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<title>3D intersection sampler</title>
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<h1>3D intersection sampler</h1>
<!-- plane-plane -->
<h2>Plane–plane</h2>
<p>This template is based on the <a href="https://github.com/jsxgraph/jsxgraph/blob/main/examples/intersection_plane_plane.html">plane–plane intersection example</a> in the <a href="https://github.com/jsxgraph/jsxgraph/tree/main/examples">examples folder</a> included with the source code.</p>
<div id="plane-plane-board" class="jxgbox" style="width:600px; height:600px"></div>
<script type="text/javascript">
// to prevent variable name conflicts, we define variables locally using `let`
// and put the code for each board in its own block
{
// create a JSXGraph board and draw a 3D view on it
let board = JXG.JSXGraph.initBoard(
'plane-plane-board',
{
boundingbox: [-8, 8, 8,-8],
axis: false,
showCopyright: false,
showNavigation: false
}
);
let view = board.create(
'view3d',
[[-4.5, -4.5], [9, 9],
[[0, 3], [0, 3], [0, 3]]],
{
xPlaneRear: {fillOpacity: 0.2, gradient: null},
yPlaneRear: {fillOpacity: 0.2, gradient: null},
zPlaneRear: {fillOpacity: 0.2, gradient: null}
}
);
// create a point and two planes passing though it
let basePoint = view.create(
'point3d',
[1, 1, 1],
{
withLabel: false,
strokeWidth: 1,
size: 5,
strokeColor: '#300060',
fillColor: 'white',
gradientSecondColor: '#5000a0',
highlightStrokeColor: '#300060'
}
);
let planeHoriz = view.create(
'plane3d',
[basePoint, [1, 0, 0], [0, 1, 0]],
{
strokeWidth: 1,
strokeColor: '#0000ff',
strokeOpacity: 0.5,
fillColor: '#0000ff',
fillOpacity: 0.1,
gradient: null
}
);
let planeSloped = view.create(
'plane3d',
[basePoint, [-2, 1, 1], [1, -2, 1]],
{
strokeWidth: 1,
strokeColor: '#00ff80',
strokeOpacity: 0.5,
fillColor: '#00ff80',
fillOpacity: 0.1,
gradient: null
}
);
// create the line where the two planes intersect
let intersectionLine = view.create(
'intersectionline3d',
[planeHoriz, planeSloped],
{
strokeOpacity: 0.5,
highlightStrokeColor: 'black',
highlightStrokeOpacity: 0.5
}
);
}
</script>
<!-- plane-sphere -->
<h2>Plane–sphere</h2>
<p>This template is based on the <a href="https://github.com/jsxgraph/jsxgraph/blob/main/examples/intersection_plane_sphere.html">plane–sphere intersection example</a> in the <a href="https://github.com/jsxgraph/jsxgraph/tree/main/examples">examples folder</a> included with the source code.</p>
<div id="plane-sphere-board" class="jxgbox" style="width:600px; height:600px"></div>
<script type="text/javascript">
// to prevent variable name conflicts, we define variables locally using `let`
// and put the code for each board in its own block
{
// create a JSXGraph board and draw a 3D view on it
let board = JXG.JSXGraph.initBoard(
'plane-sphere-board',
{
boundingbox: [-8, 8, 8,-8],
axis: false,
showCopyright: false,
showNavigation: false
}
);
let view = board.create(
'view3d',
[[-4.5, -4.5], [9, 9],
[[0, 3], [0, 3], [0, 3]]],
{
xPlaneRear: {fillOpacity: 0.2, gradient: null},
yPlaneRear: {fillOpacity: 0.2, gradient: null},
zPlaneRear: {fillOpacity: 0.2, gradient: null}
}
);
// create a plane
let basePoint = view.create(
'point3d',
[4/3, 4/3, 4/3],
{
withLabel: false,
strokeWidth: 1,
size: 5,
strokeColor: '#300060',
fillColor: 'white',
gradientSecondColor: '#5000a0',
highlightStrokeColor: '#300060'
}
);
let plane = view.create(
'plane3d',
[basePoint, [-2, 1, 1], [1, -2, 1]],
{
strokeWidth: 1,
strokeColor: '#00ff80',
strokeOpacity: 0.5,
fillColor: '#00ff80',
fillOpacity: 0.1,
gradient: null
}
);
// create a sphere
let center = view.create(
'point3d',
[1.5, 1.5, 1.5],
{
withLabel: false,
size: 5,
strokeWidth: 1,
strokeColor: '#600030',
fillColor: 'white',
gradientSecondColor: '#a00050',
highlightStrokeColor: '#600030'
}
);
let sphere = view.create(
'sphere3d',
[center, 1],
{
strokeColor: '#0000ff',
strokeOpacity: 0.5,
gradient: 'radial',
gradientSecondColor: '#0000ff',
fillOpacity: 0.2,
}
);
// create the circle where the plane and the sphere intersect
let ixnCircle = view.create(
'intersectioncircle3d',
[plane, sphere],
{
strokeColor: 'black',
strokeOpacity: 0.5
}
);
}
</script>
<!-- sphere-sphere -->
<h2>Sphere–sphere</h2>
<p>This template is based on the <a href="https://github.com/jsxgraph/jsxgraph/blob/main/examples/intersection_sphere_sphere.html">sphere–sphere intersection example</a> in the <a href="https://github.com/jsxgraph/jsxgraph/tree/main/examples">examples folder</a> included with the source code.</p>
<div id="sphere-sphere-board" class="jxgbox" style="width:600px; height:600px"></div>
<script type="text/javascript">
// to prevent variable name conflicts, we define variables locally using `let`
// and put the code for each board in its own block
{
// create a JSXGraph board and draw a 3D view on it
let board = JXG.JSXGraph.initBoard(
'sphere-sphere-board',
{
boundingbox: [-8, 8, 8,-8],
axis: false,
showCopyright: false,
showNavigation: false
}
);
let view = board.create(
'view3d',
[[-4.5, -4.5], [9, 9],
[[0, 3], [0, 3], [0, 3]]],
{
xPlaneRear: {fillOpacity: 0.2, gradient: null},
yPlaneRear: {fillOpacity: 0.2, gradient: null},
zPlaneRear: {fillOpacity: 0.2, gradient: null}
}
);
// create two centers
let center1 = view.create(
'point3d',
[1, 1.5, 1.5],
{
withLabel: false,
size: 5,
strokeWidth: 1,
strokeColor: '#600030',
fillColor: 'white',
gradientSecondColor: '#a00050',
highlightStrokeColor: '#600030'
}
);
let center2 = view.create(
'point3d',
[2, 1.5, 1.5],
{
withLabel: false,
size: 5,
strokeWidth: 1,
strokeColor: '#600030',
fillColor: 'white',
gradientSecondColor: '#a00050',
highlightStrokeColor: '#600030'
}
);
// create two spheres
let sphere1 = view.create(
'sphere3d',
[center1, 0.75],
{
strokeColor: '#0000ff',
strokeOpacity: 0.5,
fillColor: 'white',
fillOpacity: 0.2,
gradientSecondColor: '#0000ff'
}
);
let sphere2 = view.create(
'sphere3d',
[center2, 0.75],
{
strokeColor: '#00ff80',
strokeOpacity: 0.5,
fillColor: 'white',
fillOpacity: 0.2,
gradientSecondColor: '#00ff80'
}
);
// create the circle where the spheres intersect
let ixnCircle = view.create(
'intersectioncircle3d',
[sphere1, sphere2],
{
strokeColor: 'black',
strokeOpacity: 0.5
}
);
}
</script>
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