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五参数模型变换的二十面体极值分布

五参数模型变换的二十面体极值分布
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2020-03-06 17:32
立体几何变换最值优化
该范例展示了五参数模型变换下的二十面体极值分布。涉及的核心数学概念包括变换、极值分布和立体几何。通过使用GeoGebra命令如Length、Sequence、Zip等，可以构造出变换后的二十面体，并观察其极值分布。适合高中数学教学和研究。

GeoGebra 命令及参数

  1. Length(m00(1)) → n00_1
  2. Length(m00) → n00
  3. Sequence({V00(m00(i, 1) + 1), V00(m00(i, 2) + 1), V00(m00(i, 3) + 1)}, i, 1, n00) → V00'
  4. Sequence(Dilate[Flatten[Sequence[V00'(i, j) + ((If[j < n00_1, V00'(i, j + 1), V00'(i, 1)] - V00'(i, j)) * {t, 1 - t}), j, 1, n00_1]], q, Cmi(i)], i, 1, n00) → V0a
  5. Zip(Rotate[a, α, Line[(0, 0), b]], a, V0a, b, Cmi) → V0b
  6. Join(V0b) → V0c
  7. If(t ≟ 0 ∨ t ≟ 0.5 ∨ q ≟ 1 ∨ q ≟ 0, Unique[V0c], V0c) → V0cc
  8. Length(V0cc) → läV'
  9. Sequence(Polygon[Sequence[V00(m00(i, k) + 1), k, 1, Length[m00(1)]]], i, 1, Length[m00]) → Poly3
  10. Length(V0c) → läV0c
  11. Sequence(Segment[V0c(m4(1, j)), V0c(m4(1, If[j ≟ 4, 1, j + 1]))], j, 1, 4) → seg4_i
  12. Sequence(Segment[V0c(m6(1, j)), V0c(m6(1, If[j ≟ 6, 1, j + 1]))], j, 1, 6) → seg6_i
  13. Sequence(Segment[V0c(m10(1, j)), V0c(m10(1, If[j ≟ 10, 1, j + 1]))], j, 1, 10) → seg10_i
  14. Length(V0cc) → n3
  15. Length(V00(1)) → läV00_1
  16. Sequence(Segment[V0c(m3a(1, j)), V0c(m3a(1, If[j ≟ 3, 1, j + 1]))], j, 1, 3) → seg3a_i
  17. Sequence(Segment[V0c(m3b(1, j)), V0c(m3b(1, If[j ≟ 3, 1, j + 1]))], j, 1, 3) → seg3b_i
  18. Sequence(Segment[V0c(m5a(1, j)), V0c(m5a(1, If[j ≟ 5, 1, j + 1]))], j, 1, 5) → seg5a_i
  19. KeepIf(x > 0, seg6_i) → seg6_i1
  20. KeepIf(x > 0, seg4_i) → seg4_i1
  21. KeepIf(x > 0, seg10_i) → seg10_i1
  22. Length(V0c(1)) → läV0c_1
  23. Dilate(q0, q, Cmi(1)) → q0'
  24. Sphere(O, läV0c_1) → sphe
  25. Sequence(Polygon[Sequence[V0c(m6(i, k)), k, 1, Length[m6(1)]]], i, 1, Length[m6]) → Poly6
  26. Sequence(Polygon[Sequence[V0c(m10(i, k)), k, 1, Length[m10(1)]]], i, 1, Length[m10]) → Poly10
  27. Sequence(Polygon[Sequence[V0c(m3a(i, k)), k, 1, Length[m3a(1)]]], i, 1, Length[m3a]) → Poly3a
  28. Sequence(Polygon[Sequence[V0c(m3b(i, k)), k, 1, Length[m3b(1)]]], i, 1, Length[m3b]) → Poly3b
  29. Sequence(Polygon[Sequence[V0c(m5a(i, k)), k, 1, Length[m5a(1)]]], i, 1, Length[m5a]) → Poly5a
  30. Sequence(Polygon[Sequence[V0c(m4(i, k)), k, 1, Length[m4(1)]]], i, 1, Length[m4]) → Poly4
  31. TableText(Append["segments", 1…6], Append["\fgcolor{#FE6F5E}{ poly3a} ", seg3a_i], Append["\fgcolor{#D19FE8}{ poly3b} ", seg3b_i], Append["\fgcolor{#008000}{poly\; 5\; }", seg5a_i], Append["\fgcolor{#008B8B}{poly\;6\; or\; 3 }", seg6_i1], "v") → text6c
  32. Text("" + p) → txt_p
  33. Sum(Flatten[Sequence[Append[Sequence[Element[txt_p, i], i, m1(k), m2(k)], " "], k, 1, 5]]) → txtUm1
  34. Text(text18r, A, false, true) → text18s
  35. TableText(Append["segments", 1…10], Append["\fgcolor{red}{ poly4} ", seg4_i1], Append["\fgcolor{#66CCFF}{poly\; 6\; or\; 3}", seg6_i1], Append["\fgcolor{#C19A6B}{poly\; 10\; or\; 5}", seg10_i1], "v") → text6b