MathPlotAI Logo MathPlotAI

Central Projection of a Cube

Central Projection of a Cube
Loading the math board and drawing, please wait…
2014-11-07 18:57
Solid GeometryTransformationGeometric Construction
In collections Selected Examples
This example demonstrates the central projection of a cube onto a vertical image plane, illustrating the 3D-to-2D transformation process in central projection. Key math concepts include central projection, solid geometry, spatial transformation, and projection transformation. The construction utilizes GeoGebra commands and objects such as Plane, PointIn, Intersect, Point, Cube, Ray, OrthogonalPlane, Segment, Line, and IntersectPath. It is suitable for high school and above students studying solid geometry, spatial visualization, and projection transformations, as well as for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Plane(O, xOyPlane) → π_1
  2. PointIn(π_1) → P
  3. Intersect(zAxis, yAxis) → A
  4. Point(xAxis) → B
  5. Cube(A, B, xOyPlane) → a, C, FlächeBCGF, FlächeCDHG, FlächeEFGH, KanteAD, KanteAB, KanteBC, KanteCD, KanteAE, KanteDH, KanteEH, D, KanteEF, KanteBF, KanteFG, KanteCG, KanteGH, E, F, G, H, FlächeABCD, FlächeADHE, FlächeABFE
  6. Ray(O, P) → b
  7. OrthogonalPlane(P, b) → ε
  8. Ray(O, A) → e
  9. Ray(O, B) → f
  10. Ray(O, C) → g
  11. Ray(O, D) → h_1
  12. Ray(O, E) → i
  13. Ray(O, F) → j
  14. Ray(O, G) → k
  15. Ray(O, H) → l
  16. Intersect(e, ε) → A'
  17. Intersect(f, ε) → B'
  18. Intersect(g, ε) → C'
  19. Intersect(h_1, ε) → D'
  20. Intersect(i, ε) → E'
  21. Intersect(j, ε) → F'
  22. Intersect(l, ε) → H'
  23. Segment(A', B') → c
  24. Segment(B', C') → d
  25. Segment(C', D') → m
  26. Segment(D', A') → n
  27. Segment(A', E') → p
  28. Segment(B', F') → q
  29. Intersect(k, ε) → G'
  30. Segment(C', G') → r
  31. Segment(D', H') → s
  32. Segment(E', F') → t
  33. Segment(F', G') → a_1
  34. Segment(G', H') → b_1
  35. Segment(H', E') → c_1
  36. Line(G', F') → d_1
  37. Line(C', B') → e_1
  38. Intersect(e_1, d_1) → I
  39. IntersectPath(ε, π_1) → h
  40. Line(O, KanteAB) → f_1
  41. Line(O, KanteAD) → g_1
  42. Line(E', F') → i_1
  43. Line(A', B') → j_1
  44. Intersect(j_1, i_1) → J