MathPlotAI Logo MathPlotAI

Vector Field Visualization

Vector Field Visualization
Loading the math board and drawing, please wait…
2015-10-14 19:42
VectorFunctionCoordinate GeometryCalculusGraphing
This example demonstrates the graphical representation of 2D vector fields, showing direction and magnitude of vectors at different points through dynamic arrows. Core mathematical concepts include vector fields, two-dimensional space, gradient concepts in calculus, and function graphing. Construction highlights involve using Function, Sequence, and Textfield commands, with objects like yn, ymin, ymax, ys, xn, xmin, xmax, xs, v, vh, f, g, h, Vx, Vy, list1, lista1, lista2, inputBox1, inputBox2, xplus, yplus, text2. Suitable for university-level mathematics, physics, or engineering students to understand vector field properties and practical applications.

GeoGebra Commands & Parameters

  1. Function(x, 0, 1) → f
  2. Function(x^(3), 0, 1) → g
  3. Function(sin((x * π / 2)), 0, 1) → h
  4. Sequence(Sequence[Segment[(j, k) - ((Vx(j, k), Vy(j, k)) * v), (j, k) + ((Vx(j, k), Vy(j, k)) * v)], k, ymin, ymax, ys], j, xmin, xmax, xs) → list1
  5. Sequence(Sequence[Rotate[Segment[(j, k) + ((Vx(j, k), Vy(j, k)) * v) - ((Vx(j, k), Vy(j, k)) / sqrt(Vx(j, k)^(2) + Vy(j, k)^(2)) * vh), (j, k) + ((Vx(j, k), Vy(j, k)) * v)], 330*°, (j, k) + ((Vx(j, k), Vy(j, k)) * v)], k, ymin, ymax, ys], j, xmin, xmax, xs) → lista1
  6. Sequence(Sequence[Rotate[Segment[(j, k) + ((Vx(j, k), Vy(j, k)) * v) - ((Vx(j, k), Vy(j, k)) / sqrt(Vx(j, k)^(2) + Vy(j, k)^(2)) * vh), (j, k) + ((Vx(j, k), Vy(j, k)) * v)], 30*°, (j, k) + ((Vx(j, k), Vy(j, k)) * v)], k, ymin, ymax, ys], j, xmin, xmax, xs) → lista2
  7. Textfield(Vx) → inputBox1
  8. Textfield(Vy) → inputBox2

AI Drawing Prompt Reference

Visualize a 2D vector field with dynamic arrows showing direction and magnitude at various points, using three functions to generate x and y components of the vectors, adjusting parameter ranges and step sizes to control arrow distribution, and representing vector magnitudes with arrows of different lengths, with input boxes displaying the values of vector components.
The prompt above was compiled from the original drawing commands and is for reference only.