Polynomial curve of constant width: Difference between revisions
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var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-8,8,8,-8], keepaspectratio:true}); | var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-8,8,8,-8], keepaspectratio:true}); | ||
brd.suspendUpdate(); | brd.suspendUpdate(); | ||
var a = brd.create('slider',[[-1, | var a = brd.create('slider',[[-1,6],[1,6],[-5,0.20,8]], {name:'a'}); | ||
var b = brd.create('slider',[[-1, | var b = brd.create('slider',[[-1,4],[1,5],[-5,1.15,20]], {name:'b'}); | ||
var k = brd.create('slider',[[-1, | var k = brd.create('slider',[[-1,4],[1,4],[1,1,11]], {name:'k\'', snapWidth:1}); | ||
var c = brd.create('curve',[function(phi, suspendUpdate){ | var c = brd.create('curve',[function(phi, suspendUpdate){ |
Revision as of 09:54, 7 June 2011
The curve defined by
- [math]\displaystyle{ p(\phi) = a\cdot cos(k\cdot\phi/2)+b }[/math]
in polar form is smooth and of constant width for odd values of [math]\displaystyle{ k }[/math]. In the visuzalitaion with JSXGraph below [math]\displaystyle{ k }[/math] is determined
- [math]\displaystyle{ k = 2k'+1. }[/math]
References
The underlying JavaScript code
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-8,8,8,-8], keepaspectratio:true});
brd.suspendUpdate();
var a = brd.create('slider',[[-1,1.8],[1,1.8],[-5,0.20,5]], {name:'a'});
var b = brd.create('slider',[[-1,1.6],[1,1.6],[-5,1.15,10]], {name:'b'});
var k = brd.create('slider',[[-1,1.4],[1,1.4],[1,1,11]], {name:'k\'', snapWidth:1});
var c = brd.create('curve',[function(phi, suspendUpdate){
var kk, aa, bb, p, ps, co, si;
//if (!suspendUpdate) {
aa = a.Value();
bb = b.Value();
kk = 2*k.Value()+1;
//}
co = Math.cos(kk*phi*0.5);
si = Math.sin(kk*phi*0.5);
p = aa*co*co+bb;
ps = -aa*kk*co*si;
return p*Math.cos(phi)-ps*Math.sin(phi);
},
function(phi, suspendUpdate){
var kk, aa, bb, p, ps, co, si;
//if (!suspendUpdate) {
aa = a.Value();
bb = b.Value();
kk = 2*k.Value()+1;
//}
co = Math.cos(kk*phi*0.5);
si = Math.sin(kk*phi*0.5);
p = aa*co*co+bb;
ps = -aa*kk*co*si;
return p*Math.sin(phi)+ps*Math.cos(phi);
},
0, Math.PI*2], {strokeWidth:10, strokeColor:'#ad5544'});
brd.unsuspendUpdate();