Difference between revisions of "Tschirnhausen Cubic Catacaustic"
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function(){ | function(){ | ||
//var a = dir.stdform[1], b = dir.stdform[2], | //var a = dir.stdform[1], b = dir.stdform[2], | ||
− | var a = reflectionpoint.X() | + | var a = -reflectionpoint.X()+radpoint.X(), |
− | b = reflectionpoint.Y() | + | b = -reflectionpoint.Y()+radpoint.Y(), |
t = reflectionpoint.position, | t = reflectionpoint.position, | ||
u = JXG.Math.Numerics.D(cubic.X)(t), | u = JXG.Math.Numerics.D(cubic.X)(t), |
Revision as of 16:11, 13 January 2011
The Tschirnhausen cubic (black curve) is defined parametrically as
- [math] x = a3(t^2-3) [/math]
- [math] y = at(t^2-3) [/math]
Its catcaustic (red curve) with radiant point [math](-8a,p)[/math] is the semicubical parabola with parametric equations
- [math] x = a6(t^2-1) [/math]
- [math] y = a4t^3 [/math]
References
The underlying JavaScript code
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-10,10,10,-10], keepaspectratio:true, axis:true});
brd.suspendUpdate();
var a = brd.create('slider',[[-5,6],[5,6],[-5,1,5]], {name:'a'});
var cubic = brd.create('curve',
[function(t){ return a.Value()*3*(t*t-3);},
function(t){ return a.Value()*t*(t*t-3);},
-5, 5
],
{strokeWidth:1, strokeColor:'black'});
var radpoint = brd.create('point',[function(){ return -a.Value()*8;},0],{name:'radiant point'});
var cataustic = brd.create('curve',
[function(t){ return a.Value()*6*(t*t-1);},
function(t){ return a.Value()*4*t*t*t;},
-4, 4
],
{strokeWidth:1, strokeColor:'red'});
brd.unsuspendUpdate();