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3D Vector and Surface Drawing

3D Vector and Surface Drawing
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2020-10-24 19:18
VectorSolid GeometryCalculus
This example demonstrates how to use GeoGebra to draw 3D vectors and surfaces. Key mathematical concepts include vectors, surface drawing, and curve fitting. Using commands like Surface, Line, Join, and Sequence, 3D space vectors and surfaces can be constructed. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Surface(x(O) + ((R + (r * cos(i + t))) * cos(k)), y(O) + ((R + (r * cos(i + t))) * sin(k)), z(O) + (r * sin(i + t)), k, 0, (2 * π), i, 0, 6.28319) → d
  2. Line(A, yAxis) → f
  3. Join(Sequence[Sequence[(x(O) + ((R + (r * cos(i + t))) * cos(k)), y(O) + ((R + (r * cos(i + t))) * sin(k)), z(O) + (r * sin(i + t))), k, 0, (2 * π)], i, 0, 6.28319, (2 * π / n)]) → l2
  4. Sequence(CurveCartesian[x(O) + ((R + (r * cos(i + t))) * cos(k)), y(O) + ((R + (r * cos(i + t))) * sin(k)), z(O) + (r * sin(i + t)), k, 0, (2 * π)], i, 0, 6.28319, (2 * π / n)) → l1
  5. Sequence(Segment[Element[l2, i], Element[l2, i + k]], i, 1, Length[l2]) → l3

AI Drawing Prompt Reference

Draw a 3D torus-like surface in space, formed by rotating a circular ring around an axis. The surface is covered with a grid of curves: multiple circular loops spaced evenly along the ring's circumference, and additional connecting segments between adjacent loops to create a mesh. Include a straight vertical line nearby as a reference axis. The result should show a clear three-dimensional ring shape with visible grid lines.
The prompt above was compiled from the original drawing commands and is for reference only.