Hyperbola III: Difference between revisions
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Example and visualization for principal axis transformation | |||
<jsxgraph width="500" height="500"> | <jsxgraph width="500" height="500"> | ||
JXG.Options.label.autoPosition = true; | JXG.Options.label.autoPosition = true; | ||
JXG.Options.text.fontSize = 16; | JXG.Options.text.fontSize = 16; | ||
JXG.Options.line.strokeWidth = 0.8; | JXG.Options.line.strokeWidth = 0.8; | ||
JXG.Options.point.size = 1; | |||
var board = JXG.JSXGraph.initBoard('jxgbox', { boundingbox: [-5, 5, 5, -5], axis: true, showClearTraces: true}); | var board = JXG.JSXGraph.initBoard('jxgbox', { boundingbox: [-5, 5, 5, -5], axis: true, showClearTraces: true}); | ||
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const sq5 = Math.sqrt(5); | const sq5 = Math.sqrt(5); | ||
var f1 = board.create('point', [-sq5 | // Start with the Euclidean normal form of the quadric, | ||
var f2 = board.create('point', [ sq5 | // because we easily can read off the focal points. | ||
var p = board.create('point', [ | var f1 = board.create('point', [0, -sq5], {name:"f'", fixed: true}); | ||
var f2 = board.create('point', [0, sq5], {name:"f", fixed: true}); | |||
var p = board.create('point', [2, Math.sqrt(2)], {name:"p", fixed: true}); | |||
var o = board.create('point', [0, 0], {withLabel:false, color: 'blue', fixed: true, trace:true}); | |||
var e1 = board.create('point', [1, 0], {withLabel:false, color: 'blue', fixed: true}); | |||
var e2 = board.create('point', [0, 1], {withLabel:false, color: 'blue', fixed: true}); | |||
// Undo the principal axis transformation to recompute the original form of the quadric | |||
var phi0 = board.create('transform', [-Math.PI * 0.25], {type: 'rotate'}); | |||
var t0 = board.create('transform', [-2, 1], {type: 'translate'}); | |||
t0.bindTo([f1, f2, p, o, e1, e2]); | |||
phi0.bindTo([f1, f2, p, o, e1, e2]); | |||
var hyp = board.create('hyperbola', [f1, f2, p]); | var hyp = board.create('hyperbola', [f1, f2, p]); | ||
// Create transformed axes | |||
var ax_z1 = board.create('line', [o, e1], {lastArrow: true, strokeColor:'black'}); | |||
var ax_z2 = board.create('line', [o, e2], {lastArrow: true, strokeColor:'black'}); | |||
board.update(); | |||
// Visualization of the principal axis transformation | |||
var alpha = board.create('slider', [[1,4], [3,4], [0, 0, 45]], {name:'α', unitLabel:'°'}); | |||
var f = board.create('slider', [[1,3.5], [3,3.5], [0, 0, 1]], {name:'f'}); | |||
var phi = board.create('transform', [function(){ return alpha.Value() * Math.PI / 180; }], {type: 'rotate'}); | |||
var t = board.create('transform', [function(){ return 2*f.Value(); }, function(){ return -f.Value(); }], {type: 'translate'}); | |||
phi.bindTo([f1, f2, p, e1, e2, o]); | |||
t.bindTo([f1, f2, p, e1, e2, o]); | |||
</jsxgraph> | </jsxgraph> | ||
=== The underlying JavaScript code === | === The underlying JavaScript code === | ||
<source lang="javascript"> | <source lang="javascript"> | ||
JXG.Options.label.autoPosition = true; | |||
JXG.Options.text.fontSize = 16; | |||
JXG.Options.line.strokeWidth = 0.8; | |||
JXG.Options.point.size = 1; | |||
var board = JXG.JSXGraph.initBoard('jxgbox', { boundingbox: [-5, 5, 5, -5], axis: true, showClearTraces: true}); | |||
const sq5 = Math.sqrt(5); | |||
// Start with the Euclidean normal form of the quadric, | |||
// because we easily can read off the focal points. | |||
var f1 = board.create('point', [0, -sq5], {name:"f'", fixed: true}); | |||
var f2 = board.create('point', [0, sq5], {name:"f", fixed: true}); | |||
var p = board.create('point', [2, Math.sqrt(2)], {name:"p", fixed: true}); | |||
var o = board.create('point', [0, 0], {withLabel:false, color: 'blue', fixed: true, trace:true}); | |||
var e1 = board.create('point', [1, 0], {withLabel:false, color: 'blue', fixed: true}); | |||
var e2 = board.create('point', [0, 1], {withLabel:false, color: 'blue', fixed: true}); | |||
// Undo the principal axis transformation to recompute the original form of the quadric | |||
var phi0 = board.create('transform', [-Math.PI * 0.25], {type: 'rotate'}); | |||
var t0 = board.create('transform', [-2, 1], {type: 'translate'}); | |||
t0.bindTo([f1, f2, p, o, e1, e2]); | |||
phi0.bindTo([f1, f2, p, o, e1, e2]); | |||
var hyp = board.create('hyperbola', [f1, f2, p]); | |||
// Create transformed axes | |||
var ax_z1 = board.create('line', [o, e1], {lastArrow: true, strokeColor:'black'}); | |||
var ax_z2 = board.create('line', [o, e2], {lastArrow: true, strokeColor:'black'}); | |||
board.update(); | |||
// Visualization of the principal axis transformation | |||
var alpha = board.create('slider', [[1,4], [3,4], [0, 0, 45]], {name:'α', unitLabel:'°'}); | |||
var f = board.create('slider', [[1,3.5], [3,3.5], [0, 0, 1]], {name:'f'}); | |||
var phi = board.create('transform', [function(){ return alpha.Value() * Math.PI / 180; }], {type: 'rotate'}); | |||
var t = board.create('transform', [function(){ return 2*f.Value(); }, function(){ return -f.Value(); }], {type: 'translate'}); | |||
phi.bindTo([f1, f2, p, e1, e2, o]); | |||
t.bindTo([f1, f2, p, e1, e2, o]); | |||
</source> | </source> | ||
[[Category:Examples]] | [[Category:Examples]] | ||
[[Category:Geometry]] | [[Category:Geometry]] |
Latest revision as of 15:45, 6 July 2021
Example and visualization for principal axis transformation
The underlying JavaScript code
JXG.Options.label.autoPosition = true;
JXG.Options.text.fontSize = 16;
JXG.Options.line.strokeWidth = 0.8;
JXG.Options.point.size = 1;
var board = JXG.JSXGraph.initBoard('jxgbox', { boundingbox: [-5, 5, 5, -5], axis: true, showClearTraces: true});
const sq5 = Math.sqrt(5);
// Start with the Euclidean normal form of the quadric,
// because we easily can read off the focal points.
var f1 = board.create('point', [0, -sq5], {name:"f'", fixed: true});
var f2 = board.create('point', [0, sq5], {name:"f", fixed: true});
var p = board.create('point', [2, Math.sqrt(2)], {name:"p", fixed: true});
var o = board.create('point', [0, 0], {withLabel:false, color: 'blue', fixed: true, trace:true});
var e1 = board.create('point', [1, 0], {withLabel:false, color: 'blue', fixed: true});
var e2 = board.create('point', [0, 1], {withLabel:false, color: 'blue', fixed: true});
// Undo the principal axis transformation to recompute the original form of the quadric
var phi0 = board.create('transform', [-Math.PI * 0.25], {type: 'rotate'});
var t0 = board.create('transform', [-2, 1], {type: 'translate'});
t0.bindTo([f1, f2, p, o, e1, e2]);
phi0.bindTo([f1, f2, p, o, e1, e2]);
var hyp = board.create('hyperbola', [f1, f2, p]);
// Create transformed axes
var ax_z1 = board.create('line', [o, e1], {lastArrow: true, strokeColor:'black'});
var ax_z2 = board.create('line', [o, e2], {lastArrow: true, strokeColor:'black'});
board.update();
// Visualization of the principal axis transformation
var alpha = board.create('slider', [[1,4], [3,4], [0, 0, 45]], {name:'α', unitLabel:'°'});
var f = board.create('slider', [[1,3.5], [3,3.5], [0, 0, 1]], {name:'f'});
var phi = board.create('transform', [function(){ return alpha.Value() * Math.PI / 180; }], {type: 'rotate'});
var t = board.create('transform', [function(){ return 2*f.Value(); }, function(){ return -f.Value(); }], {type: 'translate'});
phi.bindTo([f1, f2, p, e1, e2, o]);
t.bindTo([f1, f2, p, e1, e2, o]);