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Matrix to 3D Surface

Matrix to 3D Surface
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2018-01-14 22:38
SequenceSolid GeometryMatrixGraphing
This example demonstrates the conversion of matrix data into a 3D surface plot. Key math concepts include matrix operations, 3D space representation, and surface generation. Construction highlights involve using GeoGebra's Sequence command for sequence generation, Surface command for 3D plotting, and objects A-Z along with list objects like liste1-liste4. Suitable for high school and above students studying spatial geometry, data visualization, and matrix applications.

GeoGebra Commands & Parameters

  1. Sequence(Surface[(x((Element[LP, i] * (1 - v)) + (Element[LP, i + 5] * v)) * (1 - u)) + (x((Element[LP, i + 1] * (1 - v)) + (Element[LP, i + 6] * v)) * u), (y((Element[LP, i] * (1 - u)) + (Element[LP, i + 1] * u)) * (1 - v)) + (y((Element[LP, i + 5] * (1 - u)) + (Element[LP, i + 6] * u)) * v), ((z(Element[LP, i]) * (1 - u)) * (1 - v)) + ((z(Element[LP, i + 1]) * u) * (1 - v)) + ((z(Element[LP, i + 5]) * (1 - u)) * v) + ((z(Element[LP, i + 6]) * u) * v), u, 0, 1, v, 0, 1], i, 1, 4) → liste1
  2. Surface((x((Element[LP, 1] * (1 - v)) + (Element[LP, 6] * v)) * (1 - u)) + (x((Element[LP, 2] * (1 - v)) + (Element[LP, 7] * v)) * u), (y((Element[LP, 1] * (1 - u)) + (Element[LP, 2] * u)) * (1 - v)) + (y((Element[LP, 6] * (1 - u)) + (Element[LP, 7] * u)) * v), ((z(Element[LP, 1]) * (1 - u)) * (1 - v)) + ((z(Element[LP, 2]) * u) * (1 - v)) + ((z(Element[LP, 6]) * (1 - u)) * v) + ((z(Element[LP, 7]) * u) * v), u, 0, 1, v, 0, 1) → a
  3. Sequence(Surface[(x((Element[LP, i] * (1 - v)) + (Element[LP, i + 5] * v)) * (1 - u)) + (x((Element[LP, i + 1] * (1 - v)) + (Element[LP, i + 6] * v)) * u), (y((Element[LP, i] * (1 - u)) + (Element[LP, i + 1] * u)) * (1 - v)) + (y((Element[LP, i + 5] * (1 - u)) + (Element[LP, i + 6] * u)) * v), ((z(Element[LP, i]) * (1 - u)) * (1 - v)) + ((z(Element[LP, i + 1]) * u) * (1 - v)) + ((z(Element[LP, i + 5]) * (1 - u)) * v) + ((z(Element[LP, i + 6]) * u) * v), u, 0, 1, v, 0, 1], i, 6, 9) → liste2
  4. Sequence(Surface[(x((Element[LP, i] * (1 - v)) + (Element[LP, i + 5] * v)) * (1 - u)) + (x((Element[LP, i + 1] * (1 - v)) + (Element[LP, i + 6] * v)) * u), (y((Element[LP, i] * (1 - u)) + (Element[LP, i + 1] * u)) * (1 - v)) + (y((Element[LP, i + 5] * (1 - u)) + (Element[LP, i + 6] * u)) * v), ((z(Element[LP, i]) * (1 - u)) * (1 - v)) + ((z(Element[LP, i + 1]) * u) * (1 - v)) + ((z(Element[LP, i + 5]) * (1 - u)) * v) + ((z(Element[LP, i + 6]) * u) * v), u, 0, 1, v, 0, 1], i, 11, 14) → liste3
  5. Sequence(Surface[(x((Element[LP, i] * (1 - v)) + (Element[LP, i + 5] * v)) * (1 - u)) + (x((Element[LP, i + 1] * (1 - v)) + (Element[LP, i + 6] * v)) * u), (y((Element[LP, i] * (1 - u)) + (Element[LP, i + 1] * u)) * (1 - v)) + (y((Element[LP, i + 5] * (1 - u)) + (Element[LP, i + 6] * u)) * v), ((z(Element[LP, i]) * (1 - u)) * (1 - v)) + ((z(Element[LP, i + 1]) * u) * (1 - v)) + ((z(Element[LP, i + 5]) * (1 - u)) * v) + ((z(Element[LP, i + 6]) * u) * v), u, 0, 1, v, 0, 1], i, 16, 19) → liste4