多边形交点演示 by PommierMS
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①本范例演示两个多边形在平移和旋转后的交点情况;②涉及的核心数学概念包括多边形、交点、几何变换、坐标几何;③作图要点提炼自构造摘要,使用了Point, Polygon, Min, Max, ConvexHull, Translate, IntersectPath, Distance, Segment, Length等GeoGebra命令和对象;④适合高中阶段学习解析几何、几何变换的学生,可用于理解多边形位置关系和动态变化。
GeoGebra 命令及参数
Point(Circle[A, 1.3050670480860362]) → BPolygon(A, B, C, D, E, F, G) → poly1, a, b, c, d, e, f, gMin({x(A), x(B), x(C), x(D), x(E), x(F), x(G)}) → x_{min}Max({x(A), x(B), x(C), x(D), x(E), x(F), x(G)}) → x_{max}Min({y(A), y(B), y(C), y(D), y(E), y(F), y(G)}) → y_{min}Max({y(A), y(B), y(C), y(D), y(E), y(F), y(G)}) → y_{max}ConvexHull({A, B, C, D, E, F, G}) → graphe1Polygon(D_0, A_0, B_0, C_0) → poly2, d_0, a_0, b_0, c_0Point(Circle[H, 1.1744944318141146]) → IPolygon(H, I, J, K, L, M) → poly3, h_1, i_1, j_1, k_1, l_1, m_1Min({x(H), x(I), x(J), x(K), x(L), x(M)}) → x'_{min}Max({x(H), x(I), x(J), x(K), x(L), x(M)}) → x'_{max}Min({y(H), y(I), y(J), y(K), y(L), y(M)}) → y'_{min}Max({y(H), y(I), y(J), y(K), y(L), y(M)}) → y'_{max}Polygon(A'_0, B'_0, C'_0, D'_0) → poly4, a_1, b_1, c_1, d_1ConvexHull({H, I, J, K, L, M}) → graphe2Polygon(U_4, U_1, U_2, U_3) → poly5, u_4, u_1, u_2, u_3Translate(H, Vector[D'_0, U_4] + (v * (Vector[U_4, U_3] - Vector[D'_0, C'_0])) + (w * (Vector[U_4, U_1] - Vector[D'_0, A'_0]))) → H'Translate(I, Vector[D'_0, U_4] + (v * (Vector[U_4, U_3] - Vector[D'_0, C'_0])) + (w * (Vector[U_4, U_1] - Vector[D'_0, A'_0]))) → I'Translate(J, Vector[D'_0, U_4] + (v * (Vector[U_4, U_3] - Vector[D'_0, C'_0])) + (w * (Vector[U_4, U_1] - Vector[D'_0, A'_0]))) → J'Translate(K, Vector[D'_0, U_4] + (v * (Vector[U_4, U_3] - Vector[D'_0, C'_0])) + (w * (Vector[U_4, U_1] - Vector[D'_0, A'_0]))) → K'Translate(L, Vector[D'_0, U_4] + (v * (Vector[U_4, U_3] - Vector[D'_0, C'_0])) + (w * (Vector[U_4, U_1] - Vector[D'_0, A'_0]))) → L'Translate(M, Vector[D'_0, U_4] + (v * (Vector[U_4, U_3] - Vector[D'_0, C'_0])) + (w * (Vector[U_4, U_1] - Vector[D'_0, A'_0]))) → M'Polygon(H', I', J', K', L', M') → poly3', h', i', j', k', l', m'Translate(A'_0, Vector[D'_0, U_4] + (v * (Vector[U_4, U_3] - Vector[D'_0, C'_0])) + (w * (Vector[U_4, U_1] - Vector[D'_0, A'_0]))) → NTranslate(B'_0, Vector[D'_0, U_4] + (v * (Vector[U_4, U_3] - Vector[D'_0, C'_0])) + (w * (Vector[U_4, U_1] - Vector[D'_0, A'_0]))) → OTranslate(C'_0, Vector[D'_0, U_4] + (v * (Vector[U_4, U_3] - Vector[D'_0, C'_0])) + (w * (Vector[U_4, U_1] - Vector[D'_0, A'_0]))) → PTranslate(D'_0, Vector[D'_0, U_4] + (v * (Vector[U_4, U_3] - Vector[D'_0, C'_0])) + (w * (Vector[U_4, U_1] - Vector[D'_0, A'_0]))) → QPolygon(N, O, P, Q) → poly4', n_1, o_1, p_1, q_1ConvexHull({H', I', J', K', L'}) → graphe3IntersectPath(poly1, poly3') → poly6, R, g_1, q_4, r_4, s_4, t_4, S, T, W_2, Z_2, A_3, B_3, e_1, f_1Min(Lx) → x_{inf}Min(Ly) → y_{inf}Max(Lx) → x_{sup}Max(Ly) → y_{Sup}Polygon({(x_{inf}, y_{inf}), (x_{sup}, y_{inf}), (x_{sup}, y_{Sup}), (x_{inf}, y_{Sup})}) → poly7Distance(O, P) → v_1Distance(Q, P) → w_1Distance(C_0, D_0) → o_2Distance(C_0, B_0) → v_2Segment(C_0, B_0) → q_3Segment(A_0, B_0) → r_3Segment(N, O) → s_3Segment(P, O) → t_3Segment((x_{inf}, y_{Sup}), (x_{sup}, y_{Sup})) → a_4Segment((x_{inf}, y_{Sup}), (x_{inf}, y_{inf})) → b_4Length(a_4) → w_2Length(r_3) → dist_r3Length(s_3) → dist_{L_1}
AI 绘图提示语参考
绘制一个多边形并进行平移和旋转,然后计算两个多边形的交集。首先创建一个多边形,然后找到其顶点的最小和最大x、y坐标,接着创建另一个多边形并进行平移和旋转,最后计算两个多边形的交集,显示交集多边形的边界。
以上提示语为根据原始绘图命令整理而来,仅供参考。