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3D ruled surface: hyperboloid
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<iframe 
    src="http://jsxgraph.org/share/iframe/3d-ruled-surface-hyperboloid" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: 3D ruled surface: hyperboloid" 
    allowfullscreen
></iframe>
This code has to 
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    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]
            ]
        ], {
            zPlaneRear: {
                fillColor: 'blue'
            }
        });
    
    var phi = board.create('slider', [
        [-7, -6],
        [5, -6],
        [-Math.PI / 2, 0.5, Math.PI / 2]
    ], {
        name: 'φ',
        snapWidth: 0.1
    });
    var c = view.create('parametricsurface3d', [
        (u, v) => (1 - v) * Math.cos(u - phi.Value()) + v * Math.cos(u + phi.Value()),
        (u, v) => (1 - v) * Math.sin(u - phi.Value()) + v * Math.sin(u + phi.Value()),
        (u, v) => 2 * v - 1,
        [0, 2 * Math.PI],
        [-2, 3]
    ], {
        strokeColor: '#0000ff',
        strokeWidth: 1,
        strokeOpacity: 0.9,
        stepsU: 20,
        stepsV: 1
    });
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution ShareAlike 4.0 International License.
https://creativecommons.org/licenses/by-sa/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID = 'your_div_id'; // Insert your id here!

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]
        ]
    ], {
        zPlaneRear: {
            fillColor: 'blue'
        }
    });

var phi = board.create('slider', [
    [-7, -6],
    [5, -6],
    [-Math.PI / 2, 0.5, Math.PI / 2]
], {
    name: 'φ',
    snapWidth: 0.1
});
var c = view.create('parametricsurface3d', [
    (u, v) => (1 - v) * Math.cos(u - phi.Value()) + v * Math.cos(u + phi.Value()),
    (u, v) => (1 - v) * Math.sin(u - phi.Value()) + v * Math.sin(u + phi.Value()),
    (u, v) => 2 * v - 1,
    [0, 2 * Math.PI],
    [-2, 3]
], {
    strokeColor: '#0000ff',
    strokeWidth: 1,
    strokeOpacity: 0.9,
    stepsU: 20,
    stepsV: 1
});
<jsxgraph width="100%" aspect-ratio="1 / 1" title="3D ruled surface: hyperboloid" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution ShareAlike 4.0 International License.
   https://creativecommons.org/licenses/by-sa/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
   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]
           ]
       ], {
           zPlaneRear: {
               fillColor: 'blue'
           }
       });
   
   var phi = board.create('slider', [
       [-7, -6],
       [5, -6],
       [-Math.PI / 2, 0.5, Math.PI / 2]
   ], {
       name: 'φ',
       snapWidth: 0.1
   });
   var c = view.create('parametricsurface3d', [
       (u, v) => (1 - v) * Math.cos(u - phi.Value()) + v * Math.cos(u + phi.Value()),
       (u, v) => (1 - v) * Math.sin(u - phi.Value()) + v * Math.sin(u + phi.Value()),
       (u, v) => 2 * v - 1,
       [0, 2 * Math.PI],
       [-2, 3]
   ], {
       strokeColor: '#0000ff',
       strokeWidth: 1,
       strokeOpacity: 0.9,
       stepsU: 20,
       stepsV: 1
   });
</jsxgraph>

3D ruled surface: hyperboloid

3D
3D
Analytic
A ruled surface is a special case of a parametric surface.
Have also a look at the examples 
// 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]
        ]
    ], {
        zPlaneRear: {
            fillColor: 'blue'
        }
    });

var phi = board.create('slider', [
    [-7, -6],
    [5, -6],
    [-Math.PI / 2, 0.5, Math.PI / 2]
], {
    name: 'φ',
    snapWidth: 0.1
});
var c = view.create('parametricsurface3d', [
    (u, v) => (1 - v) * Math.cos(u - phi.Value()) + v * Math.cos(u + phi.Value()),
    (u, v) => (1 - v) * Math.sin(u - phi.Value()) + v * Math.sin(u + phi.Value()),
    (u, v) => 2 * v - 1,
    [0, 2 * Math.PI],
    [-2, 3]
], {
    strokeColor: '#0000ff',
    strokeWidth: 1,
    strokeOpacity: 0.9,
    stepsU: 20,
    stepsV: 1
});

license

This example is licensed under a Creative Commons Attribution ShareAlike 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.