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Central Projection 3D Demo

Central Projection 3D Demo
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2017-11-02 22:59
VectorTrigonometrySolid GeometryParametric EquationGeometric Construction
This example demonstrates central projection in 3D space, showing the interaction between light source, objects, and projection plane. It involves core math concepts like 3D vectors, geometric transformations, solid geometry, rotation, and integer arithmetic. Construction uses commands such as Sequence, Vector, Cube, Line, Intersect, OrthogonalLine, and Sphere. Suitable for high school students and math enthusiasts studying solid geometry and spatial transformations.

GeoGebra Commands & Parameters

  1. Sequence(Line[(0, k, 0), (0, k, 1)], k, -15, 15, Gitterkonstante) → L_2
  2. Sequence(Line[(0, 0, k), (0, 1, k)], k, -10, 10, Gitterkonstante) → L_3
  3. Vector(O, E_1) → u
  4. Vector(O, E_2) → v
  5. Vector(O, E_3) → w
  6. Cube(O, A, B) → a, C, FlächeBCGF, FlächeDEFG, KanteCO, KanteAO, KanteAB, KanteBC, KanteDO, KanteCG, KanteDG, KanteDE, D, KanteAE, KanteEF, KanteBF, KanteFG, E, F, G, FlächeABCO, FlächeCGDO, FlächeAEDO, FlächeABFE
  7. Line(D, B) → f_1
  8. Line(G, A) → g
  9. Intersect(g, f_1) → M
  10. OrthogonalLine(M, FlächeABCO) → f
  11. Intersect(f, FlächeABCO) → H
  12. Sphere(M, H) → b

AI Drawing Prompt Reference

Demonstrate central projection in 3D by drawing a cube with grid lines, a light source at one corner of the cube, and three lines from the source to the cube's vertices. Show the intersection of the cube with a projection plane, draw a perpendicular line from the intersection point to the cube's surface, and create a sphere centered on this line to illustrate the interaction between light, objects, and the projection plane.
The prompt above was compiled from the original drawing commands and is for reference only.