Reuleaux pentagon: Difference between revisions

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<jsxgraph width="0" height="0" box="nix"></jsxgraph>
<html>
<html>
<script type="text/javascript" src="/~alfred/jsxgraph/trunk/src/Roulette.js"></script>
<form>
<form>
<input type="button" value="start" onclick="rol.start()">
<input type="button" value="start" onclick="start();">
<input type="button" value="stop" onclick="rol.stop()">
<input type="button" value="stop" onclick="stop();">
<input type="button" value="one step" onclick="rol.rolling()">
<input type="button" value="one step" onclick="rol5.rolling();rol3.rolling();">
</form></html>
</form></html>


<jsxgraph width="600" height="600" box="jxgbox">
<jsxgraph width="600" height="600" box="jxgbox">
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,5,5,-5]});
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,7,5,-3]});
brd.renderer.container.style.backgroundColor = '#3d1c24';          // background color board
 
brd.suspendUpdate();
brd.suspendUpdate();
// Pentagon
var A = brd.create('point',[-2,-2]);
var B = brd.create('point',[2,-2]);
var pol5 = brd.create('regularpolygon',[A,B,5], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0});
for (var i=0;i<5;i++) pol5.vertices[i].setProperty({color:'#3d1c24'});
var diagPentagon = (1+Math.sqrt(5))*0.5*A.Dist(B);
// Triangle
var C = brd.create('point',[-2,-2]);
var D = brd.create('point',[C.X()+3/5*diagPentagon, C.Y()]);
var pol3 = brd.create('regularpolygon',[C,D,3], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0});
for (i=0;i<3;i++) pol3.vertices[i].setProperty({color:'#3d1c24'});
// Heptagon
var E = brd.create('point',[-2,-2]);
//
// Side length of the heptagon depending on the diagonal of the pentagon:
// r_7 = 7/5*r_5
var diagHeptagon = 7/5*diagPentagon;
// s_7 = r_7*sqrt(2)*sqrt(1-cos(pi/7)) (law of cosines)
var sideHeptagon = Math.sqrt(2*(1-Math.cos(Math.PI/7)))*diagHeptagon;
//
var F = brd.create('point',[E.X()+sideHeptagon, E.Y()]);
var pol7 = brd.create('regularpolygon',[E,F,7], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0});
for (i=0;i<7;i++) pol7.vertices[i].setProperty({color:'#3d1c24'});
// Create the Reuleauc curves
var reuleauxHeptagon = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol7.vertices, 7),
      {strokeWidth:6, strokeColor:'#d66d55', fillColor:'#d6bb55', highlightFillColor:'#d6bb55'});
var reuleauxPentagon = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol5.vertices, 5),
      {strokeWidth:6, strokeColor:'#d66d55', fillColor:'#ad5544', highlightFillColor:'#ad5544'});
var reuleauxTriangle = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol3.vertices, 3),
      {strokeWidth:6, strokeColor:'#d66d55', fillColor:'#703545', highlightFillColor:'#703545'});
brd.unsuspendUpdate();


var pi2 = 2.0*Math.PI;
var rol5 = brd.createRoulette(reuleauxHeptagon, reuleauxPentagon, 6*Math.PI/5, Math.PI/45, 1, 50, [A,B,C,D]);
var rol3 = brd.createRoulette(reuleauxPentagon, reuleauxTriangle, 6*Math.PI/5, Math.PI/45, -1, 50, [C,D]);
var rollIt = function() {
                rol5.rolling();
                rol3.rolling();
};
var interval;
var start = function() {
              interval = setInterval(rollIt,10);
};
var stop = function() {
              clearInterval(interval);
}
</jsxgraph>
 
===The underlying JavaScript code===
<source lang="javascript">
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,7,5,-3]});
brd.renderer.container.style.backgroundColor = '#3d1c24';         // background color board


brd.suspendUpdate();
// Pentagon
// Pentagon
var A = brd.create('point',[-2,-2]);
var A = brd.create('point',[-2,-2]);
var B = brd.create('point',[2,-2]);
var B = brd.create('point',[2,-2]);
var pol = brd.create('regularpolygon',[A,B,5], {withLines:false, fillColor:'none', highlightFillColor:'none'});
var pol5 = brd.create('regularpolygon',[A,B,5], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0});
for (var i=0;i<5;i++) pol5.vertices[i].setProperty({color:'#3d1c24'});


var diagPentagon = (1+Math.sqrt(5))*0.5*A.Dist(B);


var reuleauxPentagon = brd.create('curve',[
      function(t) {
        var pi2_5 = pi2/5;
        var p = pol.vertices;
        var d = p[0].Dist(p[2]);
        var t1 = (t%pi2 + pi2) % pi2;
        var n = Math.floor(t1 / pi2_5)%5;
        if (isNaN(n)) return n;
        var beta = JXG.Math.Geometry.rad([p[n].X()+1,p[n].Y()],p[n],p[(n+2)%5]);
        t1 -= n*pi2_5;
        t1 *=0.5;
        t1 += beta;
        return p[n].X()+d*Math.cos(t1);
      },
      function(t) {
        var pi2_5 = pi2/5;
        var p = pol.vertices;
        var d = p[0].Dist(p[2]);
        var t1 = (t%pi2 + pi2) % pi2;
        var n = Math.floor(t1 / pi2_5)%5;
        if (isNaN(n)) return n;
        var beta = JXG.Math.Geometry.rad([p[n].X()+1,p[n].Y()],p[n],p[(n+2)%5]);
        t1 -= n*pi2_5;
        t1*=0.5;
        t1 += beta;
        return p[n].Y()+d*Math.sin(t1);
      },
      0, pi2],
      {color:'#093083', highlightFillColor:'#093083'});
     
// Triangle
// Triangle
var C = brd.create('point',[-2,-2]);
var C = brd.create('point',[-2,-2]);
var D = brd.create('point',[
var D = brd.create('point',[C.X()+3/5*diagPentagon, C.Y()]);
                            C.X()+3*(1+Math.sqrt(5))/2/5*A.Dist(B),
var pol3 = brd.create('regularpolygon',[C,D,3], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0});
                            C.Y()
for (i=0;i<3;i++) pol3.vertices[i].setProperty({color:'#3d1c24'});
                          ]);
var pol3 = brd.create('regularpolygon',[C,D,3], {withLines:false, fillColor:'#e8501f', highlightFillColor:'#e8501f'});


var reuleauxTriangle = brd.create('curve',[
// Heptagon
      function(t) {
var E = brd.create('point',[-2,-2]);
        var pi2_3 = pi2/3;
 
        var p = pol3.vertices;
//
        var d = p[0].Dist(p[1]);
// Side length of the heptagon depending on the diagonal of the pentagon:
        var t1 = (t%(2*Math.PI) + pi2) % pi2;
// r_7 = 7/5*r_5
        var n = Math.floor(t1 / pi2_3)%3;
var diagHeptagon = 7/5*diagPentagon;
        if (isNaN(n)) return n;
// s_7 = r_7*sqrt(2)*sqrt(1-cos(pi/7)) (law of cosines)
        var beta = JXG.Math.Geometry.rad([p[n].X()+1,p[n].Y()],p[n],p[(n+1)%3]);
var sideHeptagon = Math.sqrt(2*(1-Math.cos(Math.PI/7)))*diagHeptagon;
        t1 -= n*pi2_3;
//
        t1*=0.5;
var F = brd.create('point',[E.X()+sideHeptagon, E.Y()]);
        t1 += beta;
var pol7 = brd.create('regularpolygon',[E,F,7], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0});
        return p[n].X()+d*Math.cos(t1);
for (i=0;i<7;i++) pol7.vertices[i].setProperty({color:'#3d1c24'});
      },
 
      function(t) {
// Create the Reuleauc curves
        var pi2_3 = pi2/3;
var reuleauxHeptagon = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol7.vertices, 7),
        var p = pol3.vertices;
      {strokeWidth:6, strokeColor:'#d66d55', fillColor:'#d6bb55', highlightFillColor:'#d6bb55'});
        var d = p[0].Dist(p[1]);
var reuleauxPentagon = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol5.vertices, 5),  
        var t1 = (t%pi2 + pi2) % pi2;
      {strokeWidth:6, strokeColor:'#d66d55', fillColor:'#ad5544', highlightFillColor:'#ad5544'});
        var n = Math.floor(t1 / pi2_3)%3;
var reuleauxTriangle = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol3.vertices, 3),  
        if (isNaN(n)) return n;
       {strokeWidth:6, strokeColor:'#d66d55', fillColor:'#703545', highlightFillColor:'#703545'});
        var beta = JXG.Math.Geometry.rad([p[n].X()+1,p[n].Y()],p[n],p[(n+1)%3]);
        t1 -= n*pi2_3;
        t1*=0.5;
        t1 += beta;
        return p[n].Y()+d*Math.sin(t1);
      },
       0, pi2],
      {color:'#e8501f', highlightFillColor:'#e8501f'});
brd.unsuspendUpdate();
brd.unsuspendUpdate();
var rol = JXG.Math.Numerics.createRoulette(reuleauxPentagon, reuleauxTriangle, 6*Math.PI/5, Math.PI/90, 10, [C,D]); </jsxgraph>


===The underlying JavaScript code===
var rol5 = brd.createRoulette(reuleauxHeptagon, reuleauxPentagon, 6*Math.PI/5, Math.PI/45, 1, 50, [A,B,C,D]);
<source lang="javascript">
var rol3 = brd.createRoulette(reuleauxPentagon, reuleauxTriangle, 6*Math.PI/5, Math.PI/45, -1, 50, [C,D]);
var rollIt = function() {
                rol5.rolling();
                rol3.rolling();
};
var interval;
var start = function() {
              interval = setInterval(rollIt,10);
};
var stop = function() {
              clearInterval(interval);
}
</source>
</source>



Latest revision as of 15:50, 20 February 2013

The underlying JavaScript code

var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,7,5,-3]});
brd.renderer.container.style.backgroundColor = '#3d1c24';          // background color board

brd.suspendUpdate();
// Pentagon
var A = brd.create('point',[-2,-2]);
var B = brd.create('point',[2,-2]);
var pol5 = brd.create('regularpolygon',[A,B,5], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0});
for (var i=0;i<5;i++) pol5.vertices[i].setProperty({color:'#3d1c24'});

var diagPentagon = (1+Math.sqrt(5))*0.5*A.Dist(B);

// Triangle
var C = brd.create('point',[-2,-2]);
var D = brd.create('point',[C.X()+3/5*diagPentagon, C.Y()]);
var pol3 = brd.create('regularpolygon',[C,D,3], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0});
for (i=0;i<3;i++) pol3.vertices[i].setProperty({color:'#3d1c24'});

// Heptagon
var E = brd.create('point',[-2,-2]);

//
// Side length of the heptagon depending on the diagonal of the pentagon:
// r_7 = 7/5*r_5
var diagHeptagon = 7/5*diagPentagon;
// s_7 = r_7*sqrt(2)*sqrt(1-cos(pi/7)) (law of cosines)
var sideHeptagon = Math.sqrt(2*(1-Math.cos(Math.PI/7)))*diagHeptagon;
// 
var F = brd.create('point',[E.X()+sideHeptagon, E.Y()]);
var pol7 = brd.create('regularpolygon',[E,F,7], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0});
for (i=0;i<7;i++) pol7.vertices[i].setProperty({color:'#3d1c24'});

// Create the Reuleauc curves
var reuleauxHeptagon = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol7.vertices, 7), 
       {strokeWidth:6, strokeColor:'#d66d55', fillColor:'#d6bb55', highlightFillColor:'#d6bb55'});
var reuleauxPentagon = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol5.vertices, 5), 
       {strokeWidth:6, strokeColor:'#d66d55', fillColor:'#ad5544', highlightFillColor:'#ad5544'});
var reuleauxTriangle = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol3.vertices, 3), 
       {strokeWidth:6, strokeColor:'#d66d55', fillColor:'#703545', highlightFillColor:'#703545'});
brd.unsuspendUpdate();

var rol5 = brd.createRoulette(reuleauxHeptagon, reuleauxPentagon, 6*Math.PI/5, Math.PI/45, 1, 50, [A,B,C,D]); 
var rol3 = brd.createRoulette(reuleauxPentagon, reuleauxTriangle, 6*Math.PI/5, Math.PI/45, -1, 50, [C,D]); 
var rollIt = function() {
                rol5.rolling();
                rol3.rolling();
};
var interval;
var start = function() {
              interval = setInterval(rollIt,10);
};
var stop = function() {
              clearInterval(interval);
}