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Anamorphic Images: Geometric Construction and Principles

Anamorphic Images: Geometric Construction and Principles
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2020-04-24 11:05
TrigonometryCoordinate GeometrySolid GeometryTransformationGeometric Construction
This GeoGebra example demonstrates how to construct anamorphic images, a visual art form where distorted projections appear normal from a specific viewpoint. The core mathematical concepts involve similar triangles, right triangles, the tangent function, coordinate geometry, and elements of solid geometry and linear optimization. The construction uses commands such as Point, PointIn, Polygon, Segment, OrthogonalLine, and Intersect, with objects including points A through O, Q, R, polygon poly1, and various segments and lines. It is suitable for high school and college students or math enthusiasts to explore projective geometry, similarity, and the application of functions in art.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(yAxis) → B
  3. PointIn(eq1) → C
  4. Point(yAxis) → D
  5. PointIn(eq1) → E
  6. PointIn(eq1) → F
  7. PointIn(eq1) → G
  8. PointIn(eq1) → H
  9. PointIn(eq1) → I
  10. PointIn(eq1) → J
  11. PointIn(eq1) → K
  12. PointIn(eq1) → L
  13. PointIn(eq1) → M
  14. PointIn(eq1) → N
  15. PointIn(eq1) → O
  16. PointIn(eq1) → Q
  17. PointIn(eq1) → R
  18. Polygon(B, C, L, M, N, O, R, Q, A, D, E, F, G, H, I, J, K) → poly1, b, k, l, m, n, o, r, q, a, c, d, e, f, g, h, i, j
  19. Polygon(A, J_1, B_1, A_1, Z, E, D, U, B, K_1, I_1, H_1, G_1, F_1, E_1, D_1, C_1) → poly2, a_1, c_1, b_1, p, z_1, e_2, d_2, u, b_2, j_1, k_1, i_1, h_1, g_1, f_1, e_1, d_1
  20. Segment(P, F_1) → s
  21. Segment(P, E_1) → t
  22. Segment(P, D_1) → l_1
  23. Segment(P, C_1) → m_1
  24. Segment(P, B_1) → n_1
  25. Segment(P, A_1) → p_1
  26. Segment(P, Z) → q_1
  27. Segment(P, E) → r_1
  28. Segment(P, D) → s_1
  29. Segment(P, U) → t_1
  30. Segment(P, G_1) → f_2
  31. Segment(P, H_1) → g_2
  32. Segment(P, I_1) → h_2
  33. Segment(P, K_1) → i_2
  34. Segment(P, J_1) → j_2
  35. Segment(B, P) → k_2
  36. Segment(P, A) → l_2
  37. Polygon(A, C_2, S_1, R_1, Q_1, E, D, N_1, B, D_2, B_2, A_2, Z_1, W_1, V_1, U_1, T_1) → poly3, m_2, f_3, g_3, h_3, i_3, j_3, k_3, l_3, m_3, n_2, p_2, q_2, r_2, s_2, t_2, a_2, c_2
  38. OrthogonalLine(P, p_3) → n_3
  39. Intersect(n_3, p_3) → E_2
  40. Segment(P, E_2) → q_3

AI Drawing Prompt Reference

Create an anamorphic image that appears normal from a specific viewpoint. Start by creating points A and B on the y-axis, then create points C to O using a given equation. Construct a polygon poly1 with these points. Next, create another polygon poly2 that partially overlaps with poly1. From point P, draw segments to each vertex of poly2, then construct lines perpendicular to these segments and find their intersection point E2. Finally, connect P and E2.
The prompt above was compiled from the original drawing commands and is for reference only.