3D parametric surface: Klein bottle
Have also a look at "3D ruled surface: hyperboloid".
A parametric surface is defined by a function
$f: {\mathbb R}^2 \to {\mathbb R}^3, \; (u,v) \mapsto (f_x(u,v), f_y(u,v), f_z(u,v))$.
// Define the id of your board in BOARDID
var board = JXG.JSXGraph.initBoard(BOARDID, {
boundingbox: [-8, 8, 8, -8],
keepaspectratio: false,
axis: false
});
var view = board.create('view3d',
[
[-6, -3],
[8, 8],
[
[-5, 5],
[-5, 5],
[-5, 5]
]
], {});
var b = board.create('slider', [[-7, -6], [5, -6], [-3, 2, 4]], {name: 'b'});
// Klein bottle
var c = view.create('parametricsurface3d', [
(u, v) => b.Value() * (1 - Math.sin(u)) * Math.cos(u) + (2 - Math.cos(u)) * Math.cos(v) * (2 * Math.exp(-Math.pow(u / 2 - Math.PI, 2)) - 1),
(u, v) => (2 - Math.cos(u)) * Math.sin(v),
(u, v) => 4 * Math.sin(u) + 0.5 * (2 - Math.cos(u)) * Math.sin(u) * Math.cos(v) * Math.exp(-Math.pow(u - 3 * Math.PI / 2, 2)),
[0, 2 * Math.PI],
[0, 2 * Math.PI],
], {
strokeColor: 'green',
stepsU: 60,
stepsV: 60
});
This example is licensed under a Creative Commons Attribution ShareAlike 4.0 International License.
Please note that you have to mention The Center of Mobile Learning with Digital Technology in the credits.