R² 平面线性变换与矩阵作图交互演示

GeoGebra 命令及参数

1. Point(yAxis) → B
2. Polygon(A, B, C, E) → q1, a, b, c, e
3. ApplyMatrix(S_x, f) → HorizScaledFunc
4. ApplyMatrix(S_y, f) → VertScaledFunc
5. ApplyMatrix(D, f) → DilatedFunc
6. ApplyMatrix(Sh_x, f) → HorizShearFunc
7. SelectedIndex(M) → m
8. ApplyMatrix(Sh_y, f) → VertShearFunc
9. ApplyMatrix(Ref_l, f) → ReflFunc
10. SelectedIndex(L) → l
11. ApplyMatrix(R_θ, f) → RotatedFunc
12. ApplyMatrix(R_θ, E) → E'
13. ApplyMatrix(P, f) → ProjFunc
14. Textfield(f) → InputBox1
15. If(l ≟ 1, R_θ, l ≟ 6, Sh_y, l ≟ 7, Ref_l, l ≟ 8, P, l ≟ 2, S_x, l ≟ 3, S_y, l ≟ 4, D, l ≟ 5, Sh_x) → M_1
16. Circle(F, G) → CircleOffOrigin
17. ApplyMatrix(R_θ, CircleOffOrigin) → RotatedCircleOffOrigin
18. ApplyMatrix(S_x, CircleOffOrigin) → HorixScaledCirlceOffOrigin
19. ApplyMatrix(S_y, CircleOffOrigin) → VertScaledCircleOffOrigin
20. ApplyMatrix(D, CircleOffOrigin) → DilatedCircleOffOrigin
21. ApplyMatrix(Sh_x, CircleOffOrigin) → HorizShearCircleOffOrigin
22. ApplyMatrix(Sh_y, CircleOffOrigin) → VertShearOffOrigin
23. ApplyMatrix(Ref_l, CircleOffOrigin) → ReflCircleOffOrigin
24. Point(g) → H
25. Circle((0, 0), 1) → UnitCircle
26. ApplyMatrix(Ref_l, A) → A'_{10}
27. ApplyMatrix(Ref_l, B) → B'_{10}
28. ApplyMatrix(Ref_l, C) → C'_{10}
29. ApplyMatrix(Ref_l, E) → E'_{10}
30. Polygon(A'_{10}, B'_{10}, C'_{10}, E'_{10}) → ReflSquare, a'_{10}, b'_{10}, c'_{10}, e'_{10}
31. ApplyMatrix(R_θ, A) → A'_{11}
32. ApplyMatrix(R_θ, B) → B'_{11}
33. ApplyMatrix(R_θ, C) → C'_{11}
34. ApplyMatrix(R_θ, E) → E'_{11}
35. Polygon(A'_{11}, B'_{11}, C'_{11}, E'_{11}) → RotSquare, a'_{11}, b'_{11}, c'_{11}, e'_{11}
36. ApplyMatrix(S_x, A) → A'_{12}
37. ApplyMatrix(S_x, B) → B'_{12}
38. ApplyMatrix(S_x, C) → C'_{12}
39. ApplyMatrix(S_x, E) → E'_{12}
40. Polygon(A'_{12}, B'_{12}, C'_{12}, E'_{12}) → HorizScaledSquare, a'_{12}, b'_{12}, c'_{12}, e'_{12}
41. ApplyMatrix(S_x, A) → A'
42. ApplyMatrix(S_x, B) → B'
43. ApplyMatrix(S_x, C) → C'
44. ApplyMatrix(S_x, E) → E'_1
45. ApplyMatrix(S_y, A) → A'_1
46. ApplyMatrix(S_y, B) → B'_1
47. ApplyMatrix(S_y, C) → C'_1
48. ApplyMatrix(S_y, E) → E'_2
49. Polygon(A'_1, B'_1, C'_1, E'_2) → VertScaledSquare, a'_1, b'_1, c'_1, e'_2
50. ApplyMatrix(D, A) → A'_2
51. ApplyMatrix(D, B) → B'_2
52. ApplyMatrix(D, C) → C'_2
53. ApplyMatrix(D, E) → E'_3
54. ApplyMatrix(D, A) → A'_3
55. ApplyMatrix(D, B) → B'_3
56. ApplyMatrix(D, C) → C'_3
57. ApplyMatrix(D, E) → E'_4
58. Polygon(A'_3, B'_3, C'_3, E'_4) → DilatedSquare, a'_3, b'_3, c'_3, e'_4
59. ApplyMatrix(Sh_x, A) → A'_4
60. ApplyMatrix(Sh_x, B) → B'_4
61. ApplyMatrix(Sh_x, C) → C'_4
62. ApplyMatrix(Sh_x, E) → E'_5
63. Polygon(A'_4, B'_4, C'_4, E'_5) → HorizShearSquare, a'_4, b'_4, c'_4, e'_5
64. ApplyMatrix(Sh_y, A) → A'_5
65. ApplyMatrix(Sh_y, B) → B'_5
66. ApplyMatrix(Sh_y, C) → C'_5
67. ApplyMatrix(Sh_y, E) → E'_6
68. Polygon(A'_5, B'_5, C'_5, E'_6) → VertShearSquare, a'_5, b'_5, c'_5, e'_6
69. ApplyMatrix(P, A) → A'_6
70. ApplyMatrix(P, B) → B'_6
71. ApplyMatrix(P, C) → C'_6
72. ApplyMatrix(P, E) → E'_7
73. ApplyMatrix(P, A) → projA
74. ApplyMatrix(P, B) → projB
75. ApplyMatrix(P, C) → projC
76. ApplyMatrix(P, E) → projE
77. Spline({projA, projB, projC, projE}, 3) → ProjSquare
78. ApplyMatrix(R_θ, UnitCircle) → RotUnitCircle
79. ApplyMatrix(S_x, UnitCircle) → HorxShearUnitCircle
80. ApplyMatrix(S_y, UnitCircle) → VertShearUnitCircle_1
81. ApplyMatrix(D, UnitCircle) → DilateUnitCircle
82. ApplyMatrix(Sh_x, UnitCircle) → HorizShearUnitCircle
83. ApplyMatrix(Sh_y, UnitCircle) → VertShearUnitCircle
84. ApplyMatrix(Ref_l, UnitCircle) → ReflUnitCircle
85. Intersect(UnitCircle, g) → I, J
86. Segment(I, J) → ProjUnitCircle
87. Center(CircleOffOrigin) → K
88. Line(K, g) → h
89. Intersect(CircleOffOrigin, h) → N, O
90. OrthogonalLine(O, g) → i
91. OrthogonalLine(N, g) → j
92. Intersect(i, g) → Q
93. Intersect(g, h) → R
94. Intersect(j, g) → S
95. Segment(S, Q) → PorjCircleOffOrigin