Polynomial curve of constant width: Difference between revisions
From JSXGraph Wiki
A WASSERMANN (talk | contribs) No edit summary |
A WASSERMANN (talk | contribs) No edit summary |
||
Line 31: | Line 31: | ||
var p2 = brd.create('curve',[function(phi, suspendUpdate){ | var p2 = brd.create('curve',[function(phi, suspendUpdate){ | ||
var kk, aa, bb, p, ps, co, si; | var kk, aa, bb, p, ps, co, si; | ||
if ( | if (!suspendUpdate) { | ||
aa = a.Value(); | aa = a.Value(); | ||
bb = b.Value(); | bb = b.Value(); | ||
Line 44: | Line 44: | ||
function(phi, suspendUpdate){ | function(phi, suspendUpdate){ | ||
var kk, aa, bb, p, ps, co, si; | var kk, aa, bb, p, ps, co, si; | ||
if ( | if (!suspendUpdate) { | ||
aa = a.Value(); | aa = a.Value(); | ||
bb = b.Value(); | bb = b.Value(); |
Revision as of 09:51, 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:[-2,2,2,-2], 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 p = brd.create('curve',[function(phi, suspendUpdate){
var kk, aa, bb;
if (!suspendUpdate) {
aa = a.Value();
bb = b.Value();
kk = 2*k.Value()+1;
}
var co = Math.cos(kk*phi*0.5);
return aa*co*co+bb;
},[0,0], 0,Math.PI*2], {curveType:'polar', strokeWidth:10, strokeColor:'#ad5544'});
brd.unsuspendUpdate();