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基本矩阵变换

基本矩阵变换
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2016-06-22 08:18
解析几何矩阵几何作图
本范例演示了使用2x2矩阵进行基本几何变换的过程。涉及的核心数学概念包括反射、旋转、剪切、缩放等线性变换。作图要点包括使用Element、SelectedIndex、Intersect、Circle、OrthogonalLine、Polygon、Point、Vector、Determinant、ApplyMatrix、Flatten、Textfield等GeoGebra命令和对象来构建和操作图形。适合高中及以上数学学习者，用于理解矩阵变换在平面几何中的应用。

GeoGebra 命令及参数

  1. Element(Reflections, (2 * indexreflection) - 1) → reflectiony1
  2. Element(Reflections, (2 * indexreflection)) → reflectiony2
  3. SelectedIndex(Listnames) → Indexnames
  4. Intersect(xAxis, yAxis) → A
  5. Circle(A, 1) → unitcircle
  6. Intersect(unitcircle, xAxis, 1) → B
  7. OrthogonalLine(B, xAxis) → f
  8. Intersect(unitcircle, yAxis, 2) → C
  9. OrthogonalLine(C, yAxis) → g
  10. Intersect(unitcircle, yAxis, 1) → D
  11. Intersect(unitcircle, xAxis, 2) → E
  12. OrthogonalLine(E, xAxis) → h
  13. OrthogonalLine(D, f) → i
  14. Intersect(f, g) → F
  15. Intersect(g, h) → G
  16. Intersect(h, i) → H
  17. Intersect(f, i) → I
  18. Polygon(I, H, G, F) → poly1, i_1, h_1, g_1, f_1
  19. Point(poly1) → P
  20. Element(ListMatrix, Indexnames) → T
  21. Vector((0, 0), P') → u
  22. Vector(TP) → Tu
  23. Determinant(T) → det
  24. ApplyMatrix(Tanimated, I) → I'
  25. ApplyMatrix(Tanimated, H) → H'
  26. ApplyMatrix(Tanimated, G) → G'
  27. ApplyMatrix(Tanimated, F) → F'
  28. Polygon(I', H', G', F') → poly1', i'_1, h'_1, g'_1, f'_1
  29. ApplyMatrix(Tanimated, pic1) → pic1'
  30. ApplyMatrix(T, pic1) → pic1'_1
  31. Element(ListMatrixtext, Indexnames) → Ttext
  32. Flatten(T) → list1
  33. ApplyMatrix(T, I) → I'_1
  34. ApplyMatrix(T, H) → H'_1
  35. ApplyMatrix(T, G) → G'_1
  36. ApplyMatrix(T, F) → F'_1
  37. Polygon(I'_1, H'_1, G'_1, F'_1) → poly1'_1, i'_2, h'_2, g'_2, f'_2
  38. Element(list1, 1) → a
  39. Element(list1, 2) → b
  40. Element(list1, 3) → c
  41. Element(list1, 4) → d
  42. Textfield(scaling) → InputBox1
  43. Textfield(k) → InputBox2
  44. Textfield(θ) → InputBox3
  45. Textfield(m) → InputBox4