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3D Pinhole Camera Visualization

3D Pinhole Camera Visualization
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2019-06-09 18:40
Solid GeometryTransformationGeometric ConstructionSlider Animation
This GeoGebra example presents an interactive 3D pinhole camera model that can be rotated to explore the geometric principles behind pinhole imaging. It demonstrates how light rays from an object pass through a small hole and project onto an image plane, forming an inverted image. The core mathematical concepts involve similar triangles, perspective projection, intersections of lines and planes, and spatial geometry. The construction uses commands such as Segment, Point, OrthogonalLine, Line, Polygon, Prism, Intersect, Sphere, IntersectPath, and Circle to build the camera body, object, and image plane. Adjustable parameters like CamDepth, CamX, and CamY allow dynamic manipulation of the camera position and depth, making it easy to observe how image size and orientation change. This resource is suitable for high school and university students studying solid geometry, similarity, optics, or introductory computer graphics.

GeoGebra Commands & Parameters

  1. Segment(C, D) → g
  2. Point(g) → V
  3. OrthogonalLine(V, g, xOyPlane) → g_1
  4. Point(g_1) → W
  5. OrthogonalLine(W, h_1) → i_1
  6. Point(i_1) → Z
  7. Line(B, P) → j
  8. Polygon(Fr1, Fr4, Fr3, Fr2) → q1, fr1, fr4, fr3, fr2
  9. OrthogonalLine(Z, q1) → r_1
  10. Prism(q1, (-CamDepth)) → b, H, edge1, edge2, edge3, edge4, edge5, edge6, edge7, edge8, I, J, K, face1, face2, face3, face4, face5
  11. Intersect(r_1, p) → I_1
  12. Intersect(j, p) → S
  13. Sphere(B, 1.5) → a
  14. Segment(A, B) → f
  15. Point(f) → E
  16. Segment(F, E) → h
  17. Segment(E, G) → i
  18. Line(A, P) → k
  19. Line(E, P) → l
  20. Line(G, P) → m
  21. Line(F, P) → n
  22. Line(C, P) → q
  23. Line(D, P) → r
  24. Intersect(r, p) → L
  25. Intersect(q, p) → M
  26. Intersect(n, p) → N
  27. Intersect(m, p) → O
  28. Intersect(l, p) → Q
  29. Intersect(k, p) → R
  30. Intersect(f, a) → T,
  31. Line(T, P) → s
  32. Intersect(s, p) → U
  33. Segment(M, L) → t
  34. Segment(R, S) → d
  35. Segment(Q, O) → e
  36. Segment(Q, N) → f_1
  37. Line(T, P) → j_1
  38. Intersect(j_1, p) → A_1
  39. Sphere(S, A_1) → c
  40. Segment(B, S) → k_1
  41. Segment(V, R) → l_1
  42. Segment(F, N) → n_1
  43. Segment(G, O) → p_1
  44. IntersectPath(p, c) → c_1
  45. Circle(SSSS, AA) → s_1
  46. Segment(RR, AA) → t_1
  47. Segment(MM, LL) → a_1
  48. Segment(NNNN, QQ) → b_1
  49. Segment(QQ, OO) → f_2

AI Drawing Prompt Reference

Draw a 3D pinhole camera model with the camera body, object, and image plane. Start by constructing the camera body, then place the object and determine the image plane's position. Adjust the camera's depth and position to observe changes in image size and orientation.
The prompt above was compiled from the original drawing commands and is for reference only.