三维篮球投篮与反弹轨迹模拟

GeoGebra 命令及参数

1. Min(sqrt(x(G12toeR)^(2) + y(G12toeR)^(2)), sqrt(x(G12toeL)^(2) + y(G12toeL)^(2))) → Gtoedist
2. Segment(Ghand_L0, G4_L) → gghandsho_L0
3. Distance(GHLdet, G4_L) → GHLrad
4. Intersect(yAxis, xAxis) → O
5. Mirror(E_1, O) → E_2
6. Semicircle(E_1, E_2) → c
7. Distance(A_{xy}, O) → distA
8. If(t < t_c, ωk, (ℯ^((-(t - t_c))) * ωk)) → ω
9. Distance(Hxy2, C_c) → dist2_{ring}
10. Distance(Hxy1, C_c) → dist1_{ring}
11. Distance(A_{xy}, (x(Vpar), y(Vpar))) → VAxy
12. Distance(GHRdet, G4_R) → GHRrad
13. If(t < td, Point[{GHLx(t), GHLy(t), GHLz(t)}], Point[{GHLx2(t), GHLy2(t), GHLz2(t)}]) → Ghand_L
14. If(sqrt((x(G4_L) - x(O'))^(2) + (y(G4_L) - y(O'))^(2)) - sqrt((x(Ghand_L) - x(O'))^(2) + (y(Ghand_L) - y(O'))^(2)) > 0, 1, -1) → fwd_L
15. Vector(((((-fwd_L) * cos(α)) * cos(π / 2 - ϕhs_{LR})), (((-fwd_L) * sin(α)) * cos(π / 2 - ϕhs_{LR})), ((-fwd_L) * cos(ϕhs_{LR})))) → elbdisp_{unitLR}
16. Distance(Ghand_L, G4_L) → gghandsho_L
17. If(gghandsho_L^(2) > armlen^(2), 0, (1 / 2 * sqrt(armlen^(2) - gghandsho_L^(2)))) → elbdisp_L
18. Midpoint(Ghand_L, G4_L) → elbL_0
19. If(t < td, Point[{GHRx(t), GHRy(t), GHRz(t)}], Point[{GHRx2(t), GHRy2(t), GHRz2(t)}]) → Ghand_R
20. Distance(Ghand_R, G4_R) → gghandsho_R
21. Mirror(U_1, Xf) → U_2
22. Mirror(U_3, Xc) → U_4
23. Segment(E_1, U_1) → u_1
24. Segment(E_2, U_2) → u_2
25. Mirror(U_5, Xf) → U_6
26. Mirror(U_7, Xc) → U_8
27. Polygon(U_5, U_3, U_4, U_6) → poly1, u_5, u_3, u_4, u_6
28. Semicircle(U_8, U_7) → d
29. Surface(((R_{ring} + (r_{ring} * cos(u))) * cos(v)), ((R_{ring} + (r_{ring} * cos(u))) * sin(v)), (r_{ring} * sin(u)) + h, u, 0, (2 * π), v, 0, (2 * π)) → ring
30. Polygon(T_1, T_2, T_4, T_3) → poly_{bckb}, t_1, t_2, t_4, t_3
31. Segment(C_b, C_t) → csost
32. Dilate(poly_{bckb}, 0.5, C_t) → poly2_{tabint}
33. Dilate(poly_{bckb}, 0.25, C_t) → poly2_{sost}
34. Prism(poly2_{sost}, -3.1998318771914116) → a, B, edge1, edge2, edge3, edge4, edge5, edge6, edge7, edge8, C, D, E, face1, face2, face3, face4, face5
35. Mirror(U_9, Xff) → U_{10}
36. Polygon(U_5, U_9, U_{10}, U_6) → poly2, u_7, u_9, u_{10}, u_8
37. Polygon(C, C', C_{xyr}, C_{xy}) → poly3, c_1, c', c_{xyr}, c_{xy}
38. Polygon(B, B', B_{xyr}, B_{xy}) → poly4, b, b', b_{xyr}, b_{xy}
39. Polygon(B', C', C, B) → poly5, b'_1, c'_1, c_2, b_1
40. Polygon(B_{xyr}, C_{xyr}, C', B') → poly6, b_2, c_3, c'_2, b'_2
41. Polygon(C_{xy}, B_{xy}, B, C) → poly7, c_4, b_3, b_4, c_5
42. Point(face2) → G
43. Segment(F, G) → f
44. Mirror(F, planexz) → F'
45. Mirror(G, planexz) → G'
46. Segment(F', G') → f'
47. CurveCartesian(((-u)) / 5 + R_{ring}, 0, h - u, u, 0, 0.4) → fnet
48. Surface(fnet, 360°, zAxis) → net
49. Vector(A, A') → u
50. Segment(A, A_{xy}) → i
51. Mirror(TL1, Xf) → TL1'
52. Mirror(TL2, xAxis) → TL2'
53. Semicircle(TL2, TL2') → k
54. Segment(TL1, TL2) → j
55. Segment(TL1', TL2') → l
56. Segment(TL2', TL2) → m
57. CurveCartesian((x(P) - (w * cos(α)), y(P) - (w * sin(α)), z(P) + (w * (((-g) * t) + v0_z) / v0_s)), w, -2 / v_0, 4 / v_0) → tgtra
58. If(resultptsnew ≟ 3, "OK - 3pts", resultptsnew ≟ 2, "OK - 2pts", "Fail") → result
59. CurveCartesian(((v0_x * t) + x(A), (v0_y * t) + y(A), ((-1 / 2 * g) * t^(2)) + (v0_z * t) + z(A)), t, 0, tz_0) → tra
60. If((checkv0 < 0) ∧ (checkv0_m > 0), (v_0 / g * sqrt(v_0^(2) - ((2 * g) * (h - z(A))))), distA) → s0_{cond}
61. Segment(G4, G0) → trunk
62. Segment(G6, G8) → legl_2
63. Segment(G0, G6) → legl_1
64. Segment(G0, G7) → legr_1
65. Segment(G7, G9) → legr_2
66. Line(A_{xy}, O) → n
67. OrthogonalLine(A_{xy}, n, xOyPlane) → p
68. Line(G1, p) → q
69. Rotate(Head, headangle, q) → Head'
70. Segment(G9, G12toeL) → footL
71. Segment(G8, G12toeR) → footR
72. Midpoint(Ghand_R, G4_R) → elbR_0
73. Translate(elbL_0, Vector[(elbdisp_L * elbdisp_{unitLR})]) → Gelb_L
74. Segment(Gelb_L, Ghand_L) → arml_2
75. Segment(G4_L, Gelb_L) → arml_1
76. If(gghandsho_R^(2) > armlen^(2), 0, (1 / 2 * sqrt(armlen^(2) - gghandsho_R^(2)))) → elbdisp_R
77. Translate(elbR_0, Vector[(elbdisp_R * elbdisp_{unitLR})]) → Gelb_R
78. Segment(Gelb_R, Ghand_R) → armr_2
79. Segment(G4_R, Gelb_R) → armr_1
80. If(gghandsho_R > armlen, false, t) → o
81. Distance(Ghand_L0, (x(A) + (rball * cos(α - π / 4)) + (v0_x * t), y(A) + (rball * sin(α - π / 4)) + (v0_y * t), z(A) - (rball * sin(ϕ)) - ((1 / 2 * g) * t^(2)) + (v0_z * t))) → distx
82. Line(elbL_0, elbdisp_{unitLR}) → elbline_L
83. Line(elbR_0, elbdisp_{unitLR}) → elbline_R
84. Locus(Ghand_L, t) → loc1
85. Textfield(timelimit) → SetGameTime
86. If(condtot, If[Gtoedist > 6.25, 3, 2], 0) → e
87. If(0 < t < t_c, true, false) → flyingball
88. If(time - floor(time) ≥ 0.95, LaTeX[floor(time + 1) + ".0"], If[time - floor(time) < 0.05, LaTeX[floor(time) + ".0"], LaTeX[round(time, 1)]]) → timeroundfix1
89. TableText({{"", "shots", "ok/shots", "ok%"}, {"total shots", 2, 3, 4}, {"2pts shots", 2, 3, 4}, {"3pts shots", 2, 3, 4}, {1, 2, 3, 4}}, "c_|||h") → ttxtest
90. Polygon(U_3, U_4, U_{10}, U_9) → polyfloor, r, s, f_1, g_1
91. Circle(O_{ring}, R_{ring}, zAxis) → liring
92. Vector(A, A + Dilate[ic00(2), vsca]) → uv
93. Sphere(Prun, rball) → ball_1
94. If(Distance[Prun, liring] < r_{ring} + rball, true, false) → impring
95. ClosestPoint(liring, Prun) → Q
96. Line(Prun, Q) → pq
97. If(Distance[Prun, plaz] < rball + 0.02, true, false) → impfloor
98. If(Distance[Prun, ClosestPointRegion[poly_{bckb}, Prun]] < rball, true, false) → impbackboard
99. Plane(A, AV, Vpar) → αpla
100. Circle((x(Prun), y(Prun), 0), rball, xOyPlane) → ballshdw
101. Segment((x(T_3), y(T_3), 0), (x(T_4), y(T_4), 0)) → shdwbb
102. Circle((x(O_{ring}), y(O_{ring}), 0), R_{ring}, zAxis) → ringshdw
103. Element(listvectordirection, If[faces > 0, faces, 5]) → Selectedvector
104. Segment((x(C_t), y(C_t), 0), (x(C_b), y(C_b), 0)) → shdwringsup
105. Segment((x(G), y(G), 0), (x(D) + 0.37, y(D), 0)) → shdwGD
106. Segment((x(G'), y(G'), 0), (x(E) + 0.37, y(E), 0)) → shdwG'E
107. Polygon((x(G), y(G), 0.02), (x(G'), y(G'), 0.02), (x(E) + 0.42, y(E), 0.02), (x(D) + 0.42, y(D), 0.02)) → shdwsup, h_1, i_1, j_1, k_1
108. Dilate(d, 0.1, Xc) → d_c
109. CurveCartesian(((x(ic(2)) * τ) + x(ic(1)), (y(ic(2)) * τ) + y(ic(1)), ((-1 / 2 * g) * τ^(2)) + (z(ic(2)) * τ) + z(ic(1))), τ, 0, tzrun_0) → trarun
110. Dilate(vvar, vsca) → vvar'
111. Translate(Prun, Vector[Dilate[vvar', 0.95]]) → vtpoint
112. If(tresultpts, If[Gtoedist ≥ 6.25, 3, 2], 0) → resultpts
113. If((z(Prun) > h - rball) ∧ (z(Prun) < h) ∧ (z(vvar) < 0), true, false) → tresult
114. If(tresult_t > 0, 0, 0) → tscore
115. If(x(A) ≥ 0, ((atan(y(A) / x(A)) * 180 / π))°, If[y(A) > 0, ((atan(y(A) / x(A)) * 180 / π) + 180)°, ((atan(y(A) / x(A)) * 180 / π) - 180)°]) → αtgt
116. Segment(P, Q) → pqseg
117. If(αFT, αtgt - 15°, -180°) → αminFT
118. If(αFT, αtgt + 15°, 180°) → αmaxFT