_2, h_6) → K_2Mirror(J_2, h_6) → L_2Mirror(E, h_6) → E'_{1}Segment(L_2, E'_{1}) → i_6Mirror(H_1, h_6) → M_2Mirror(H_1, h_6) → N_2Mirror(I_1, h_6) → O_2Segment(N_2, O_2) → j_6Mirror(H_1, h_6) → P_2Mirror(A''', h_6) → Q_2Segment(P_2, Q_2) → k_6Mirror(F_2, h_6) → R_2Mirror(A''', h_6) → S_2Segment(R_2, S_2) → l_6Mirror(F_2, h_6) → T_2Mirror(G_1, h_6) → U_2Segment(T_2, U_2) → m_6Mirror(G_1, h_6) → V_2Mirror(A''', h_6) → W_2Segment(V_2, W_2) → n_6Mirror(F_1, h_6) → Z_2Mirror(G_1, h_6) → A_3Segment(Z_2, A_3) → p_6Mirror(D_2, h_6) → B_3Mirror(F_1, h_6) → C_3Segment(B_3, C_3) → q_6Mirror(D_2, h_6) → D_3Mirror(E_1, h_6) → E_3Segment(D_3, E_3) → r_6Mirror(D_2, h_6) → F_3Mirror(B''', h_6) → G_3Segment(F_3, G_3) → s_6Mirror(B''', h_6) → H_3Mirror(E_1, h_6) → I_3Segment(H_3, I_3) → t_6Mirror(D_1, h_6) → J_3Mirror(E_1, h_6) → K_3Segment(J_3, K_3) → a_6Mirror(B_2, h_6) → L_3Mirror(C_1, h_6) → M_3Segment(L_3, M_3) → b_6Mirror(B_2, h_6) → N_3Mirror(D_1, h_6) → O_3Segment(N_3, O_3) → c_6Mirror(B_2, h_6) → P_3Mirror(A'', h_6) → A'''_{3}Segment(P_3, A'''_{3}) → d_6Mirror(A'', h_6) → A'''_{4}Mirror(C_1, h_6) → Q_3Segment(A'''_{4}, Q_3) → e_6Mirror(B_1, h_6) → R_3Mirror(C_1, h_6) → S_3Segment(R_3, S_3) → f_7Mirror(Z_1, h_6) → T_3Mirror(B_1, h_6) → U_3Segment(T_3, U_3) → g_7Mirror(Z_1, h_6) → V_3Mirror(A_1, h_6) → W_3Segment(V_3, W_3) → h_7Mirror(Z_1, h_6) → Z_3Mirror(B'', h_6) → B'''_{3}Segment(Z_3, B'''_{3}) → i_7Mirror(B'', h_6) → B'''_{4}Mirror(A_1, h_6) → A_4Segment(B'''_{4}, A_4) → j_7Mirror(B_1, h_6) → B_4Mirror(B'', h_6) → B'''_{5}Segment(B_4, B'''_{5}) → k_7Mirror(Z, h_6) → Z'Mirror(A_1, h_6) → C_4Segment(Z', C_4) → l_7Mirror(V_1, h_6) → D_4Mirror(W, h_6) → W'Segment(D_4, W') → m_7Mirror(Z, h_6) → Z'_{1}Mirror(V_1, h_6) → E_4Mirror(Z, h_6) → Z'_{2}Segment(E_4, Z'_{2}) → n_7Mirror(V_1, h_6) → F_4Mirror(A', h_6) → A''_{4}Segment(F_4, A''_{4}) → p_7Mirror(A', h_6) → A''_{5}Mirror(W, h_6) → W'_{1}Segment(A''_{5}, W'_{1}) → q_7Mirror(Z, h_6) → Z'_{3}Mirror(A', h_6) → A''_{6}Segment(Z'_{3}, A''_{6}) → r_7Mirror(A''_{6}, h_6) → G_4Mirror(V, h_6) → V'Mirror(B', h_6) → B''_{3}Segment(V', B''_{3}) → s_7Mirror(B', h_6) → B''_{4}Mirror(U, h_6) → U'Segment(B''_{4}, U') → t_7Mirror(T_1, h_6) → H_4Mirror(U, h_6) → U'_{1}Segment(H_4, U'_{1}) → a_7Mirror(T_1, h_6) → I_4Mirror(B', h_6) → B''_{5}Segment(I_4, B''_{5}) → b_7Mirror(T_1, h_6) → J_4Mirror(V, h_6) → V'_{1}Segment(J_4, V'_{1}) → c_7Mirror(T, h_6) → T'Mirror(U, h_6) → U'_{2}Segment(T', U'_{2}) → d_7Mirror(R_1, h_6) → K_4Mirror(Q, h_6) → Q'Segment(K_4, Q') → e_7Mirror(T, h_6) → T'_{1}Mirror(R_1, h_6) → L_4Mirror(A, h_6) → A'_{3}Segment(L_4, A'_{3}) → f_8Mirror(R_1, h_6) → M_4Mirror(T, h_6) → T'_{2}Segment(M_4, T'_{2}) → g_8Mirror(A, h_6) → A'_{4}Mirror(Q, h_6) → Q'_{1}Segment(A'_{4}, Q'_{1}) → h_8Mirror(T, h_6) → T'_{3}Mirror(A, h_6) → A'_{5}Segment(T'_{3}, A'_{5}) → i_8Mirror(B, h_6) → B'_{2}Mirror(H_2, h_6) → N_4Segment(B'_{2}, N_4) → j_8Mirror(N, h_6) → N'Mirror(Q, h_6) → Q'_{2}Segment(N', Q'_{2}) → k_8Mirror(D_1, h_6) → O_4Mirror(A'', h_6) → A'''_{5}Segment(O_4, A'''_{5}) → l_8Mirror(V, h_6) → V'_{2}Mirror(W, h_6) → W'_{2}Segment(V'_{2}, W'_{2}) → m_8Mirror(F_2, h_6) → P_4Mirror(H_1, h_6) → Q_4Segment(P_4, Q_4) → n_8Mirror(F_1, h_6) → R_4Mirror(B''', h_6) → S_4Segment(R_4, S_4) → p_8Polygon(T_4, U_4, V_4, Z_4) → q9, q_8, u_4, v_4, z_4Prism(q9, -7) → w_3, D_5, edge9, edge10, edge12, edge11, edge13, edge15, edge16, edge14, E_5, F_5, G_5, face6, face8, face9, face7, face10Mirror(w_3, eq1) → v_3
AI 绘图提示语参考
在坐标平面内先给出一对互相垂直的坐标轴,并取两点分别落在 x 轴上用于确定初始折线方向;通过连接该点与垂直于对应轴的直线,得到多条基准直线。随后围绕相应的交点做连续旋转,逐步生成一串新的顶点与其对应的直线,使前后两段都以固定角度逐次折转。用这些旋转得到的多段直线的两两交点形成一组端点,再用端点依次拼接成多块四边形构成“滚动桥”的轮廓,最后再加上从关键端点出发的附加线段形成延伸结构。
以上提示语为根据原始绘图命令整理而来,仅供参考。