logo家乐福(贝塞尔曲线)
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这个范例演示了如何使用贝塞尔曲线绘制家乐福标志。涉及的核心数学概念包括贝塞尔曲线、向量和几何变换。通过使用Polygon、LineBisector、Vector、Line、Mirror、Intersect等GeoGebra命令,可以构造出标志的各个部分。适合高中及以上学生或教师用于教学和学习几何变换和曲线绘制。
GeoGebra 命令及参数
Polygon(A, B, 8) → polígono1, f, D, E, F, G, H, g, h, i, j, k, l, m, CLineBisector(C, D) → pVector(H, G) → uLine(M, p) → f_1Mirror(F, f_1) → F'Mirror(F', f_1) → F''Line(J, p) → rLineBisector(A, B) → nVector(A, B) → vLine(N, n) → h_1Intersect(h_1, r) → PLine(O, n) → g_1Line(F, p) → aIntersect(g_1, a) → QIntersect(g_1, r) → S_1Line(H, W) → r_3Mirror(P, r_3) → P'_1Midpoint(S_1, P'_1) → A_2Intersect(n, p) → ICircleArc(I, F, G) → cMirror(c, p) → c'Mirror(c', n) → c''Mirror(G, n) → G'Mirror(H, n) → H'LineBisector(J, D) → tLineBisector(F, K) → qIntersect(q, t) → LCircleArc(L, F, K) → eMirror(P, f_1) → P'Mirror(Q, f_1) → Q'CircleArc(R, Q, Q') → c_1LineBisector(P, Q) → i_1Intersect(i_1, a) → SCircleArc(I, A, B) → e_1Rotate(e_1, 90°, I) → k_1LineBisector(H, K) → sOrthogonalLine(R, f_1) → bIntersect(b, s) → TCircleArc(U, K, H) → p_1Mirror(W, h_1) → W'LineBisector(Q, W) → j_1Intersect(j_1, n) → ZIntersect(j_1, a) → A_1Midpoint(A_1, Z) → B_1LineBisector(W', F) → l_1Intersect(l_1, j_1) → C_1CircleArc(C_1, F, W') → r_1Intersect(t, g_1) → E_1CircleArc(E_1, D, J) → dIntersect(h_1, f_1) → D_1Segment(J, F_1) → m_1Translate(W, Vector[(-2 * v)]) → W'_1Mirror(F_1, h_1) → I_1Segment(I_1, W'_1) → n_1Mirror(I_1, f_1) → G_1Mirror(W'_1, f_1) → J_1Segment(G_1, J_1) → a_1Mirror(c', f_1) → c''_1Mirror(c'', f_1) → c'''Mirror(r_1, f_1) → d_2Mirror(p_1, f_1) → e_2Mirror(J, f_1) → J'Mirror(F_1, f_1) → K_1Segment(J', K_1) → b_1Mirror(d, f_1) → d'Mirror(e, f_1) → e'Mirror(e_1, f_1) → h_2Mirror(k_1, f_1) → k_2Polygon(W, W', F, Q) → c1, w, w', f_3, q_2Mirror(W, f_1) → W'_2Mirror(W', f_1) → W''Mirror(Q, f_1) → Q'_1Polygon(W'_2, W'', F', Q'_1) → c1', w'_2, w'', f', q'_1Polygon(J, K_1, J') → t1, j', j_2, l_2Polygon(W'_1, J_1, G_1) → t2, m_2, w'_1, n_2Intersect(a, m_1) → L_1Mirror(L_1, f_1) → M_1Polygon(Q, L_1, M_1, Q') → c3, q_4, p_2, r_2, s_2Polygon(B, C, D, J) → c4, b_2, c_3, d_3, j_3Polygon(F, K, H, A) → c5, f_5, k_3, h_3, a_2Mirror(D, f_1) → D'Mirror(D, f_1) → D'_1Mirror(B, f_1) → B'_2Mirror(C, f_1) → C'_2Mirror(D, f_1) → D'_2Mirror(J, f_1) → J'_3Polygon(B'_2, C'_2, D'_2, J'_3) → c4', b'_2, c'_2, d'_2, j'_3Mirror(F, f_1) → F'_1Mirror(H, f_1) → H'_1Mirror(H, f_1) → H'_2Mirror(H, f_1) → H'_3Mirror(F, f_1) → F'_2Mirror(F, f_1) → F'_3Mirror(K, f_1) → K'_3Mirror(H, f_1) → H'_4Mirror(A, f_1) → A'_2Polygon(F'_3, K'_3, H'_4, A'_2) → c5', f'_3, k'_3, h'_4, a'_2Polygon(F', A'_2, B'_2, J') → c2, i_2, t_2, g_3, i_3Mirror(A'_2, f_1) → N_1Mirror(B'_2, f_1) → O_1Mirror(J', f_1) → J''Polygon(F'', N_1, O_1, J'') → c2', f'', l_3, o_1, j''Mirror(H_1, f_1) → P_1Intersect(h_1, r_3) → Q_1Vector(H, Q_1) → u_1Mirror(W, f_1) → W'_3Mirror(Q, f_1) → Q'_2Mirror(W', f_1) → W''_1Mirror(H_1, f_1) → U_1Mirror(F'', f_1) → F'''Mirror(K, f_1) → K'Mirror(A, f_1) → A'Mirror(B, f_1) → B'CurveCartesian(((1 - t)^(2) * F'') + (((2 * (1 - t)) * t) * B_2) + (t^(2) * W), t, 0, 1) → d_1Mirror(d_1, f_1) → t_1CurveCartesian(((1 - t)^(2) * W) + (((2 * (1 - t)) * t) * A_2) + (t^(2) * Q), t, 0, 1) → q_1Mirror(q_1, f_1) → v_1CurveCartesian(((1 - t)^(2) * W'_1) + (((2 * (1 - t)) * t) * W_1) + (t^(2) * J_1), t, 0, 1) → s_1Intersect(n, r) → Z_1
AI 绘图提示语参考
绘制Carrefour标志,使用贝塞尔曲线和几何变换。首先绘制多边形,然后通过镜像、旋转和中点构造关键点和曲线。最后,利用线段的中垂线和交点确定标志的各个部分。
以上提示语为根据原始绘图命令整理而来,仅供参考。