149 lines
4.9 KiB
HTML
149 lines
4.9 KiB
HTML
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<!DOCTYPE html>
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<html lang="en">
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<head>
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<title>Sphere contour challenge</title>
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<meta charset="UTF-8" />
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<link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/jsxgraph/distrib/jsxgraph.css" />
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<script type="text/javascript" charset="UTF-8" src="https://cdn.jsdelivr.net/npm/jsxgraph/distrib/jsxgraphcore.js"></script>
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</head>
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<body>
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<h1>Sphere contour challenge</h1>
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<p>Can you create something like this using <a href="https://jsxgraph.org/docs/symbols/Sphere3D.html#constructor"><code>Sphere3D</code></a>, <code>Plane3D</code>, and <a href="https://jsxgraph.org/docs/symbols/IntersectionCircle3D.html"><code>IntersectionCircle3D</code></a> elements? Don’t worry about including the colors; they’re just to clarify what happens when you move the center of the sphere.</p>
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<p>The <code>visible</code> attribute will come in handy.</p>
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<p>Since the <code>create</code> call for <code>Plane3D</code> isn’t documented, I’ve included an <a href="#create-plane">example</a> below.</p>
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<div id="sphere-contours" class="jxgbox" style="width:600px; height:600px"></div>
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<h2 id="create-plane">How to create a 3D plane</h2>
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<p>A <code>Plane3D</code> is created from a base point and two vectors. The base point can be given either in coordinates or as a <a href="https://jsxgraph.org/docs/symbols/Point3D.html#constructor"><code>Point3D</code></a>. The vectors are given in coordinates.</p>
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<div id="plane-example" class="jxgbox" style="width:600px; height:600px"></div>
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<!-- a solution to the sphere contour challenge -->
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<script type="text/javascript">
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// to prevent variable name conflicts, we define variables locally using `let`
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// and put the code for each board in its own block
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{
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// create a JSXGraph board and draw a 3D view on it
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let board = JXG.JSXGraph.initBoard(
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'sphere-contours',
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{
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boundingbox: [-8, 8, 8,-8],
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axis: false,
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showCopyright: false,
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showNavigation: false
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}
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);
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let view = board.create(
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'view3d',
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[[-4.5, -4.5], [9, 9],
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[[0, 3], [0, 3], [0, 3]]],
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{
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xPlaneRear: {fillOpacity: 0.2, gradient: null},
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yPlaneRear: {fillOpacity: 0.2, gradient: null},
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zPlaneRear: {fillOpacity: 0.2, gradient: null}
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}
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);
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// create a base point
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const nCuts = 3*4 + 1;
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let cutPositions = Array.from({length: nCuts}, (_, k) => 0.25*k);
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let cuttingPlanes = cutPositions.map(
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x => view.create(
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'plane3d',
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[[x, 1.5, 1.5], [0, 1, 0], [0, 0, 1]],
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{visible: false}
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)
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);
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// create a center for a sphere
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let center = view.create(
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'point3d',
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[1.5, 1.5, 1.5],
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{
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withLabel: false,
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size: 5,
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strokeWidth: 1,
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strokeColor: '#300060',
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fillColor: 'white',
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gradientSecondColor: '#5000a0',
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highlightStrokeColor: '#300060'
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}
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);
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// create a sphere whose center is the point `center` and whose radius is 1
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let sphere = view.create(
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'sphere3d',
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[center, 1],
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{visible: false}
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);
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// intersect the sphere with each of the cutting planes
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cuttingPlanes.forEach(
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(plane, k) => view.create(
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'intersectioncircle3d',
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[plane, sphere],
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{strokeColor: `rgb(${255*k/nCuts}, 0, 255)`}
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)
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);
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}
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</script>
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<!-- how to create a 3D plane -->
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<script type="text/javascript">
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// to prevent variable name conflicts, we define variables locally using `let`
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// and put the code for each board in its own block
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{
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// create a JSXGraph board and draw a 3D view on it
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let board = JXG.JSXGraph.initBoard(
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'plane-example',
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{
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boundingbox: [-8, 8, 8,-8],
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axis: false,
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showCopyright: false,
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showNavigation: false
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}
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);
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let view = board.create(
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'view3d',
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[[-4.5, -4.5], [9, 9],
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[[0, 3], [0, 3], [0, 3]]],
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{
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xPlaneRear: {fillOpacity: 0.2, gradient: null},
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yPlaneRear: {fillOpacity: 0.2, gradient: null},
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zPlaneRear: {fillOpacity: 0.2, gradient: null}
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}
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);
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// create a point
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let basePoint = view.create(
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'point3d',
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[1, 1, 1],
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{
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withLabel: false,
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size: 5,
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strokeWidth: 1,
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strokeColor: '#300060',
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fillColor: 'white',
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gradientSecondColor: '#5000a0',
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highlightStrokeColor: '#300060'
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}
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);
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// create a plane passing through the point
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let plane = view.create(
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'plane3d',
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[basePoint, [-2, 1, 1], [1, -2, 1]],
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{
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strokeWidth: 1,
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strokeColor: '#00ff80',
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strokeOpacity: 0.5,
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fillColor: '#00ff80',
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fillOpacity: 0.1,
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gradient: null
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}
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);
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}
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</script>
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</body>
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</html>
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