委拉斯开兹《宫娥》中的几何透视与正交线构造

GeoGebra 命令及参数

1. OrthogonalLine(B, xAxis) → a
2. Point(a) → C
3. Segment(B, C) → b
4. Point(b) → M_1
5. If(pas > 4 ∧ pas < 7, 0, -1) → t_5
6. OrthogonalLine(B_5, b) → d_5
7. OrthogonalLine(A_5, b) → p_1
8. Point(d_5) → W_2
9. OrthogonalLine(W_2, p_1) → f_3
10. Point(f_3) → Z_2
11. Point(f_3) → Y_2
12. Segment(Y_2, Z_2) → g_3
13. Point(g_3) → C_3
14. OrthogonalLine(C_3, f_3) → h_3
15. Point(d_5) → R_2
16. Point(p_1) → O_2
17. Segment(O_2, R_2) → r_2
18. Point(r_2) → S_2
19. OrthogonalLine(S_2, p_1) → s_2
20. If(pas > 0 ∧ pas < 7, 0, -1) → t_1
21. OrthogonalLine(A, b) → d
22. If(pas > 1 ∧ pas < 7, 0, -1) → t_2
23. If(pas > 2 ∧ pas < 7, 0, -1) → t_3
24. If(pas > 3 ∧ pas < 7, 0, -1) → t_4
25. If(pas > 5 ∧ pas < 7, 0, -1) → t_6
26. Point(d) → D
27. OrthogonalLine(A, b) → e
28. Dilate(D, pr, A) → E
29. Circle(A, E) → f
30. OrthogonalLine(A, e) → g
31. Intersect(f, g, 2) → F
32. OrthogonalLine(F, g) → h
33. OrthogonalLine(D, e) → i
34. Intersect(h, i) → G
35. Segment(P_1, P_7) → c
36. Polygon(A, F, G, D) → P, a_1, f_1, g_1, d_1
37. Segment(B_1, G) → j
38. Point(j) → H
39. Segment(H, D) → k
40. Point(k) → I
41. OrthogonalLine(I, b) → l
42. Intersect(g_1, l) → J
43. Segment(I, J) → m
44. Line(B_2, b) → n
45. Point(n) → K
46. Point(g_1) → L
47. Intersect(f_1, j) → N
48. Point(g_1) → O
49. Intersect(f_1, j) → Q
50. Intersect(f_1, j) → R
51. Intersect(f_1, j) → T
52. Intersect(f_1, j) → U
53. Point(f_1) → V
54. Point(f_1) → W
55. Point(f_1) → Y
56. Segment(K, L) → p
57. Segment(K, O) → q
58. Segment(K, W) → r
59. Segment(K, V) → s
60. OrthogonalLine(B_3, b) → t
61. Point(t) → S
62. Point(t) → Z
63. Point(t) → C_1
64. Point(t) → D_1
65. OrthogonalLine(S, t) → b_1
66. OrthogonalLine(Z, t) → c_1
67. OrthogonalLine(C_1, t) → e_1
68. Intersect(r, b_1) → E_1
69. Intersect(b_1, q) → F_1
70. Intersect(b_1, p) → G_1
71. Intersect(b_1, l) → H_1
72. Intersect(c_1, r) → I_1
73. Intersect(c_1, q) → J_1
74. Intersect(c_1, p) → K_1
75. Intersect(c_1, l) → L_1
76. Intersect(e_1, l) → N_1
77. Intersect(e_1, p) → O_1
78. Intersect(e_1, q) → Q_1
79. Intersect(e_1, r) → R_1
80. OrthogonalLine(D_1, t) → h_1
81. Intersect(l, h_1) → S_1
82. Intersect(h_1, p) → T_1
83. Intersect(h_1, q) → U_1
84. Polygon(H_1, G_1, K_1, L_1) → V_1, h_2, g_2, k_1, l_1
85. Polygon(F_1, E_1, I_1, J_1) → W_1, f_2, e_2, i_1, j_1
86. Polygon(N_1, O_1, T_1, S_1) → Y_1, n_1, o_1, t_7, s_1
87. Polygon(Q_1, R_1, W, U_1) → Z_1, q_1, r_1, w, u_1
88. Line(B_4, b) → m_1
89. Point(m_1) → C_2
90. Segment(K, C_2) → a_2
91. Mirror(K, n) → K'
92. Mirror(L, n) → L'
93. Mirror(K, n) → K'_1
94. Mirror(C_2, n) → C_2'
95. Line(E_2, m_1) → d_2
96. Point(d_2) → F_2
97. Segment(E_2, F_2) → i_2
98. Point(m_1) → G_2
99. Segment(K, G_2) → j_2
100. Point(m_1) → H_2
101. Segment(K, H_2) → k_2
102. Mirror(K, n) → K'_2
103. Mirror(G_2, n) → G_2'
104. Segment(K'_2, G_2') → l_2
105. Mirror(K, n) → K'_3
106. Mirror(H_2, n) → H_2'
107. Segment(K'_3, H_2') → m_2
108. Point(i_2) → I_2
109. OrthogonalLine(I_2, b) → n_2
110. Intersect(l_2, n_2) → J_2
111. Intersect(n_2, j_2) → K_2
112. OrthogonalLine(J_2, n_2) → p_2
113. OrthogonalLine(K_2, n_2) → q_2
114. Intersect(m_2, p_2) → L_2
115. Intersect(k_2, q_2) → M_2
116. Polygon(L_2, J_2, K_2, M_2) → Q_2, l_3, j_3, k_3, m_3
117. Point(d_5) → D_2
118. Point(d_5) → N_2
119. Line(D_2, b) → b_2
120. Line(N_2, b) → c_2
121. Point(b_2) → T_2
122. Point(c_2) → U_2
123. Intersect(s_2, h_3) → V_2
124. Segment(V_2, T_2) → a_3
125. Segment(V_2, U_2) → b_3
126. OrthogonalLine(U_2, a_3) → c_3
127. Mirror(V_2, c_3) → V_2'
128. Mirror(U_2, c_3) → U_2'
129. Segment(V_2', U_2') → d_3
130. Segment(V_2', T_2) → e_3
131. Dilate(A, fi, D) → E_3
132. OrthogonalLine(B_6, b) → i_3