鞍面在轴测投影中的等高线
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①本范例演示了鞍面在轴测投影下的等高线图形;②涉及的核心数学概念包括曲面、轴测投影、几何作图;③作图要点——从下方『构造摘要』提炼用到了Segment(线段)、Line(直线)、Intersect(交点)、OrthogonalLine(垂线)、Point(点)、Locus(轨迹)、Polygon(多边形)等GeoGebra命令/对象;④适合高中及以上学生学习和理解三维几何与投影变换。
GeoGebra 命令及参数
Segment(D, A') → fSegment(A', B) → gLine(B, f) → hLine(D, g) → iIntersect(h, i) → C'Segment(D, C') → jSegment(C', B) → kOrthogonalLine(A', g) → lOrthogonalLine(C', j) → mPoint(l) → APoint(m) → CSegment(A, A') → nSegment(C, C') → pSegment(D, A) → qSegment(A, B) → rSegment(B, C) → sSegment(C, D) → tLine(D, C) → s_2Intersect(s_2, r) → ESegment(C, E) → aLine(E, n) → bIntersect(i, b) → FIntersect(g, b) → GSegment(E, F) → f_1Segment(F, C') → cLine(F, k) → dLine(B, j) → eIntersect(d, e) → HSegment(F, H) → g_1Segment(H, B) → h_1Line(G, k) → i_1Intersect(j, i_1) → ISegment(G, I) → j_1Segment(H, I) → k_1Intersect(k, k_1) → JLine(I, n) → l_1Line(J, l_1) → m_1Intersect(t, l_1) → KIntersect(s, m_1) → LSegment(K, I) → q_1Segment(L, J) → t_1Segment(J, I) → a_1Point(a_1) → MLine(M, j_1) → c_1Intersect(j, c_1) → NIntersect(c_1, g) → OLine(N, n) → d_1Line(O, d_1) → e_1Segment(K, I) → n_1Intersect(d_1, t) → PIntersect(e_1, r) → QSegment(P, Q) → f_2Line(M, n) → g_2Intersect(g_2, f_2) → RLocus(R, M) → ponthalmaz1Segment(L, J) → p_1Segment(D, C) → r_1Segment(C, B) → s_1Segment(A, D) → b_1Intersect(r_1, b_1) → TIntersect(r_1, s_1) → UPoint(r_1) → VIntersect(h_1, s_1) → SSegment(A, S) → h_2Intersect(b_1, h_2) → WPolygon(D, U, S, W) → q1, d_2, u, s_3, wPoint(ponthalmaz1) → ZPoint(ponthalmaz1) → A_1Point(ponthalmaz1) → B_1Point(ponthalmaz1) → C_1Point(ponthalmaz1) → D_1Point(ponthalmaz1) → E_1Point(ponthalmaz1) → F_1Point(ponthalmaz1) → G_1Point(ponthalmaz1) → H_1Polygon(U, S, G_1, H_1, K, L, Z, A_1, B_1, C_1, D_1, E_1, F_1) → poligon1, u_1, p_2, q_2, r_2, k_3, s_4, l_2, z_1, i_2, j_2, k_2, m_2, n_2
AI 绘图提示语参考
绘制一个鞍形曲面的轴测投影轮廓图。先构造一个空间四边形底面,并作出其轴测投影。从底面的两个顶点分别作垂线,确定曲面上两个高点,连接形成曲面边界。在投影面上,通过交点与辅助线,逐步构造出曲面的等高线:先画出两条主轮廓线,再通过交点与平行线,生成多条内部等高线,最终形成完整的鞍面轮廓。
以上提示语为根据原始绘图命令整理而来,仅供参考。