三维无人机模型2
几何画板及绘图内容加载中,请稍等……
①本范例演示了一个三维无人机模型的构建过程;②涉及的核心数学概念包括立体几何、平行四边形、余弦定理、椭圆、积分计算和分布;③作图要点提炼自构造摘要,使用了Circle(圆)、Point(点)、Polygon(多边形)、Rotate(旋转)、Intersect(相交)、Prism(棱柱)、Midpoint(中点)、Pyramid(金字塔)、Cylinder(圆柱)、Ray(射线)、Sphere(球体)、Line(线)、OrthogonalLine(垂线)、Plane(平面)、Mirror(镜像)、Segment(线段)等GeoGebra命令和对象;④适合高中及以上学段学习立体几何、积分计算和三维建模的学生,也可用于数学教学演示。
GeoGebra 命令及参数
Circle(A, sqrt(20), xOyPlane) → dPoint(d) → BPoint(d) → CPoint(d) → DPoint(d) → EPolygon(B, E, D, C) → q1, b_1, e, d_1, c_1Rotate(q1, (-α), A) → q1'Rotate(B, (-α), A) → B'Rotate(C, (-α), A) → C'Rotate(E, (-α), A) → E'Rotate(D, (-α), A) → D'Circle(B', sqrt(5), xOyPlane) → fCircle(C', sqrt(5), xOyPlane) → gIntersect(f, g, 1) → FPoint(zAxis) → GPrism(q1', k) → l, L, edge5, edge6, edge7, edge8, edgeLM, edgeMN, edgeNO, edgeLO, M, N, O, face5, face7, face8, face6, faceLMNOPrism(q1', m) → n, P, edge9, edge10, edge11, edge12, edgePQ, edgeQR, edgeRS, edgePS, Q, R, S, face9, face11, face12, face10, facePQRSMidpoint(B', C') → IPyramid(facePQRS, G) → h, faceGPQ, faceGQR, faceGRS, faceGPS, edgeGP, edgeGQ, edgeGR, edgeGSCircle(I, C', xOyPlane) → pCylinder(p, t) → v, e_1, a_1Cylinder(p, f_1) → g_1, h_1, i_1Midpoint(D', E') → HMidpoint(H, A) → JMidpoint(I, A) → KMidpoint(edgeGQ) → UIntersect(edgeRS, edgeGR) → VMidpoint(edgeGR) → ZMidpoint(edgeGS) → A_1Midpoint(edgeGP) → B_1Polygon(B_1, U, Z, A_1) → q2, i, u_1, z_1, sRay(J, Z) → j_1Point(edge10) → C_1Polygon(U, C_1, V, Z) → q3, u_2, k_1, v_1, z_2Sphere(Z, 1) → oIntersect(j_1, o, 2) → D_1Line(D_1, k_1) → l_1Midpoint(A, J) → TMidpoint(z_1) → WMidpoint(W, Z) → E_1Ray(T, E_1) → m_1Line(D_1, i) → n_1Intersect(m_1, n_1) → F_1Line(F_1, l_1) → p_1Polygon(D_1, F_1, T, J) → q4, q_1, r_1, t_1, j_2Prism(q4, s_1) → w_1, K_1, edge18, edge20, edge19, edge17, edge21, edge23, edge24, edge22, L_1, M_1, N_1, face16, face17, face15, face14, face18Line(L_1, p_1) → f_2Line(K_1, p_1) → g_2Sphere(F_1, 1) → o_1Intersect(p_1, o_1, 2) → G_1Line(G_1, q_1) → h_2Intersect(h_2, l_1) → H_1Polygon(D_1, H_1, G_1, F_1) → q5, i_2, k_2, l_2, m_2Prism(q5, b_2) → c_2, Q_1, edge25, edge28, edge27, edge26, edge29, edge31, edge32, edge30, R_1, S_1, T_1, face20, face22, face21, face19, face23Midpoint(R_1, G_1) → J_1Line(J_1, p_1) → n_2Sphere(J_1, 5) → a_2Intersect(n_2, a_2) → O_1, P_1Midpoint(J_1, P_1) → U_1OrthogonalLine(U_1, q2) → p_2Sphere(U_1, 0.4) → d_2Intersect(p_2, d_2, 1) → V_1Intersect(p_2, d_2, 2) → W_1Cylinder(V_1, W_1, 2.5) → e_2, q_2, r_2, o_2Rotate(P_1, (-β), p_2) → Z_1Rotate(Z_1, 15°, p_2) → A_2Polygon(A_2, U_1, Z_1) → t1, s_2, t_2, f_3Sphere(U_1, 2.2) → v_2Intersect(t_2, v_2, 1) → B_2Intersect(s_2, v_2) → C_2, H_2Polygon(B_2, C_2, U_1) → t2, g_3, h_3, i_3Rotate(t2, -90°, p_2) → t2'Rotate(t2, 180°, p_2) → t2'_1Rotate(t2, -270°, p_2) → t2'_2Line(V_1, n_2) → j_3Cylinder(V_1, W_1, 0.1) → w_2, c_3, d_3, a_3Intersect(j_3, face18) → D_2Point(j_3) → E_2Intersect(j_3, q4) → F_2Midpoint(F_2, D_2) → G_2Midpoint(B_1, A_1) → I_2Plane(I_2, A, H) → p_3Mirror(o_2, p_3) → b_3Mirror(t2'_1, p_3) → t3Mirror(t2'_2, p_3) → t4Mirror(t2', p_3) → t2''Mirror(t2, p_3) → t2'_3Mirror(a_3, p_3) → e_3Mirror(d_3, p_3) → q_3Mirror(c_3, p_3) → r_3Mirror(r_2, p_3) → k_3Mirror(q_2, p_3) → s_3Intersect(j_3, q_2) → J_2,Point(q_2) → K_2Point(j_3) → L_2Midpoint(N_1, M_1) → M_2Cylinder(M_2, V_1, 0.15) → l_3, t_3, c_4, m_3Sphere(V_1, 0.2) → n_3Mirror(m_3, p_3) → o_3Mirror(n_3, p_3) → u_3Intersect(edgePS, edgePQ) → N_2Intersect(edgePS, edge12) → O_2Segment(O_2, A_1) → f_4Segment(B_1, N_2) → g_4Mirror(q4, p_3) → q4'Mirror(q5, p_3) → q5'Mirror(R_1, p_3) → P_2Mirror(Q_1, p_3) → Q_2Segment(P_2, Q_2) → edge29'Mirror(K_1, p_3) → R_2Mirror(N_1, p_3) → S_2Segment(R_2, S_2) → edge22'Mirror(face23, p_3) → face23'Mirror(face18, p_3) → face18'Mirror(K_1, p_3) → T_2Mirror(N_1, p_3) → U_2Segment(T_2, U_2) → edge22'_1Mirror(face20, p_3) → face20'Mirror(face14, p_3) → face14'Mirror(D_1, p_3) → V_2Mirror(H_1, p_3) → W_2Segment(V_2, W_2) → h_4Mirror(Q_1, p_3) → Z_2Mirror(D_1, p_3) → A_3Segment(Z_2, A_3) → edge25'Mirror(R_1, p_3) → B_3Mirror(Q_1, p_3) → C_3Segment(B_3, C_3) → edge29'_1Mirror(K_1, p_3) → D_3Mirror(N_1, p_3) → E_3Segment(D_3, E_3) → edge22'_2Intersect(edgeQR, k_1) → F_3Midpoint(F_3, O_2) → G_3Midpoint(G_3, O_2) → H_3Midpoint(G_3, H_3) → I_3Midpoint(I_3, H_3) → J_3OrthogonalLine(J_3, p_3) → i_4Point(i_4) → K_3OrthogonalLine(E_3, edgeMN, space) → j_4Line(K_3, edge8) → k_4Point(k_4) → L_3Plane(L_3, J_3, K_3) → p_4Mirror(o_2, p_4) → v_3Mirror(r_2, p_4) → d_4Mirror(F_1, p_4) → M_3Mirror(T, p_4) → T'Segment(M_3, T') → l_4Mirror(t2', p_4) → t2''_1Mirror(t2'_1, p_4) → t5Mirror(t2'_2, p_4) → t6Mirror(t2, p_4) → t2'_4Mirror(d_3, p_4) → e_4Mirror(n_3, p_4) → w_3Mirror(m_3, p_4) → a_4Mirror(a_3, p_4) → b_4Mirror(e_3, p_4) → m_4Mirror(b_3, p_4) → n_4Mirror(k_3, p_4) → q_4Mirror(t4, p_4) → t4'Mirror(t2'_3, p_4) → t7Mirror(t2'', p_4) → t2'''Mirror(o_3, p_4) → o_4Mirror(u_3, p_4) → r_4Mirror(t3, p_4) → t3'Mirror(q_3, p_4) → s_4Mirror(face18, p_4) → face18'_1Mirror(face23, p_4) → face23'_1Mirror(R_1, p_4) → N_3Mirror(Q_1, p_4) → O_3Segment(N_3, O_3) → edge29'_2Mirror(K_1, p_4) → P_3Mirror(N_1, p_4) → Q_3Segment(P_3, Q_3) → edge22'_3Mirror(q_2, p_4) → t_4Mirror(s_3, p_4) → c_5Mirror(B_3, p_4) → R_3Mirror(C_3, p_4) → S_3Mirror(D_3, p_4) → T_3Mirror(E_3, p_4) → U_3Mirror(face14, p_4) → face14'_1Mirror(J, p_3) → J'Mirror(D_1, p_3) → V_3Segment(J', V_3) → h_5Mirror(q4, p_4) → q4'_1Mirror(q5, p_4) → q5'_1Mirror(F_1, p_4) → W_3Mirror(T, p_4) → T'_1Segment(W_3, T'_1) → i_5Mirror(G_1, p_4) → Z_3Mirror(F_1, p_4) → A_4Segment(Z_3, A_4) → j_5Mirror(D_1, p_4) → B_4Mirror(H_1, p_4) → C_4Segment(B_4, C_4) → k_5Mirror(J, p_4) → J'_1Mirror(D_1, p_4) → D_4Segment(J'_1, D_4) → l_5Mirror(F_1, p_4) → E_4Mirror(D_1, p_4) → F_4Segment(E_4, F_4) → m_5Mirror(M_1, p_4) → G_4Mirror(L_1, p_4) → H_4Segment(G_4, H_4) → edge23'Mirror(K_1, p_4) → I_4Mirror(N_1, p_4) → J_4Segment(I_4, J_4) → edge22'_4Mirror(B_4, p_3) → K_4Mirror(C_4, p_3) → L_4Segment(K_4, L_4) → f_5Mirror(q5'_1, p_3) → q6Mirror(W_3, p_3) → M_4Mirror(T'_1, p_3) → N_4Segment(M_4, N_4) → g_5Mirror(J'_1, p_3) → O_4Mirror(D_4, p_3) → P_4Segment(O_4, P_4) → n_5Mirror(E_4, p_3) → Q_4Mirror(F_4, p_3) → R_4Segment(Q_4, R_4) → p_5Mirror(q4'_1, p_3) → q7Mirror(I_4, p_3) → S_4Mirror(J_4, p_3) → T_4Segment(S_4, T_4) → q_5Mirror(N_3, p_3) → U_4Mirror(O_3, p_3) → V_4Segment(U_4, V_4) → r_5Mirror(face23'_1, p_3) → q8Mirror(face18'_1, p_3) → q9Mirror(W_3, p_3) → W_4Mirror(T'_1, p_3) → Z_4Segment(W_4, Z_4) → s_5Mirror(Z_3, p_3) → A_5Mirror(A_4, p_3) → B_5Segment(A_5, B_5) → t_5Mirror(G_4, p_3) → C_5Mirror(H_4, p_3) → D_5Segment(C_5, D_5) → edge23''Mirror(T_1, p_4) → E_5Mirror(S_1, p_4) → F_5Segment(E_5, F_5) → edge32'Mirror(p_4, p_3) → p_6Mirror(E_5, p_3) → G_5Mirror(F_5, p_3) → H_5Segment(G_5, H_5) → edge32''Mirror(T_1, p_3) → I_5Mirror(S_1, p_3) → J_5Segment(I_5, J_5) → edge32'_1Mirror(M_1, p_3) → K_5Mirror(L_1, p_3) → L_5Segment(K_5, L_5) → edge23'_1Mirror(N_3, p_3) → M_5Mirror(O_3, p_3) → N_5Segment(M_5, N_5) → a_5Mirror(I_4, p_3) → O_5Mirror(J_4, p_3) → P_5Segment(O_5, P_5) → b_5Line(A, T) → d_5Point(d_5) → Q_5Prism(face7, v_4) → w_4, W_5, edge33, edge34, edge36, edge35, edge37, edge39, edge40, edge38, Z_5, A_6, B_6, face24, face26, face27, face25, face28Intersect(edge6, edge35) → S_5Point(edgeMN) → T_5Line(Q_5, i) → e_5Polygon(C_1, S_5, T_5, F_3) → q10, f_6, g_6, h_6, i_6Pyramid(q10, v_5) → w_5, V_5, face29, face31, face30, face13, edge13, edge15, edge16, edge14Line(Z, z_1) → j_6Line(U, i) → k_6Intersect(j_6, i_5) → C_6Intersect(k_6, s_5) → U_5Line(C_6, zAxis) → l_6Point(l_6) → D_6Line(D_6, yAxis) → r_6Intersect(z_2, j_2) → E_6Line(E_6, l_6) → m_6Line(U_5, l_6) → n_6Line(U, l_6) → q_6Intersect(m_6, r_6) → F_6Segment(E_6, F_6) → t_6Segment(C_6, D_6) → b_6Sphere(F_6, 1) → u_4Intersect(r_6, u_4, 1) → G_6Sphere(D_6, 1) → c_6Intersect(r_6, c_6, 2) → H_6Segment(G_6, H_6) → s_6Mirror(G_6, eq1) → I_6Mirror(H_6, eq1) → J_6Segment(I_6, J_6) → d_6Mirror(E_6, eq1) → K_6Mirror(F_6, eq1) → L_6Segment(K_6, L_6) → e_6Mirror(C_6, eq1) → M_6Mirror(D_6, eq1) → N_6Segment(M_6, N_6) → f_7
AI 绘图提示语参考
绘制一个3D无人机模型,包含底座、机身、螺旋桨和尾翼。首先画一个圆d,从中选取四个点B、C、D、E,构成一个四边形q1。然后围绕点A旋转q1和点B、C、D、E,生成新的图形q1'、B'、C'、E'、D'。接着画两个以B'、C'为圆心的圆f和g,求交点F。使用z轴上的点G作为顶点,构造一个金字塔h。画一个以I为圆心的圆p,围绕它画两个圆柱v和g_1。构造点H、J、K、U、V、Z、A_1、B_1,使用这些点构造新的图形q2、q3、q4,并围绕它们构造新的棱柱w_1。
以上提示语为根据原始绘图命令整理而来,仅供参考。