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Polygon Intersection Demo by PommierMS

Polygon Intersection Demo by PommierMS
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2016-01-13 07:57
PolygonCoordinate GeometryGeometric Construction
This example demonstrates the intersection of two polygons after translation and rotation. It involves core math concepts like polygons, intersection points, geometric transformations, and coordinate geometry. Key GeoGebra commands and objects used include Point, Polygon, Min, Max, ConvexHull, Translate, IntersectPath, Distance, Segment, Length. Suitable for high school students learning coordinate geometry and geometric transformations to understand polygon positional relationships and dynamic changes.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 1.3050670480860362]) → B
  2. Polygon(A, B, C, D, E, F, G) → poly1, a, b, c, d, e, f, g
  3. Min({x(A), x(B), x(C), x(D), x(E), x(F), x(G)}) → x_{min}
  4. Max({x(A), x(B), x(C), x(D), x(E), x(F), x(G)}) → x_{max}
  5. Min({y(A), y(B), y(C), y(D), y(E), y(F), y(G)}) → y_{min}
  6. Max({y(A), y(B), y(C), y(D), y(E), y(F), y(G)}) → y_{max}
  7. ConvexHull({A, B, C, D, E, F, G}) → graphe1
  8. Polygon(D_0, A_0, B_0, C_0) → poly2, d_0, a_0, b_0, c_0
  9. Point(Circle[H, 1.1744944318141146]) → I
  10. Polygon(H, I, J, K, L, M) → poly3, h_1, i_1, j_1, k_1, l_1, m_1
  11. Min({x(H), x(I), x(J), x(K), x(L), x(M)}) → x'_{min}
  12. Max({x(H), x(I), x(J), x(K), x(L), x(M)}) → x'_{max}
  13. Min({y(H), y(I), y(J), y(K), y(L), y(M)}) → y'_{min}
  14. Max({y(H), y(I), y(J), y(K), y(L), y(M)}) → y'_{max}
  15. Polygon(A'_0, B'_0, C'_0, D'_0) → poly4, a_1, b_1, c_1, d_1
  16. ConvexHull({H, I, J, K, L, M}) → graphe2
  17. Polygon(U_4, U_1, U_2, U_3) → poly5, u_4, u_1, u_2, u_3
  18. Translate(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'
  19. 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'
  20. 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'
  21. 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'
  22. 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'
  23. 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'
  24. Polygon(H', I', J', K', L', M') → poly3', h', i', j', k', l', m'
  25. 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]))) → N
  26. Translate(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]))) → O
  27. Translate(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]))) → P
  28. Translate(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]))) → Q
  29. Polygon(N, O, P, Q) → poly4', n_1, o_1, p_1, q_1
  30. ConvexHull({H', I', J', K', L'}) → graphe3
  31. IntersectPath(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_1
  32. Min(Lx) → x_{inf}
  33. Min(Ly) → y_{inf}
  34. Max(Lx) → x_{sup}
  35. Max(Ly) → y_{Sup}
  36. Polygon({(x_{inf}, y_{inf}), (x_{sup}, y_{inf}), (x_{sup}, y_{Sup}), (x_{inf}, y_{Sup})}) → poly7
  37. Distance(O, P) → v_1
  38. Distance(Q, P) → w_1
  39. Distance(C_0, D_0) → o_2
  40. Distance(C_0, B_0) → v_2
  41. Segment(C_0, B_0) → q_3
  42. Segment(A_0, B_0) → r_3
  43. Segment(N, O) → s_3
  44. Segment(P, O) → t_3
  45. Segment((x_{inf}, y_{Sup}), (x_{sup}, y_{Sup})) → a_4
  46. Segment((x_{inf}, y_{Sup}), (x_{inf}, y_{inf})) → b_4
  47. Length(a_4) → w_2
  48. Length(r_3) → dist_r3
  49. Length(s_3) → dist_{L_1}

AI Drawing Prompt Reference

Draw a polygon and then translate and rotate it. Create a polygon first, find the minimum and maximum x and y coordinates of its vertices, then create another polygon and translate and rotate it. Finally, calculate the intersection of the two polygons and display the boundary of the intersection polygon.
The prompt above was compiled from the original drawing commands and is for reference only.