达·芬奇的棱柱透视图
几何画板及绘图内容加载中,请稍等……
这个范例演示了达·芬奇的棱柱透视图。核心数学概念包括几何、棱柱和透视。通过使用Mirror、Polygon、PointIn等GeoGebra命令,可以构造棱柱的透视图。适合初中及以上学生学习几何透视和立体几何。
GeoGebra 命令及参数
Mirror(B, A) → B'Mirror(D, A) → D'Polygon(D', B', D, B) → poly1, d', b', d, b_1PointIn(poly1) → NPointIn(poly1) → LPolygon(L, N, 4, xOyPlane) → poly2, k, l, m, n, M, B_1Point(b') → ESegment(E, O) → fPoint(f) → PLine(L, zAxis) → r_4Intersect(xAxis, yAxis) → E_1Mirror(F_1, yAxis) → G_1Mirror(FF, yAxis) → FF'Polygon(FF', FF, F_1, G_1) → poly5, ff', ff, f_2, g_2Midpoint(d) → FSegment(F, D) → cPoint(c) → GLine(G, b') → eIntersect(e, d') → HPolygon(R, Q, H, G) → poly3, r, q, h, gSegment(L, E) → tIntersect(t, e) → ULine(U, f) → c_1Segment(P, L) → iIntersect(c_1, i) → VLine(V, q) → r_2Intersect(r_2, h) → B_2Segment(V, B_2) → t_2Mirror(H, D') → H'Midpoint(D', F) → IMidpoint(d') → JSegment(P, N) → jIntersect(e, h) → TSegment(P, B_1) → sSegment(N, E) → e_1Intersect(e_1, e) → A_1Line(A_1, f) → g_1Intersect(j, g_1) → C_1Segment(P, E) → i_1Segment(D, E) → j_1Line(C_1, V) → l_1Intersect(l_1, r) → J_1Intersect(l_1, h) → K_1Segment(R, J_1) → m_1Segment(G, K_1) → n_1Intersect(h, n_1) → M_1Intersect(h, poly1) → S_1, S_2Line(V, r) → q_2Intersect(q_2, poly3) → Z_1, A_2Segment(V, A_2) → s_2Line(VD, g_2) → a_3Line(VH, ff') → b_3Intersect(a_3, b_3) → C_2Line(C_1, r) → c_3Line(C_1, g) → d_3Intersect(h, poly1) → D_2, D_3Intersect(h, poly1) → E_2, E_3Intersect(c_3, q) → F_2Intersect(h, poly1) → G_2, G_3Intersect(d_3, h) → H_2Segment(F_2, C_1) → e_3Segment(C_1, H_2) → f_3Line(CH, ff') → g_3Line(CL, g_2) → h_3Intersect(g_3, h_3) → I_2Sequence(R + (i * Vector[R, Q]), i, 0, 1, 1 / o_1) → l1Sequence(G + (i * Vector[R, Q]), i, 0, 1, 1 / o_1) → l2Sequence(G + (i * Vector[G, R]), i, 0, 1, 1 / u_1) → l3Sequence(H + (i * Vector[G, R]), i, 0, 1, 1 / u_1) → l4Sequence(Segment[Element[l1, i], Element[l2, i]], i, 1, Length[l1]) → l5Sequence(Segment[Element[l3, i], Element[l4, i]], i, 1, Length[l3]) → l6Line(P, A) → j_3Point(j_3) → CLine(C, xAxis) → k_3Sphere(C, 0.2) → u_2Sphere(C - (0, 0.13, -0.05), 0.3) → o_2Point(r_4) → L_2Segment(L_2, P) → n_3Intersect(n_3, poly3) → P_2Segment(P, M) → pIntersect(p, poly3) → KIntersect(s, poly3) → SPolygon(K, C_1, V, S) → q1, k_1, f_1, v_1, s_1Prism(poly2, L_2) → a_1, W, arêteNW, arête2, arête3, arête4, arête6, arête7, arête5, D_1, I_1, face1, face2, face4, face3, face5, arête1Segment(P, I_1) → h_1Segment(P, D_1) → p_1Segment(P, W) → q_1Segment(E, A) → r_1Intersect(q_1, poly3) → L_1Intersect(p_1, poly3) → N_1Intersect(h_1, poly3) → O_1Polygon(N_1, L_1, P_2, O_1) → q2, t_1, d_1, p_2, h_2Polygon(N_1, K, C_1, L_1) → q3, i_2, k_2, j_2, l_2Polygon(L_1, C_1, V, P_2) → q4, m_2, n_2, v_2, a_2Polygon(N_1, O_1, S, K) → q5, b_2, c_2, s_3, k_4Polygon(O_1, P_2, V, S) → q6, d_2, e_2, v_3, s_4
AI 绘图提示语参考
绘制一个棱柱的透视示意图。先画一个四边形作为棱柱的底面,并在其内部取两个点。从这两个点出发,构建一个与水平面相关的四边形,形成棱柱的顶面。在底面的边上取点,连接该点与空间中的固定点,形成一条视线,并在视线上取点。接着,通过一系列辅助线与交点,逐步构建出棱柱的侧面和透视投影线,包括连接顶点与底边中点的线段、延长线及其交点,最终形成完整的透视棱柱图形,并标注出各关键交点。
以上提示语为根据原始绘图命令整理而来,仅供参考。