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Astana National Library Model

Astana National Library Model
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2015-07-30 19:08
FunctionCoordinate GeometryGeometric Construction
In collections surface 3D surface 3D My 3D Collection
This example demonstrates the appearance model of the Astana National Library. It involves concepts from architecture and coordinate geometry. Using GeoGebra commands such as CurveCartesian, Surface, Sequence, Segment, and Point, the appearance of the building can be constructed. Suitable for architecture and coordinate geometry learners.

GeoGebra Commands & Parameters

  1. CurveCartesian(((1 - ((c * 3 / 4) * cos((u * 3 / 4)))) * cos(u)), ((1 - ((c * 3 / 4) * cos((u * 3 / 4)))) * sin(u)), (((-c) * 3 / 4) * sin((u * 3 / 4))), u, 0, 25.132741228718345) → cc
  2. CurveCartesian(((1 + ((c * 3 / 4) * cos((u * 3 / 4)))) * cos(u)), ((1 + ((c * 3 / 4) * cos((u * 3 / 4)))) * sin(u)), ((c * 3 / 4) * sin((u * 3 / 4))), u, 0, 25.132741228718345) → ccc
  3. Surface((((1 - ((c * 3 / 4) * cos((u * 3 / 4)))) * cos(u)) * (1 - v)) + ((v * (1 + ((c * 3 / 4) * cos(((u + (2 * π)) * 3 / 4))))) * cos(u + (2 * π))), (((1 - ((c * 3 / 4) * cos((u * 3 / 4)))) * sin(u)) * (1 - v)) + ((v * (1 + ((c * 3 / 4) * cos(((u + (2 * π)) * 3 / 4))))) * sin(u + (2 * π))), ((((-c) * 3 / 4) * sin((u * 3 / 4))) * (1 - v)) + (((v * c) * 3 / 4) * sin(((u + (2 * π)) * 3 / 4))), u, 0, tmax, v, 0, 1) → s
  4. Surface((((1 - ((c * 3 / 4) * cos((u * 3 / 4)))) * cos(u)) * (1 - v)) + ((v * (1 + ((c * 3 / 4) * cos(((u + (2 * π)) * 3 / 4))))) * cos(u + (2 * π))), (((1 - ((c * 3 / 4) * cos((u * 3 / 4)))) * sin(u)) * (1 - v)) + ((v * (1 + ((c * 3 / 4) * cos(((u + (2 * π)) * 3 / 4))))) * sin(u + (2 * π))), ((((-c) * 3 / 4) * sin((u * 3 / 4))) * (1 - v)) + (((v * c) * 3 / 4) * sin(((u + (2 * π)) * 3 / 4))), u, 0, (d * 6.28319), v, 0, 1) → s1
  5. Surface((((1 - ((c * 3 / 4) * cos((u * 3 / 4)))) * cos(u)) * (1 - v)) + ((v * (1 + ((c * 3 / 4) * cos(((u + (2 * π)) * 3 / 4))))) * cos(u + (2 * π))), (((1 - ((c * 3 / 4) * cos((u * 3 / 4)))) * sin(u)) * (1 - v)) + ((v * (1 + ((c * 3 / 4) * cos(((u + (2 * π)) * 3 / 4))))) * sin(u + (2 * π))), ((((-c) * 3 / 4) * sin((u * 3 / 4))) * (1 - v)) + (((v * c) * 3 / 4) * sin(((u + (2 * π)) * 3 / 4))), u, 6.28319, (2 * π) + ((d * 2) * π), v, 0, 1) → s2
  6. Surface((((1 - ((c * 3 / 4) * cos((u * 3 / 4)))) * cos(u)) * (1 - v)) + ((v * (1 + ((c * 3 / 4) * cos(((u + (2 * π)) * 3 / 4))))) * cos(u + (2 * π))), (((1 - ((c * 3 / 4) * cos((u * 3 / 4)))) * sin(u)) * (1 - v)) + ((v * (1 + ((c * 3 / 4) * cos(((u + (2 * π)) * 3 / 4))))) * sin(u + (2 * π))), ((((-c) * 3 / 4) * sin((u * 3 / 4))) * (1 - v)) + (((v * c) * 3 / 4) * sin(((u + (2 * π)) * 3 / 4))), u, 12.56637, (4 * π) + ((d * 2) * π), v, 0, 1) → s3
  7. Surface((((1 - ((c * 3 / 4) * cos((u * 3 / 4)))) * cos(u)) * (1 - v)) + ((v * (1 + ((c * 3 / 4) * cos(((u + (2 * π)) * 3 / 4))))) * cos(u + (2 * π))), (((1 - ((c * 3 / 4) * cos((u * 3 / 4)))) * sin(u)) * (1 - v)) + ((v * (1 + ((c * 3 / 4) * cos(((u + (2 * π)) * 3 / 4))))) * sin(u + (2 * π))), ((((-c) * 3 / 4) * sin((u * 3 / 4))) * (1 - v)) + (((v * c) * 3 / 4) * sin(((u + (2 * π)) * 3 / 4))), u, 18.84956, (6 * π) + ((d * 2) * π), v, 0, 1) → s4
  8. Sequence(Segment[cc(i), ccc(i + (2 * π))], i, 0, tmax, (8 * π / n)) → liste1
  9. Segment(cc(tt), ccc(tt + (2 * π))) → i
  10. Point(Ray[A, A + (1, 0)]) → B

AI Drawing Prompt Reference

Create a futuristic architectural model with two symmetric spatial curves forming the building's outline: one curves inward, the other outward. Generate a continuous surface between these curves to create the facade, smoothly transitioning along the height. The surface is divided into several segments covering different angular ranges, giving a spiral upward form. Add a series of straight line segments connecting the inner and outer curves at regular intervals, serving as structural or decorative elements. Finally, place a point in front of the building as a reference location.
The prompt above was compiled from the original drawing commands and is for reference only.