Shadow of a Cube: Geometric Construction and Coordinate Transformation

GeoGebra Commands & Parameters

1. Rotate(P, α, xAxis) → P'
2. Rotate(P', β, yAxis) → P''
3. Rotate(P'', γ, zAxis) → P'''
4. Intersect(xAxis, zAxis) → O
5. Point(zAxis) → Q
6. Vector(O, Q) → u
7. Translate(P''', u) → l1
8. Point(l1) → I
9. Point(l1) → J
10. Point(l1) → K
11. Point(l1) → L
12. Polygon(I, J, K, L) → q1, i, j, k, l
13. Point(l1) → M
14. Point(l1) → N
15. Polygon(M, L, I, N) → q2, m, l_1, i_1, n
16. Point(l1) → R
17. Point(l1) → S
18. Polygon(N, R, S, M) → q3, n_1, r, s, m_1
19. Point(l1) → T
20. Point(l1) → U
21. Polygon(S, T, U, R) → q4, s_1, t, u_1, r_1
22. Point(l1) → V
23. Polygon(M, V, T, S) → q5, m_2, v, t_1, s_2
24. Point(l1) → W
25. Polygon(N, W, U, R) → q6, n_2, w, u_2, r_2
26. Point(yAxis) → Z
27. Point(xAxis) → A_1
28. Point(yAxis) → B_1
29. Plane(Z, A_1, B_1) → p
30. Point(v) → D_1
31. Ray(C_1, D_1) → f
32. Point(l1) → E_1
33. Ray(C_1, E_1) → g
34. Point(l1) → F_1
35. Ray(C_1, F_1) → h
36. Point(l1) → G_1
37. Ray(C_1, G_1) → q
38. Point(t_1) → H_1
39. Ray(C_1, H_1) → a
40. Point(u_2) → I_1
41. Ray(C_1, I_1) → b
42. Point(m_1) → J_1
43. Ray(C_1, J_1) → c
44. Point(l1) → K_1
45. Ray(C_1, K_1) → d
46. Intersect(h, p) → L_1
47. Intersect(c, p) → M_1
48. Intersect(q, p) → N_1
49. Intersect(d, p) → O_1
50. Intersect(g, p) → P_1
51. Intersect(b, p) → Q_1
52. Intersect(f, p) → R_1
53. Intersect(a, p) → S_1
54. Polygon(S_1, P_1, R_1) → t1, e, f_1, p_1
55. Polygon(N_1, R_1, S_1) → t2, g_1, h_1, j_1
56. Polygon(M_1, Q_1, L_1) → t3, k_1, q_1, a_1
57. Polygon(Q_1, P_1, S_1) → t4, b_1, c_1, d_1
58. Polygon(L_1, S_1, Q_1) → t5, e_1, f_2, g_2
59. Polygon(N_1, S_1, L_1) → t6, h_2, i_2, j_2
60. Polygon(M_1, L_1, N_1) → t7, k_2, l_2, p_2
61. Polygon(Q_1, L_1, P_1) → t8, q_2, t_2, a_2
62. Polygon(O_1, Q_1, M_1) → t9, b_2, o_1, c_2
63. Polygon(O_1, S_1, Q_1) → t10, d_2, e_2, f_3
64. Polygon(M_1, N_1, O_1) → t11, g_3, h_3, i_3
65. Polygon(S_1, O_1, N_1) → t12, j_3, k_3, l_3