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2D Affine Transformations

2D Affine Transformations
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2017-07-21 01:10
PolygonVectorCoordinate GeometryTransformation
In collections Mathematics of Computer Graphics
This example demonstrates affine transformations in 2D space and their effects on polygons. It involves core math concepts like affine transformations, polygon transformations, coordinate geometry, and vector operations. Constructed using GeoGebra commands: Reverse, Segment, TableText, Textfield, Polygon. Suitable for high school and above mathematics education to understand and apply properties of affine transformations.

GeoGebra Commands & Parameters

  1. Reverse(H) → K
  2. Segment(A, D) → c
  3. Segment(D, C) → d
  4. Segment(C, B) → e
  5. Segment(B, A) → f
  6. Segment(A_1, D_1) → g
  7. Segment(D_1, C_1) → h
  8. Segment(C_1, B_1) → i
  9. Segment(B_1, A_1) → j
  10. Reverse(W) → W2
  11. TableText({W2}, "h") → text1
  12. Textfield(θ_1) → InputBox1
  13. Textfield(θ_2) → InputBox2
  14. Textfield(sx) → InputBox3
  15. Textfield(sy) → InputBox4
  16. Textfield(a_1) → InputBox5
  17. Textfield(b_1) → InputBox6
  18. Textfield(a_2) → InputBox7
  19. Textfield(b_2) → InputBox8
  20. Polygon(A, B, C, D) → P, a, b, c_1, d_1
  21. Polygon(A_1, B_1, C_1, D_1) → P', a_3, b_3, c_2, d_2
  22. Polygon(A_2, B_2, C_2, D_2) → P_2, a_4, b_4, c_3, d_3