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Diamond Shape 3D Geometry Demo

Diamond Shape 3D Geometry Demo
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2015-08-10 23:12
VectorSolid GeometryParametric EquationGeometric ConstructionSlider Animation
This example dynamically constructs a diamond-shaped 3D solid, demonstrating the process of building three-dimensional geometric shapes. It involves core math concepts like solid geometry, vector operations, parametric equations, and geometric transformations. Key GeoGebra commands and objects used include Sequence, Translate, Rotate, Intersect, Polygon, Angle, Point, Segment, and Vector. Suitable for high school and above students learning 3D geometry and vector transformations.

GeoGebra Commands & Parameters

  1. Sequence(((di / 2 * cos(i)), (di / 2 * sin(i))), i, 0, 6.28319, 0.7854) → liste2
  2. Sequence(Plane[Col, Element[liste2, i], Rotate[(0, 0, 0), 90*°, Line[Element[liste2, i], zAxis]]], i, 1, 9) → liste15
  3. Sequence(IntersectPath[Element[liste15, i], Element[liste15, i + 1]], i, 1, 8) → liste16
  4. Sequence(((ta / 2 * cos(i)), (ta / 2 * sin(i)), co), i, 0, 6.28319, 0.7854) → liste1
  5. Sequence(Plane[Element[liste1, i], Element[liste2, i], Rotate[(0, 0, 0), 90*°, Line[Element[liste2, i], zAxis]]], i, 1, 9) → liste3
  6. Sequence(IntersectPath[Element[liste3, i], Element[liste3, i + 1]], i, 1, 8) → liste4
  7. Sequence(Intersect[Plane[(0, 0, dco), Plane[xAxis, yAxis]], Element[liste4, i]], i, 1, 8) → liste5
  8. Translate(Polygon[Sequence[(x(Element[liste1, i]), y(Element[liste1, i])), i, 1, 8]], Vector[(0, 0, co)]) → poly1
  9. Sequence(Polygon[Element[liste1, i], Element[liste1, i + 1], Element[liste5, i]], i, 1, 8) → liste6
  10. Sequence(Polygon[Element[liste1, i], Element[Append[liste5, Element[liste5, 1]], i], Element[liste2, i], Element[liste5, i - 1]], i, 2, 8) → liste8
  11. Rotate(Element[liste8, 1], -0.7853981633974483, zAxis) → poly2
  12. Sequence(((di / 2 * cos(i)), (di / 2 * sin(i))), i, 0.3927, 6.67589, 0.7854) → liste9
  13. Sequence(Polygon[Element[liste2, i], Element[liste9, i], Element[liste5, i]], i, 1, 8) → liste7
  14. Sequence(Intersect[Element[liste16, i], Plane[(0, 0, (-dcu)), Plane[xAxis, yAxis]]], i, 1, 8) → liste11
  15. Sequence(Polygon[Element[liste2, i + 1], Element[liste9, i], Element[liste5, i]], i, 1, 8) → liste10
  16. Sequence(Polygon[Element[liste2, i], Element[liste9, i], Element[liste11, i]], i, 1, 8) → liste12
  17. Sequence(Polygon[Element[liste2, i + 1], Element[liste9, i], Element[liste11, i]], i, 1, 8) → liste13
  18. Sequence(Polygon[Element[liste2, i + 1], Element[liste11, i], Col, Mirror[Element[liste11, i], Segment[Element[liste2, i + 1], Col]]], i, 1, 8) → liste14
  19. Intersect(Segment[A, B], y = dco) → D
  20. Intersect(Segment[A, C], y = (-dcu)) → E
  21. Polygon(A, B, B', A', C) → poly3, a, b, b', a', c
  22. Angle((0, 0), A', B') → α
  23. Angle(C, A', (0, 0)) → β
  24. Point(Ray[I_1, I_1 + (1, 0)]) → I_2
  25. Segment(A', A) → d
  26. Vector((di / 2 + cotes, 0), (di / 2 + cotes, co)) → vco1
  27. Vector((di / 2 + cotes, co), (di / 2 + cotes, 0)) → vco2
  28. Vector((di / 2 + cotes, 0), (di / 2 + cotes, (-cu))) → vcu1
  29. Vector((di / 2 + cotes, (-cu)), (di / 2 + cotes, 0)) → vcu2
  30. Vector((di / 2, co + (2 * cotes)), (((-di)) / 2, co + (2 * cotes))) → vd1
  31. Vector((((-di)) / 2, co + (2 * cotes)), (di / 2, co + (2 * cotes))) → vd2
  32. Vector((ta / 2, co + cotes), (((-ta)) / 2, co + cotes)) → vt1
  33. Vector((((-ta)) / 2, co + cotes), (ta / 2, co + cotes)) → vt2

AI Drawing Prompt Reference

Create a dynamically constructed 3D diamond solid to demonstrate the process of building three-dimensional geometric shapes. Generate two sets of circular point sequences, intersect them with planes to form the diamond base and sides, then combine vector transformations and geometric transformations to complete the solid diamond shape, suitable for students learning 3D geometry and vector transformations.
The prompt above was compiled from the original drawing commands and is for reference only.