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Quadric Best Fit Through 9 Points

Quadric Best Fit Through 9 Points
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2019-04-08 16:39
VectorCoordinate GeometrySolid GeometryMatrixOptimization
This example demonstrates the process of fitting a quadric surface through nine points. It involves core mathematical concepts such as 3D vectors, matrix operations, Singular Value Decomposition (SVD), and optimization. GeoGebra commands and objects used include Point, Sequence, Transpose, SVD, Element, Invert, and Distance. Suitable for high school students and researchers in mathematics and data analysis.

GeoGebra Commands & Parameters

  1. Point(Line[(0, 0, 0), (0, 0, 1)]) → A
  2. Point(Line[(0, 1, 0), (0, 1, 1)]) → I
  3. Point(Line[(0, -1, 0), (0, -1, 1)]) → H
  4. Point(Line[(-1, -1, 0), (-1, -1, 1)]) → G
  5. Point(Line[(-1, 0, 0), (-1, 0, 1)]) → B
  6. Point(Line[(1, 0, 0), (1, 0, 1)]) → C
  7. Point(Line[(1, -1, 0), (1, -1, 1)]) → D
  8. Point(Line[(1, 1, 0), (1, 1, 1)]) → E
  9. Point(Line[(-1, 1, 0), (-1, 1, 1)]) → F
  10. Sequence({z(Element[l1, i])}, i, 1, Length[l1]) → m2
  11. Sequence(1, i, 1, Length[l1]) → M_1
  12. Transpose(m1) → M_A
  13. SVD(M_A) → l2
  14. Element(l2, 1) → U
  15. Element(l2, 2) → W
  16. Element(l2, 3) → V
  17. Invert(W) → W_{-1}
  18. Transpose(U) → U_T
  19. Distance(I, F) → IF