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Surface through 4 Points in Space

Surface through 4 Points in Space
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2018-08-09 23:21
FunctionCoordinate GeometrySolid Geometry
In collections surface 3D /3D-Oberflächen 1
This example demonstrates how to construct a surface through four points in space. Key mathematical concepts include methods of surface construction in coordinate geometry. Construction highlights include using the Segment command to connect points, the Sequence command to generate a series of segments, and the Surface command to construct the surface. Suitable for high school mathematics education and learning solid geometry.

GeoGebra Commands & Parameters

  1. Segment(B, C) → f
  2. Segment(C, D) → g
  3. Segment(D, A) → h
  4. Segment(A, B) → i
  5. Sequence(A + (k * (B - A) / n), k, 1, n - 1) → L_1
  6. Sequence(B + (k * (C - B) / n), k, 1, n - 1) → L_2
  7. Sequence(D + (k * (C - D) / n), k, 1, n - 1) → L_3
  8. Sequence(Segment[L_1(k), L_3(k)], k, 1, n - 1) → L_5
  9. Sequence(A + (k * (D - A) / n), k, 1, n - 1) → L_4
  10. Sequence(Segment[L_2(k), L_4(k)], k, 1, n - 1) → L_6
  11. Sequence(Sequence[Intersect[L_5(j), L_6(k)], j, 1, n], k, 1, n) → L_7
  12. Surface(x(A) + (u * (x(D) - x(A))) + (v * (x(B) - x(A) + (u * (x(A) - x(B) + x(C) - x(D))))), y(A) + (u * (y(D) - y(A))) + (v * (y(B) - y(A) + (u * (y(A) - y(B) + y(C) - y(D))))), z(A) + (u * (z(D) - z(A))) + (v * (z(B) - z(A) + (u * (z(A) - z(B) + z(C) - z(D))))), u, 0, 1, v, 0, 1) → F