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立方体模型

立方体模型
几何画板及绘图内容加载中，请稍等……
2022-03-02 21:56
立体几何参数方程
所属专题 Linkages
该范例展示了立方体的几何构造。涉及的核心数学概念包括几何变换、反射和参数曲线。通过使用GeoGebra命令如If、OrthogonalLine、Circle等，可以动态地构建立方体的各个面和边。适合初中及以上学生或教师用于几何教学。

GeoGebra 命令及参数

  1. If(f ≟ 0° ∨ f ≟ 90° ∨ f ≟ 180° ∨ f ≟ 270° ∨ f ≟ 360°, f + 0.001, f) → f'
  2. If(b ≟ 0° ∨ b ≟ 90° ∨ b ≟ 180° ∨ b ≟ 270° ∨ b ≟ 360°, b + 0.001, b) → b'
  3. If(a ≟ 0° ∨ a ≟ 90° ∨ a ≟ 180° ∨ a ≟ 270° ∨ a ≟ 360°, a + 0.001, a) → a'
  4. If(j ≟ 0° ∨ j ≟ 90° ∨ j ≟ 180° ∨ j ≟ 270° ∨ j ≟ 360°, j + 0.001, j) → j'
  5. If(a ≟ 90°, 2, If[a ≟ 270°, 0, Ny + (cos(b) * Ny) + ((sin(b) * NPy) * sqrt(Nx^(2) + Ny^(2) + Nz^(2)) / sqrt(NPx^(2) + nada^(2) + NPz^(2)))]) → By
  6. If(a ≟ 90° ∨ a ≟ 270°, 0, Nz + (cos(b) * Nz) + ((sin(b) * NPz) * sqrt(Nx^(2) + Ny^(2) + Nz^(2)) / sqrt(NPx^(2) + nada^(2) + NPz^(2)))) → Bz
  7. If(e ≟ 0° ∨ e ≟ 90° ∨ e ≟ 180° ∨ e ≟ 270° ∨ e ≟ 360°, e + 0.001, e) → e'
  8. If((((((sgn(cos(e)) * sgn(cos(a))) * sgn(cos(j))) * sgn(cos(f))) * sgn(cos(d))) * sgn(cos(b))) ≟ 0, (((((sgn(cos(e + 0.01°)) * sgn(cos(a + 0.01°))) * sgn(cos(j + 0.01°))) * sgn(cos(f + 0.01°))) * sgn(cos(d + 0.01°))) * sgn(cos(b + 0.01°))), (((((sgn(cos(e)) * sgn(cos(a))) * sgn(cos(j))) * sgn(cos(f))) * sgn(cos(d))) * sgn(cos(b)))) → signo
  9. If(d ≟ 0° ∨ d ≟ 90° ∨ d ≟ 180° ∨ d ≟ 270° ∨ d ≟ 360°, d + 0.001, d) → d'
  10. OrthogonalLine(C, xAxis) → zz2
  11. Circle(C, 0.62) → zz0
  12. Intersect(zz0, zz2, 1) → ZZ4
  13. Intersect(zz0, zz2, 2) → ZZ3
  14. Ellipse(ZZ3, ZZ4, 0.65) → zElipse2
  15. Point(zElipse2) → Z
  16. OrthogonalLine(C, yAxis) → zz1
  17. Intersect(zz0, zz1, 2) → ZZ2
  18. Intersect(zz0, zz1, 1) → ZZ1
  19. Ellipse(ZZ1, ZZ2, 0.65) → zElipse1
  20. Point(zElipse1) → XY
  21. Punto3D(C, XY, Z, LJ1) → J1
  22. Punto3D(C, XY, Z, LJ2) → J2
  23. Punto3D(C, XY, Z, LE) → E
  24. Intersect(zElipse2, zz2) → ZZ7, ZZ8
  25. Angle(ZZ8, C, Z) → zAngInc
  26. Intersect(zElipse1, zz1) → ZZ5, ZZ6
  27. Angle(ZZ6, C, XY) → zAngRot
  28. Segment(ZZ5, ZZ6) → zz4
  29. Segment(ZZ7, ZZ8) → zz3
  30. Intersect(zElipse2, zElipse1, 1) → zPunto1
  31. Intersect(zElipse2, zElipse1, 4) → zPunto2
  32. Segment(zPunto1, zPunto2) → zSeg2
  33. Point(Circle[AuxX, distancia3D]) → AuxY
  34. Segment(AuxX, AuxY) → segmentodistancia3D
  35. Punto3D(C, XY, Z, LU) → U
  36. Punto3D(C, XY, Z, LO) → O
  37. Punto3D(C, XY, Z, LF) → F
  38. Punto3D(C, XY, Z, LA) → A
  39. Polygon(O, E, U) → poly1, poly1c, poly1b, poly1a
  40. Punto3D(C, XY, Z, LB) → B
  41. Segment(O, U) → barraOU
  42. Segment(O, E) → barraOE
  43. Segment(U, F) → barraUF
  44. Segment(F, E) → barraEF
  45. Segment(O, A) → barraOA
  46. Segment(A, B) → barraAB
  47. If(isomero, J1, J2) → J
  48. Segment(B, J) → barraBJ
  49. Segment(U, B) → barraUB
  50. Segment(F, J) → barraFJ
  51. Punto3D(C, XY, Z, LD) → D
  52. Segment(A, D) → barraAD
  53. Segment(E, D) → barraED
  54. Segment(D, J) → barraDJ
  55. Punto3D(C, XY, Z, LM) → M
  56. Punto3D(C, XY, Z, LMP) → MP
  57. Punto3D(C, XY, Z, LNP) → NP
  58. If((((((sgn(cos(e)) * sgn(cos(a))) * sgn(cos(j))) * sgn(cos(f))) * sgn(cos(d))) * sgn(cos(b))) ≟ 0, (((((sgn(cos(e - 0.01°)) * sgn(cos(a - 0.01°))) * sgn(cos(j - 0.01°))) * sgn(cos(f - 0.01°))) * sgn(cos(d - 0.01°))) * sgn(cos(b - 0.01°))), (((((sgn(cos(e)) * sgn(cos(a))) * sgn(cos(j))) * sgn(cos(f))) * sgn(cos(d))) * sgn(cos(b)))) → c
  59. Sequence({((-cos(e)) * arista), (sin(e) * arista), 0}, e, 8°, 300.00000000000006°, 72°) → LCE, {{-4.951340343707852, 0.6958655048003272, 0}, {-0.8682408883346521, 4.92403876506104, 0}, {4.414737964294635, 2.3473578139294533, 0}, {3.5966990016932554, -3.4732918522949867, 0}, {-2.191855733945387, -4.493970231495835, 0}}
  60. Conic(Punto3D[C, XY, Z, Element[LCE, 1]], Punto3D[C, XY, Z, Element[LCE, 2]], Punto3D[C, XY, Z, Element[LCE, 3]], Punto3D[C, XY, Z, Element[LCE, 4]], Punto3D[C, XY, Z, Element[LCE, 5]]) → CE
  61. Sequence({(arista * (Ex / 2 - (((sgn(cos(e)) * dF) * cos(f)) * sin(aF)))), (arista * ((Ey + 1) / 2 + ((dF * cos(f)) * cos(aF)))), ((arista * dF) * sin(f))}, f, 8°, 300.00000000000006°, 72°) → LCFF, {{-4.975667684019047, 4.980645841196502, 0.49229718133007855}, {-2.934118977107226, 2.937054564122473, 3.483561676900716}, {-0.2926308715371856, 0.29292364882176347, 1.660662336901143}, {-0.7016501483281518, 0.7023521495355842, -2.4572159088589807}, {-3.59592606900891, 3.599523794240345, -3.179305286272957}}
  62. Conic(Punto3D[C, XY, Z, Element[LCFF, 1]], Punto3D[C, XY, Z, Element[LCFF, 2]], Punto3D[C, XY, Z, Element[LCFF, 3]], Punto3D[C, XY, Z, Element[LCFF, 4]], Punto3D[C, XY, Z, Element[LCFF, 5]]) → CFF
  63. Sequence({((arista * sin(j)) * cos(a)), (arista * sin(a)), ((arista * cos(j)) * cos(a))}, a, 8°, 300.00000000000006°, 72°) → LCA, {{0, 0.6958655048003272, 4.951340343707852}, {0, 4.92403876506104, 0.8682408883346521}, {0, 2.3473578139294533, -4.414737964294635}, {0, -3.4732918522949867, -3.5966990016932554}, {0, -4.493970231495835, 2.191855733945387}}
  64. Conic(Punto3D[C, XY, Z, Element[LCA, 1]], Punto3D[C, XY, Z, Element[LCA, 2]], Punto3D[C, XY, Z, Element[LCA, 3]], Punto3D[C, XY, Z, Element[LCA, 4]], Punto3D[C, XY, Z, Element[LCA, 5]]) → CA
  65. Sequence({((arista * sin(j)) * cos(a)), (arista * sin(a)), ((arista * cos(j)) * cos(a))}, j, 8°, 300.00000000000006°, 72°) → LCJ, {{0.6958655048003272, 0, 4.951340343707852}, {4.92403876506104, 0, 0.8682408883346521}, {2.3473578139294533, 0, -4.414737964294635}, {-3.4732918522949867, 0, -3.5966990016932554}, {-4.493970231495835, 0, 2.191855733945387}}
  66. Conic(Punto3D[C, XY, Z, Element[LCJ, 1]], Punto3D[C, XY, Z, Element[LCJ, 2]], Punto3D[C, XY, Z, Element[LCJ, 3]], Punto3D[C, XY, Z, Element[LCJ, 4]], Punto3D[C, XY, Z, Element[LCJ, 5]]) → CJ
  67. Sequence({(arista * ((((((sqrt(2) * cos(a)) * sin(d)) * sin(e)) * cos(j)) * sqrt((((-cos(a)) * cos(e)) * sin(j)) + (sin(a) * sin(e)) + 1) / ((2 * sqrt(((cos(a))^(2) * (((sin(e))^(2) * (sin(j))^(2)) + (cos(j))^(2))) + (((((2 * sin(a)) * cos(a)) * sin(e)) * cos(e)) * sin(j)) + ((sin(a))^(2) * (cos(e))^(2)))))) + (cos(a) * ((cos(d) * sin(j) / 2) + sin(j) / 2)) - (cos(d) * cos(e) / 2) - cos(e) / 2)), (arista * ((((((sqrt(2) * cos(a)) * sin(d)) * cos(e)) * cos(j)) * sqrt((((-cos(a)) * cos(e)) * sin(j)) + (sin(a) * sin(e)) + 1) / ((2 * sqrt(((cos(a))^(2) * (((sin(e))^(2) * (sin(j))^(2)) + (cos(j))^(2))) + (((((2 * sin(a)) * cos(a)) * sin(e)) * cos(e)) * sin(j)) + ((sin(a))^(2) * (cos(e))^(2)))))) + (sin(a) * (cos(d) / 2 + 1 / 2)) + (cos(d) * sin(e) / 2) + sin(e) / 2)), (arista * ((cos(a) * ((cos(d) * cos(j) / 2) + cos(j) / 2)) - (((sqrt(2) * sin(d)) * (((cos(a) * sin(e)) * sin(j)) + (sin(a) * cos(e)))) * sqrt((((-cos(a)) * cos(e)) * sin(j)) + (sin(a) * sin(e)) + 1) / ((2 * sqrt(((cos(a))^(2) * (((sin(e))^(2) * (sin(j))^(2)) + (cos(j))^(2))) + (((((2 * sin(a)) * cos(a)) * sin(e)) * cos(e)) * sin(j)) + ((sin(a))^(2) * (cos(e))^(2))))))))}, d, 8°, 300.00000000000006°, 72°) → LCD, {{-4.975670171853926, 0.4920512172381114, 4.975670171853926}, {-2.934120444167326, 3.481821201600095, 2.934120444167326}, {-0.29263101785268253, 1.6598326281007467, 0.29263101785268253}, {-0.7016504991533723, -2.4559882217977695, 0.7016504991533723}, {-3.5959278669726933, -3.177716825141184, 3.5959278669726933}}
  68. Conic(Punto3D[C, XY, Z, Element[LCD, 1]], Punto3D[C, XY, Z, Element[LCD, 2]], Punto3D[C, XY, Z, Element[LCD, 3]], Punto3D[C, XY, Z, Element[LCD, 4]], Punto3D[C, XY, Z, Element[LCD, 5]]) → CD
  69. Sequence({(arista * (((((sqrt(2) * sin(b)) * cos(j)) * sgn(cos(a))) * sqrt(sin(a) + 1) / 2) + (cos(a) * ((cos(b) * sin(j) / 2) + sin(j) / 2)))), (arista * ((sin(a) * (cos(b) / 2 + 1 / 2)) + cos(b) / 2 + 1 / 2)), (arista * ((cos(a) * ((cos(b) * cos(j) / 2) + cos(j) / 2)) - ((((sqrt(2) * sin(b)) * sin(j)) * sgn(cos(a))) * sqrt(sin(a) + 1) / 2)))}, b, 8°, 300.00000000000006°, 72°) → LCB, {{0.4920512172381114, 4.975670171853926, 4.975670171853926}, {3.481821201600095, 2.934120444167326, 2.934120444167326}, {1.6598326281007467, 0.29263101785268253, 0.29263101785268253}, {-2.4559882217977695, 0.7016504991533723, 0.7016504991533723}, {-3.177716825141184, 3.5959278669726933, 3.5959278669726933}}
  70. Conic(Punto3D[C, XY, Z, Element[LCB, 1]], Punto3D[C, XY, Z, Element[LCB, 2]], Punto3D[C, XY, Z, Element[LCB, 3]], Punto3D[C, XY, Z, Element[LCB, 4]], Punto3D[C, XY, Z, Element[LCB, 5]]) → CB
  71. Segment(O, F) → g
  72. Segment(O, D) → h
  73. Segment(O, B) → i

AI 绘图提示语参考

画一个三维立方体的几何构造示意：先在空间里建立基准圆与两条互相垂直的方向线，通过圆与垂线的交点形成两个椭圆弧的关键点，并在三维坐标中取出上、下对应的高度点以得到立方体的顶点。随后将这些顶点连接成棱段，画出前后面与侧面的边界，形成多边形面，同时标出体对角相关的关键连线（例如从某顶点到另一对应点的连段）。保持所有棱段为直线连接关系，整体呈现立方体的透视结构。
以上提示语为根据原始绘图命令整理而来，仅供参考。