// Define the id of your board in BOARDID
var board = JXG.JSXGraph.initBoard(BOARDID, {
boundingbox: [-8, 8, 8, -8],
keepaspectratio: false,
axis: false
});
var box = [-5, 5];
var view = board.create('view3d',
[
[-6, -3],
[8, 8],
[box, box, box]
], {
xPlaneRear: {
visible: false
},
yPlaneRear: {
visible: false
},
});
// Slider to manipulate the function F below.
var s = board.create('slider', [[-7, -6], [5, -6], [-3, 0.3, 4]], {name: 's'});
// Function F to be plotted
var F = (x, y) => s.Value() * x * y + 2;
// 3D surface
var c = view.create('functiongraph3d', [F, box, box], {
strokeWidth: 0.5,
stepsU: 70,
stepsV: 70
});
// 3D point: point on xy plane
var Axy = view.create('point3d', [2, 2, -5], {
withLabel: false,
size: 5
});
// Project Axy to the surface
var A = view.create('point3d', [
() => [Axy.X(), Axy.Y(), F(Axy.X(), Axy.Y())]
], {
withLabel: false
});
view.create('line3d', [Axy, A], {
dash: 1
});
// Hard coded, partial derivatives of F in point A
var dFx = () => s.Value() * A.Y(),
dFy = () => s.Value() * A.X(),
dFx_vec = [1, 0, dFx],
dFy_vec = [0, 1, dFy];
// Gradient plane
var plane1 = view.create('plane3d', [A, dFx_vec, dFy_vec, [() => -dFx(), dFx], [() => -dFy(), dFy]], {
fillOpacity: 0.8,
fillColor: 'red'
});
var a = view.create('line3d', [A, dFx_vec, [0, dFx]]);
var b = view.create('line3d', [A, dFy_vec, [0, dFy]]);