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Traffic Matrix & Flow Network

Traffic Matrix & Flow Network
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2019-07-29 09:15
VectorFunctionCoordinate GeometryMatrix
This example demonstrates the visualization and calculation of traffic matrices and flow networks in a two-dimensional space. Core mathematical concepts include matrix operations, linear equations, vectors, and functions. Construction highlights involve GeoGebra commands like ReducedRowEchelonForm, Simplify, Slope, and Vector, along with objects such as xn2, xp2, yp1. Suitable for high school and above learners to understand the application of linear algebra in traffic flow analysis.

GeoGebra Commands & Parameters

  1. ReducedRowEchelonForm(m4) → m5
  2. Simplify(Element[m5, 1, 5] - (x * Element[m5, 1, 4])) → f1
  3. Simplify(Element[m5, 2, 5] - (x * Element[m5, 2, 4])) → f2
  4. Simplify(Element[m5, 3, 5] - (x * Element[m5, 3, 4])) → f3
  5. Slope(f1) → mf1
  6. Slope(f2) → mf2
  7. Slope(f3) → mf3
  8. RemoveUndefined(Sequence[If[Element[mL, i] > 0 ∧ Element[bL, i] < 0, Element[Solutions[Element[fL, i]], 1]], i, 1, Length[bL]]) → Lmin
  9. RemoveUndefined(Sequence[If[Element[mL, i] < 0 ∧ Element[bL, i] > 0, Element[Solutions[Element[fL, i]], 1]], i, 1, Length[bL]]) → Lmax
  10. If(Length[Lmin] ≟ 0, 0, Max[Lmin]) → xmin
  11. Intersect(xAxis, yAxis) → A
  12. Point(yAxis) → B
  13. Point(xAxis) → D
  14. Point(yAxis) → E
  15. Point(yAxis) → H
  16. Polygon(E, F, G, H) → c2, e, f_1, g, h
  17. Point(yAxis) → I
  18. Point(yAxis) → L
  19. Polygon(I, J, K, L) → c3, i, j, k, l
  20. Polygon(M, N, O, P) → c4, m, n, o, p
  21. Polygon(Q, R, S, T) → c5, q, r, s, t
  22. Polygon(U, V, W, Z) → c6, u, v, w, z_1
  23. Point(xAxis) → A_1
  24. Point(xAxis) → B_1
  25. Polygon(E_1, F_1, G_1, H_1) → c8, e_1, g_1, h_1, i_1
  26. Polygon(I_1, J_1, K_1, L_1) → c9, j_1, k_1, l_1, m_1
  27. Polygon(A, B_1, L_1, L) → c10, a_2, n_5, p_1, l_2
  28. Textfield(yp1) → CasillaDeEntrada1
  29. Textfield(yp2) → CasillaDeEntrada2
  30. Textfield(xn1) → CasillaDeEntrada3
  31. Textfield(xn2) → CasillaDeEntrada4
  32. Textfield(xp1) → CasillaDeEntrada7
  33. Textfield(xp2) → CasillaDeEntrada8
  34. Vector(S_1, T_1) → q_1
  35. Vector(U_1, V_1) → r_1
  36. Sum(l3) → sumaSol
  37. LaTeX(sumaSol, true, true) → texto7
  38. Textfield(s_n) → CasillaDeEntrada9
  39. Vector(P_1, O_1) → v_1
  40. Vector(N_1, M_1) → u_1
  41. If(Length[Lmax] ≟ 0, If[xmin > 0, 1 / 0, 0], Min[Lmax]) → xmax
  42. Vector(G_2, H_2) → t_1
  43. Vector(I_2, J_2) → u_2
  44. Vector(K_2, L_2) → v_2
  45. Vector(F_2, E_2) → w_2
  46. Vector(D_2, C_2) → b_2
  47. Vector(B_2, A_2) → c_2