MathPlotAI Logo MathPlotAI

3D Vector Fields Visualization

3D Vector Fields Visualization
Loading the math board and drawing, please wait…
2016-04-11 18:30
VectorSolid GeometryCalculusParametric EquationGraphing
This example demonstrates the distribution and variation phenomena of vector fields in 3D space. Core mathematical concepts include vectors, 3D coordinate systems, and vector fields in calculus. Construction highlights involve Geogebra commands/objects like Sequence, Textfield, Element, spacing, extent, grid, xcomp/ycomp/zcomp, scale, vectors, InputBoxes, text elements, parameters (a), axes, vector components (u_1-u_4), listvectordirection, Selectedvector, and buttons. Suitable for university students and teachers in mathematics, physics, and related fields for teaching demonstrations and conceptual understanding.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[Sequence[(i, j, k), i, (-extent), extent, spacing], j, (-extent), extent, spacing], k, (-extent), extent, spacing) → grid, {{{(-3, -3, -3), (-2, -3, -3), (-1, -3, -3), (0, -3, -3), (1, -3, -3), (2, -3, -3), (3, -3, -3)}, {(-3, -2, -3), (-2, -2, -3), (-1, -2, -3), (0, -2, -3), (1, -2, -3), (2, -2, -3), (3, -2, -3)}, {(-3, -1, -3), (-2, -1, -3), (-1, -1, -3), (0, -1, -3), (1, -1, -3), (2, -1, -3), (3, -1, -3)}, {(-3, 0, -3), (-2, 0, -3), (-1, 0, -3), (0, 0, -3), (1, 0, -3), (2, 0, -3), (3, 0, -3)}, {(-3, 1, -3), (-2, 1, -3), (-1, 1, -3), (0, 1, -3), (1, 1, -3), (2, 1, -3), (3, 1, -3)}, {(-3, 2, -3), (-2, 2, -3), (-1, 2, -3), (0, 2, -3), (1, 2, -3), (2, 2, -3), (3, 2, -3)}, {(-3, 3, -3), (-2, 3, -3), (-1, 3, -3), (0, 3, -3), (1, 3, -3), (2, 3, -3), (3, 3, -3)}}, {{(-3, -3, -2), (-2, -3, -2), (-1, -3, -2), (0, -3, -2), (1, -3, -2), (2, -3, -2), (3, -3, -2)}, {(-3, -2, -2), (-2, -2, -2), (-1, -2, -2), (0, -2, -2), (1, -2, -2), (2, -2, -2), (3, -2, -2)}, {(-3, -1, -2), (-2, -1, -2), (-1, -1, -2), (0, -1, -2), (1, -1, -2), (2, -1, -2), (3, -1, -2)}, {(-3, 0, -2), (-2, 0, -2), (-1, 0, -2), (0, 0, -2), (1, 0, -2), (2, 0, -2), (3, 0, -2)}, {(-3, 1, -2), (-2, 1, -2), (-1, 1, -2), (0, 1, -2), (1, 1, -2), (2, 1, -2), (3, 1, -2)}, {(-3, 2, -2), (-2, 2, -2), (-1, 2, -2), (0, 2, -2), (1, 2, -2), (2, 2, -2), (3, 2, -2)}, {(-3, 3, -2), (-2, 3, -2), (-1, 3, -2), (0, 3, -2), (1, 3, -2), (2, 3, -2), (3, 3, -2)}}, {{(-3, -3, -1), (-2, -3, -1), (-1, -3, -1), (0, -3, -1), (1, -3, -1), (2, -3, -1), (3, -3, -1)}, {(-3, -2, -1), (-2, -2, -1), (-1, -2, -1), (0, -2, -1), (1, -2, -1), (2, -2, -1), (3, -2, -1)}, {(-3, -1, -1), (-2, -1, -1), (-1, -1, -1), (0, -1, -1), (1, -1, -1), (2, -1, -1), (3, -1, -1)}, {(-3, 0, -1), (-2, 0, -1), (-1, 0, -1), (0, 0, -1), (1, 0, -1), (2, 0, -1), (3, 0, -1)}, {(-3, 1, -1), (-2, 1, -1), (-1, 1, -1), (0, 1, -1), (1, 1, -1), (2, 1, -1), (3, 1, -1)}, {(-3, 2, -1), (-2, 2, -1), (-1, 2, -1), (0, 2, -1), (1, 2, -1), (2, 2, -1), (3, 2, -1)}, {(-3, 3, -1), (-2, 3, -1), (-1, 3, -1), (0, 3, -1), (1, 3, -1), (2, 3, -1), (3, 3, -1)}}, {{(-3, -3, 0), (-2, -3, 0), (-1, -3, 0), (0, -3, 0), (1, -3, 0), (2, -3, 0), (3, -3, 0)}, {(-3, -2, 0), (-2, -2, 0), (-1, -2, 0), (0, -2, 0), (1, -2, 0), (2, -2, 0), (3, -2, 0)}, {(-3, -1, 0), (-2, -1, 0), (-1, -1, 0), (0, -1, 0), (1, -1, 0), (2, -1, 0), (3, -1, 0)}, {(-3, 0, 0), (-2, 0, 0), (-1, 0, 0), (0, 0, 0), (1, 0, 0), (2, 0, 0), (3, 0, 0)}, {(-3, 1, 0), (-2, 1, 0), (-1, 1, 0), (0, 1, 0), (1, 1, 0), (2, 1, 0), (3, 1, 0)}, {(-3, 2, 0), (-2, 2, 0), (-1, 2, 0), (0, 2, 0), (1, 2, 0), (2, 2, 0), (3, 2, 0)}, {(-3, 3, 0), (-2, 3, 0), (-1, 3, 0), (0, 3, 0), (1, 3, 0), (2, 3, 0), (3, 3, 0)}}, {{(-3, -3, 1), (-2, -3, 1), (-1, -3, 1), (0, -3, 1), (1, -3, 1), (2, -3, 1), (3, -3, 1)}, {(-3, -2, 1), (-2, -2, 1), (-1, -2, 1), (0, -2, 1), (1, -2, 1), (2, -2, 1), (3, -2, 1)}, {(-3, -1, 1), (-2, -1, 1), (-1, -1, 1), (0, -1, 1), (1, -1, 1), (2, -1, 1), (3, -1, 1)}, {(-3, 0, 1), (-2, 0, 1), (-1, 0, 1), (0, 0, 1), (1, 0, 1), (2, 0, 1), (3, 0, 1)}, {(-3, 1, 1), (-2, 1, 1), (-1, 1, 1), (0, 1, 1), (1, 1, 1), (2, 1, 1), (3, 1, 1)}, {(-3, 2, 1), (-2, 2, 1), (-1, 2, 1), (0, 2, 1), (1, 2, 1), (2, 2, 1), (3, 2, 1)}, {(-3, 3, 1), (-2, 3, 1), (-1, 3, 1), (0, 3, 1), (1, 3, 1), (2, 3, 1), (3, 3, 1)}}, {{(-3, -3, 2), (-2, -3, 2), (-1, -3, 2), (0, -3, 2), (1, -3, 2), (2, -3, 2), (3, -3, 2)}, {(-3, -2, 2), (-2, -2, 2), (-1, -2, 2), (0, -2, 2), (1, -2, 2), (2, -2, 2), (3, -2, 2)}, {(-3, -1, 2), (-2, -1, 2), (-1, -1, 2), (0, -1, 2), (1, -1, 2), (2, -1, 2), (3, -1, 2)}, {(-3, 0, 2), (-2, 0, 2), (-1, 0, 2), (0, 0, 2), (1, 0, 2), (2, 0, 2), (3, 0, 2)}, {(-3, 1, 2), (-2, 1, 2), (-1, 1, 2), (0, 1, 2), (1, 1, 2), (2, 1, 2), (3, 1, 2)}, {(-3, 2, 2), (-2, 2, 2), (-1, 2, 2), (0, 2, 2), (1, 2, 2), (2, 2, 2), (3, 2, 2)}, {(-3, 3, 2), (-2, 3, 2), (-1, 3, 2), (0, 3, 2), (1, 3, 2), (2, 3, 2), (3, 3, 2)}}, {{(-3, -3, 3), (-2, -3, 3), (-1, -3, 3), (0, -3, 3), (1, -3, 3), (2, -3, 3), (3, -3, 3)}, {(-3, -2, 3), (-2, -2, 3), (-1, -2, 3), (0, -2, 3), (1, -2, 3), (2, -2, 3), (3, -2, 3)}, {(-3, -1, 3), (-2, -1, 3), (-1, -1, 3), (0, -1, 3), (1, -1, 3), (2, -1, 3), (3, -1, 3)}, {(-3, 0, 3), (-2, 0, 3), (-1, 0, 3), (0, 0, 3), (1, 0, 3), (2, 0, 3), (3, 0, 3)}, {(-3, 1, 3), (-2, 1, 3), (-1, 1, 3), (0, 1, 3), (1, 1, 3), (2, 1, 3), (3, 1, 3)}, {(-3, 2, 3), (-2, 2, 3), (-1, 2, 3), (0, 2, 3), (1, 2, 3), (2, 2, 3), (3, 2, 3)}, {(-3, 3, 3), (-2, 3, 3), (-1, 3, 3), (0, 3, 3), (1, 3, 3), (2, 3, 3), (3, 3, 3)}}}
  2. Sequence(Sequence[Sequence[Vector[(i, j, k), (i, j, k) + (scale * (xcomp(i, j, k), ycomp(i, j, k), zcomp(i, j, k)))], i, (-extent), extent, spacing], j, (-extent), extent, spacing], k, (-extent), extent, spacing) → vectors, {{{(-0.10444444444444434, -0.10444444444444434, -0.10444444444444434), (-0.08545454545454545, -0.12818181818181795, -0.12818181818181795), (-0.049473684210526336, -0.148421052631579, -0.148421052631579), (0, -0.15666666666666673, -0.15666666666666673), (0.049473684210526336, -0.148421052631579, -0.148421052631579), (0.08545454545454545, -0.12818181818181795, -0.12818181818181795), (0.10444444444444434, -0.10444444444444434, -0.10444444444444434)}, {(-0.12818181818181795, -0.08545454545454545, -0.12818181818181795), (-0.11058823529411743, -0.11058823529411743, -0.1658823529411766), (-0.06714285714285717, -0.13428571428571434, -0.2014285714285715), (0, -0.1446153846153848, -0.21692307692307677), (0.06714285714285717, -0.13428571428571434, -0.2014285714285715), (0.11058823529411743, -0.11058823529411743, -0.1658823529411766), (0.12818181818181795, -0.08545454545454545, -0.12818181818181795)}, {(-0.148421052631579, -0.049473684210526336, -0.148421052631579), (-0.13428571428571434, -0.06714285714285717, -0.2014285714285715), (-0.08545454545454545, -0.08545454545454545, -0.25636363636363635), (0, -0.09400000000000008, -0.28200000000000003), (0.08545454545454545, -0.08545454545454545, -0.25636363636363635), (0.13428571428571434, -0.06714285714285717, -0.2014285714285715), (0.148421052631579, -0.049473684210526336, -0.148421052631579)}, {(-0.15666666666666673, 0, -0.15666666666666673), (-0.1446153846153848, 0, -0.21692307692307677), (-0.09400000000000008, 0, -0.28200000000000003), (0, 0, -0.31333333333333346), (0.09400000000000008, 0, -0.28200000000000003), (0.1446153846153848, 0, -0.21692307692307677), (0.15666666666666673, 0, -0.15666666666666673)}, {(-0.148421052631579, 0.049473684210526336, -0.148421052631579), (-0.13428571428571434, 0.06714285714285717, -0.2014285714285715), (-0.08545454545454545, 0.08545454545454545, -0.25636363636363635), (0, 0.09400000000000008, -0.28200000000000003), (0.08545454545454545, 0.08545454545454545, -0.25636363636363635), (0.13428571428571434, 0.06714285714285717, -0.2014285714285715), (0.148421052631579, 0.049473684210526336, -0.148421052631579)}, {(-0.12818181818181795, 0.08545454545454545, -0.12818181818181795), (-0.11058823529411743, 0.11058823529411743, -0.1658823529411766), (-0.06714285714285717, 0.13428571428571434, -0.2014285714285715), (0, 0.1446153846153848, -0.21692307692307677), (0.06714285714285717, 0.13428571428571434, -0.2014285714285715), (0.11058823529411743, 0.11058823529411743, -0.1658823529411766), (0.12818181818181795, 0.08545454545454545, -0.12818181818181795)}, {(-0.10444444444444434, 0.10444444444444434, -0.10444444444444434), (-0.08545454545454545, 0.12818181818181795, -0.12818181818181795), (-0.049473684210526336, 0.148421052631579, -0.148421052631579), (0, 0.15666666666666673, -0.15666666666666673), (0.049473684210526336, 0.148421052631579, -0.148421052631579), (0.08545454545454545, 0.12818181818181795, -0.12818181818181795), (0.10444444444444434, 0.10444444444444434, -0.10444444444444434)}}, {{(-0.12818181818181795, -0.12818181818181795, -0.08545454545454545), (-0.11058823529411743, -0.1658823529411766, -0.11058823529411743), (-0.06714285714285717, -0.2014285714285715, -0.13428571428571434), (0, -0.21692307692307677, -0.1446153846153848), (0.06714285714285717, -0.2014285714285715, -0.13428571428571434), (0.11058823529411743, -0.1658823529411766, -0.11058823529411743), (0.12818181818181795, -0.12818181818181795, -0.08545454545454545)}, {(-0.1658823529411766, -0.11058823529411743, -0.11058823529411743), (-0.15666666666666673, -0.15666666666666673, -0.15666666666666673), (-0.10444444444444434, -0.20888888888888868, -0.20888888888888868), (0, -0.23499999999999988, -0.23499999999999988), (0.10444444444444434, -0.20888888888888868, -0.20888888888888868), (0.15666666666666673, -0.15666666666666673, -0.15666666666666673), (0.1658823529411766, -0.11058823529411743, -0.11058823529411743)}, {(-0.2014285714285715, -0.06714285714285717, -0.13428571428571434), (-0.20888888888888868, -0.10444444444444434, -0.20888888888888868), (-0.15666666666666673, -0.15666666666666673, -0.31333333333333346), (0, -0.18799999999999994, -0.3759999999999999), (0.15666666666666673, -0.15666666666666673, -0.31333333333333346), (0.20888888888888868, -0.10444444444444434, -0.20888888888888868), (0.2014285714285715, -0.06714285714285717, -0.13428571428571434)}, {(-0.21692307692307677, 0, -0.1446153846153848), (-0.23499999999999988, 0, -0.23499999999999988), (-0.18799999999999994, 0, -0.3759999999999999), (0, 0, -0.4700000000000002), (0.18799999999999994, 0, -0.3759999999999999), (0.23499999999999988, 0, -0.23499999999999988), (0.21692307692307677, 0, -0.1446153846153848)}, {(-0.2014285714285715, 0.06714285714285717, -0.13428571428571434), (-0.20888888888888868, 0.10444444444444434, -0.20888888888888868), (-0.15666666666666673, 0.15666666666666673, -0.31333333333333346), (0, 0.18799999999999994, -0.3759999999999999), (0.15666666666666673, 0.15666666666666673, -0.31333333333333346), (0.20888888888888868, 0.10444444444444434, -0.20888888888888868), (0.2014285714285715, 0.06714285714285717, -0.13428571428571434)}, {(-0.1658823529411766, 0.11058823529411743, -0.11058823529411743), (-0.15666666666666673, 0.15666666666666673, -0.15666666666666673), (-0.10444444444444434, 0.20888888888888868, -0.20888888888888868), (0, 0.23499999999999988, -0.23499999999999988), (0.10444444444444434, 0.20888888888888868, -0.20888888888888868), (0.15666666666666673, 0.15666666666666673, -0.15666666666666673), (0.1658823529411766, 0.11058823529411743, -0.11058823529411743)}, {(-0.12818181818181795, 0.12818181818181795, -0.08545454545454545), (-0.11058823529411743, 0.1658823529411766, -0.11058823529411743), (-0.06714285714285717, 0.2014285714285715, -0.13428571428571434), (0, 0.21692307692307677, -0.1446153846153848), (0.06714285714285717, 0.2014285714285715, -0.13428571428571434), (0.11058823529411743, 0.1658823529411766, -0.11058823529411743), (0.12818181818181795, 0.12818181818181795, -0.08545454545454545)}}, {{(-0.148421052631579, -0.148421052631579, -0.049473684210526336), (-0.13428571428571434, -0.2014285714285715, -0.06714285714285717), (-0.08545454545454545, -0.25636363636363635, -0.08545454545454545), (0, -0.28200000000000003, -0.09400000000000008), (0.08545454545454545, -0.25636363636363635, -0.08545454545454545), (0.13428571428571434, -0.2014285714285715, -0.06714285714285717), (0.148421052631579, -0.148421052631579, -0.049473684210526336)}, {(-0.2014285714285715, -0.13428571428571434, -0.06714285714285717), (-0.20888888888888868, -0.20888888888888868, -0.10444444444444434), (-0.15666666666666673, -0.31333333333333346, -0.15666666666666673), (0, -0.3759999999999999, -0.18799999999999994), (0.15666666666666673, -0.31333333333333346, -0.15666666666666673), (0.20888888888888868, -0.20888888888888868, -0.10444444444444434), (0.2014285714285715, -0.13428571428571434, -0.06714285714285717)}, {(-0.25636363636363635, -0.08545454545454545, -0.08545454545454545), (-0.31333333333333346, -0.15666666666666673, -0.15666666666666673), (-0.31333333333333346, -0.31333333333333346, -0.31333333333333346), (0, -0.47, -0.47), (0.31333333333333346, -0.31333333333333346, -0.31333333333333346), (0.31333333333333346, -0.15666666666666673, -0.15666666666666673), (0.25636363636363635, -0.08545454545454545, -0.08545454545454545)}, {(-0.28200000000000003, 0, -0.09400000000000008), (-0.3759999999999999, 0, -0.18799999999999994), (-0.47, 0, -0.47), (0, 0, -0.94), (0.47, 0, -0.47), (0.3759999999999999, 0, -0.18799999999999994), (0.28200000000000003, 0, -0.09400000000000008)}, {(-0.25636363636363635, 0.08545454545454545, -0.08545454545454545), (-0.31333333333333346, 0.15666666666666673, -0.15666666666666673), (-0.31333333333333346, 0.31333333333333346, -0.31333333333333346), (0, 0.47, -0.47), (0.31333333333333346, 0.31333333333333346, -0.31333333333333346), (0.31333333333333346, 0.15666666666666673, -0.15666666666666673), (0.25636363636363635, 0.08545454545454545, -0.08545454545454545)}, {(-0.2014285714285715, 0.13428571428571434, -0.06714285714285717), (-0.20888888888888868, 0.20888888888888868, -0.10444444444444434), (-0.15666666666666673, 0.31333333333333346, -0.15666666666666673), (0, 0.3759999999999999, -0.18799999999999994), (0.15666666666666673, 0.31333333333333346, -0.15666666666666673), (0.20888888888888868, 0.20888888888888868, -0.10444444444444434), (0.2014285714285715, 0.13428571428571434, -0.06714285714285717)}, {(-0.148421052631579, 0.148421052631579, -0.049473684210526336), (-0.13428571428571434, 0.2014285714285715, -0.06714285714285717), (-0.08545454545454545, 0.25636363636363635, -0.08545454545454545), (0, 0.28200000000000003, -0.09400000000000008), (0.08545454545454545, 0.25636363636363635, -0.08545454545454545), (0.13428571428571434, 0.2014285714285715, -0.06714285714285717), (0.148421052631579, 0.148421052631579, -0.049473684210526336)}}, {{(-0.15666666666666673, -0.15666666666666673, 0), (-0.1446153846153848, -0.21692307692307677, 0), (-0.09400000000000008, -0.28200000000000003, 0), (0, -0.31333333333333346, 0), (0.09400000000000008, -0.28200000000000003, 0), (0.1446153846153848, -0.21692307692307677, 0), (0.15666666666666673, -0.15666666666666673, 0)}, {(-0.21692307692307677, -0.1446153846153848, 0), (-0.23499999999999988, -0.23499999999999988, 0), (-0.18799999999999994, -0.3759999999999999, 0), (0, -0.4700000000000002, 0), (0.18799999999999994, -0.3759999999999999, 0), (0.23499999999999988, -0.23499999999999988, 0), (0.21692307692307677, -0.1446153846153848, 0)}, {(-0.28200000000000003, -0.09400000000000008, 0), (-0.3759999999999999, -0.18799999999999994, 0), (-0.47, -0.47, 0), (0, -0.94, 0), (0.47, -0.47, 0), (0.3759999999999999, -0.18799999999999994, 0), (0.28200000000000003, -0.09400000000000008, 0)}, {(-0.31333333333333346, 0, 0), (-0.4700000000000002, 0, 0), (-0.94, 0, 0), (NaN, NaN, NaN), (0.94, 0, 0), (0.4700000000000002, 0, 0), (0.31333333333333346, 0, 0)}, {(-0.28200000000000003, 0.09400000000000008, 0), (-0.3759999999999999, 0.18799999999999994, 0), (-0.47, 0.47, 0), (0, 0.94, 0), (0.47, 0.47, 0), (0.3759999999999999, 0.18799999999999994, 0), (0.28200000000000003, 0.09400000000000008, 0)}, {(-0.21692307692307677, 0.1446153846153848, 0), (-0.23499999999999988, 0.23499999999999988, 0), (-0.18799999999999994, 0.3759999999999999, 0), (0, 0.4700000000000002, 0), (0.18799999999999994, 0.3759999999999999, 0), (0.23499999999999988, 0.23499999999999988, 0), (0.21692307692307677, 0.1446153846153848, 0)}, {(-0.15666666666666673, 0.15666666666666673, 0), (-0.1446153846153848, 0.21692307692307677, 0), (-0.09400000000000008, 0.28200000000000003, 0), (0, 0.31333333333333346, 0), (0.09400000000000008, 0.28200000000000003, 0), (0.1446153846153848, 0.21692307692307677, 0), (0.15666666666666673, 0.15666666666666673, 0)}}, {{(-0.148421052631579, -0.148421052631579, 0.049473684210526336), (-0.13428571428571434, -0.2014285714285715, 0.06714285714285717), (-0.08545454545454545, -0.25636363636363635, 0.08545454545454545), (0, -0.28200000000000003, 0.09400000000000008), (0.08545454545454545, -0.25636363636363635, 0.08545454545454545), (0.13428571428571434, -0.2014285714285715, 0.06714285714285717), (0.148421052631579, -0.148421052631579, 0.049473684210526336)}, {(-0.2014285714285715, -0.13428571428571434, 0.06714285714285717), (-0.20888888888888868, -0.20888888888888868, 0.10444444444444434), (-0.15666666666666673, -0.31333333333333346, 0.15666666666666673), (0, -0.3759999999999999, 0.18799999999999994), (0.15666666666666673, -0.31333333333333346, 0.15666666666666673), (0.20888888888888868, -0.20888888888888868, 0.10444444444444434), (0.2014285714285715, -0.13428571428571434, 0.06714285714285717)}, {(-0.25636363636363635, -0.08545454545454545, 0.08545454545454545), (-0.31333333333333346, -0.15666666666666673, 0.15666666666666673), (-0.31333333333333346, -0.31333333333333346, 0.31333333333333346), (0, -0.47, 0.47), (0.31333333333333346, -0.31333333333333346, 0.31333333333333346), (0.31333333333333346, -0.15666666666666673, 0.15666666666666673), (0.25636363636363635, -0.08545454545454545, 0.08545454545454545)}, {(-0.28200000000000003, 0, 0.09400000000000008), (-0.3759999999999999, 0, 0.18799999999999994), (-0.47, 0, 0.47), (0, 0, 0.94), (0.47, 0, 0.47), (0.3759999999999999, 0, 0.18799999999999994), (0.28200000000000003, 0, 0.09400000000000008)}, {(-0.25636363636363635, 0.08545454545454545, 0.08545454545454545), (-0.31333333333333346, 0.15666666666666673, 0.15666666666666673), (-0.31333333333333346, 0.31333333333333346, 0.31333333333333346), (0, 0.47, 0.47), (0.31333333333333346, 0.31333333333333346, 0.31333333333333346), (0.31333333333333346, 0.15666666666666673, 0.15666666666666673), (0.25636363636363635, 0.08545454545454545, 0.08545454545454545)}, {(-0.2014285714285715, 0.13428571428571434, 0.06714285714285717), (-0.20888888888888868, 0.20888888888888868, 0.10444444444444434), (-0.15666666666666673, 0.31333333333333346, 0.15666666666666673), (0, 0.3759999999999999, 0.18799999999999994), (0.15666666666666673, 0.31333333333333346, 0.15666666666666673), (0.20888888888888868, 0.20888888888888868, 0.10444444444444434), (0.2014285714285715, 0.13428571428571434, 0.06714285714285717)}, {(-0.148421052631579, 0.148421052631579, 0.049473684210526336), (-0.13428571428571434, 0.2014285714285715, 0.06714285714285717), (-0.08545454545454545, 0.25636363636363635, 0.08545454545454545), (0, 0.28200000000000003, 0.09400000000000008), (0.08545454545454545, 0.25636363636363635, 0.08545454545454545), (0.13428571428571434, 0.2014285714285715, 0.06714285714285717), (0.148421052631579, 0.148421052631579, 0.049473684210526336)}}, {{(-0.12818181818181795, -0.12818181818181795, 0.08545454545454545), (-0.11058823529411743, -0.1658823529411766, 0.11058823529411743), (-0.06714285714285717, -0.2014285714285715, 0.13428571428571434), (0, -0.21692307692307677, 0.1446153846153848), (0.06714285714285717, -0.2014285714285715, 0.13428571428571434), (0.11058823529411743, -0.1658823529411766, 0.11058823529411743), (0.12818181818181795, -0.12818181818181795, 0.08545454545454545)}, {(-0.1658823529411766, -0.11058823529411743, 0.11058823529411743), (-0.15666666666666673, -0.15666666666666673, 0.15666666666666673), (-0.10444444444444434, -0.20888888888888868, 0.20888888888888868), (0, -0.23499999999999988, 0.23499999999999988), (0.10444444444444434, -0.20888888888888868, 0.20888888888888868), (0.15666666666666673, -0.15666666666666673, 0.15666666666666673), (0.1658823529411766, -0.11058823529411743, 0.11058823529411743)}, {(-0.2014285714285715, -0.06714285714285717, 0.13428571428571434), (-0.20888888888888868, -0.10444444444444434, 0.20888888888888868), (-0.15666666666666673, -0.15666666666666673, 0.31333333333333346), (0, -0.18799999999999994, 0.3759999999999999), (0.15666666666666673, -0.15666666666666673, 0.31333333333333346), (0.20888888888888868, -0.10444444444444434, 0.20888888888888868), (0.2014285714285715, -0.06714285714285717, 0.13428571428571434)}, {(-0.21692307692307677, 0, 0.1446153846153848), (-0.23499999999999988, 0, 0.23499999999999988), (-0.18799999999999994, 0, 0.3759999999999999), (0, 0, 0.4700000000000002), (0.18799999999999994, 0, 0.3759999999999999), (0.23499999999999988, 0, 0.23499999999999988), (0.21692307692307677, 0, 0.1446153846153848)}, {(-0.2014285714285715, 0.06714285714285717, 0.13428571428571434), (-0.20888888888888868, 0.10444444444444434, 0.20888888888888868), (-0.15666666666666673, 0.15666666666666673, 0.31333333333333346), (0, 0.18799999999999994, 0.3759999999999999), (0.15666666666666673, 0.15666666666666673, 0.31333333333333346), (0.20888888888888868, 0.10444444444444434, 0.20888888888888868), (0.2014285714285715, 0.06714285714285717, 0.13428571428571434)}, {(-0.1658823529411766, 0.11058823529411743, 0.11058823529411743), (-0.15666666666666673, 0.15666666666666673, 0.15666666666666673), (-0.10444444444444434, 0.20888888888888868, 0.20888888888888868), (0, 0.23499999999999988, 0.23499999999999988), (0.10444444444444434, 0.20888888888888868, 0.20888888888888868), (0.15666666666666673, 0.15666666666666673, 0.15666666666666673), (0.1658823529411766, 0.11058823529411743, 0.11058823529411743)}, {(-0.12818181818181795, 0.12818181818181795, 0.08545454545454545), (-0.11058823529411743, 0.1658823529411766, 0.11058823529411743), (-0.06714285714285717, 0.2014285714285715, 0.13428571428571434), (0, 0.21692307692307677, 0.1446153846153848), (0.06714285714285717, 0.2014285714285715, 0.13428571428571434), (0.11058823529411743, 0.1658823529411766, 0.11058823529411743), (0.12818181818181795, 0.12818181818181795, 0.08545454545454545)}}, {{(-0.10444444444444434, -0.10444444444444434, 0.10444444444444434), (-0.08545454545454545, -0.12818181818181795, 0.12818181818181795), (-0.049473684210526336, -0.148421052631579, 0.148421052631579), (0, -0.15666666666666673, 0.15666666666666673), (0.049473684210526336, -0.148421052631579, 0.148421052631579), (0.08545454545454545, -0.12818181818181795, 0.12818181818181795), (0.10444444444444434, -0.10444444444444434, 0.10444444444444434)}, {(-0.12818181818181795, -0.08545454545454545, 0.12818181818181795), (-0.11058823529411743, -0.11058823529411743, 0.1658823529411766), (-0.06714285714285717, -0.13428571428571434, 0.2014285714285715), (0, -0.1446153846153848, 0.21692307692307677), (0.06714285714285717, -0.13428571428571434, 0.2014285714285715), (0.11058823529411743, -0.11058823529411743, 0.1658823529411766), (0.12818181818181795, -0.08545454545454545, 0.12818181818181795)}, {(-0.148421052631579, -0.049473684210526336, 0.148421052631579), (-0.13428571428571434, -0.06714285714285717, 0.2014285714285715), (-0.08545454545454545, -0.08545454545454545, 0.25636363636363635), (0, -0.09400000000000008, 0.28200000000000003), (0.08545454545454545, -0.08545454545454545, 0.25636363636363635), (0.13428571428571434, -0.06714285714285717, 0.2014285714285715), (0.148421052631579, -0.049473684210526336, 0.148421052631579)}, {(-0.15666666666666673, 0, 0.15666666666666673), (-0.1446153846153848, 0, 0.21692307692307677), (-0.09400000000000008, 0, 0.28200000000000003), (0, 0, 0.31333333333333346), (0.09400000000000008, 0, 0.28200000000000003), (0.1446153846153848, 0, 0.21692307692307677), (0.15666666666666673, 0, 0.15666666666666673)}, {(-0.148421052631579, 0.049473684210526336, 0.148421052631579), (-0.13428571428571434, 0.06714285714285717, 0.2014285714285715), (-0.08545454545454545, 0.08545454545454545, 0.25636363636363635), (0, 0.09400000000000008, 0.28200000000000003), (0.08545454545454545, 0.08545454545454545, 0.25636363636363635), (0.13428571428571434, 0.06714285714285717, 0.2014285714285715), (0.148421052631579, 0.049473684210526336, 0.148421052631579)}, {(-0.12818181818181795, 0.08545454545454545, 0.12818181818181795), (-0.11058823529411743, 0.11058823529411743, 0.1658823529411766), (-0.06714285714285717, 0.13428571428571434, 0.2014285714285715), (0, 0.1446153846153848, 0.21692307692307677), (0.06714285714285717, 0.13428571428571434, 0.2014285714285715), (0.11058823529411743, 0.11058823529411743, 0.1658823529411766), (0.12818181818181795, 0.08545454545454545, 0.12818181818181795)}, {(-0.10444444444444434, 0.10444444444444434, 0.10444444444444434), (-0.08545454545454545, 0.12818181818181795, 0.12818181818181795), (-0.049473684210526336, 0.148421052631579, 0.148421052631579), (0, 0.15666666666666673, 0.15666666666666673), (0.049473684210526336, 0.148421052631579, 0.148421052631579), (0.08545454545454545, 0.12818181818181795, 0.12818181818181795), (0.10444444444444434, 0.10444444444444434, 0.10444444444444434)}}}
  3. Textfield(xcomp) → InputBox1
  4. Textfield(ycomp) → InputBox2
  5. Textfield(zcomp) → InputBox3
  6. Element(listvectordirection, faces) → Selectedvector

AI Drawing Prompt Reference

Visualize a 3D vector field, showing the distribution and variation of vectors in space. The graph includes a 3D coordinate system grid and a series of vectors, each starting from a grid point, with direction and length representing the vector field's direction and magnitude at that point. The direction and magnitude of the vectors vary with location, demonstrating the distribution and variation of the vector field. Use input boxes to adjust the calculation formulas for the x-component, y-component, and z-component of the vectors and update the display of vectors in the graph in real-time. Additionally, you can select specific vectors for highlighting to observe and analyze the characteristics of the vector field more clearly.
The prompt above was compiled from the original drawing commands and is for reference only.