Difference between revisions of "Circle approximation"

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(6 intermediate revisions by the same user not shown)
Line 1: Line 1:
 
<jsxgraph width="600" height="600" box="box">
 
<jsxgraph width="600" height="600" box="box">
 
var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-6, 6, 6, -6], grid: true});
 
var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-6, 6, 6, -6], grid: true});
−
var n = brd.createElement('slider',[[-5,5],[4.5,5],[3,4,96]],{name:'n',snapWidth:1});
+
var n = brd.create('slider',[[-5,5],[4.5,5],[3,4,96]],{name:'n',snapWidth:1});
  
 
var p0 = brd.create('point',[0,0],{strokeColor:'black',fillColor:'white',name:''});
 
var p0 = brd.create('point',[0,0],{strokeColor:'black',fillColor:'white',name:''});
Line 25: Line 25:
 
   this.dataX = [p0.X()+circ.getRadius()];
 
   this.dataX = [p0.X()+circ.getRadius()];
 
   this.dataY = [p0.Y()];
 
   this.dataY = [p0.Y()];
−
   ptmp.setPositionDirectly(p0.X()+circ.getRadius(), p0.Y());
+
   ptmp.setPositionDirectly(JXG.COORDS_BY_USER, [p0.X()+circ.getRadius(), p0.Y()]);
 
   for (i=0;i<len;i++) {
 
   for (i=0;i<len;i++) {
 
     rot.applyOnce(ptmp);
 
     rot.applyOnce(ptmp);
Line 38: Line 38:
 
   this.dataX = [p0.X()+s];
 
   this.dataX = [p0.X()+s];
 
   this.dataY = [p0.Y()];
 
   this.dataY = [p0.Y()];
−
   ptmp.setPositionDirectly(JXG.COORDS_BY_USER, p0.X()+s,p0.Y());
+
   ptmp.setPositionDirectly(JXG.COORDS_BY_USER, [p0.X()+s,p0.Y()]);
 
   for (i=0;i<len;i++) {
 
   for (i=0;i<len;i++) {
 
     rot.applyOnce(ptmp);
 
     rot.applyOnce(ptmp);
Line 50: Line 50:
 
</jsxgraph>
 
</jsxgraph>
  
−
===The underlying JavaScript code===
+
===The JavaScript code===
 
<source lang="javascript">
 
<source lang="javascript">
 
var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-6, 6, 6, -6], grid: true});
 
var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-6, 6, 6, -6], grid: true});
 +
var n = brd.create('slider',[[-5,5],[4.5,5],[3,4,96]],{name:'n',snapWidth:1});
  
−
// Slider that controls the number n of vertices of the two polygons
 
−
var n = brd.createElement('slider',[[-5,5],[4.5,5],[3,4,96]],{name:'n',snapWidth:1});
 
−
 
−
// p0, p1 define the circle 'circ'
 
 
var p0 = brd.create('point',[0,0],{strokeColor:'black',fillColor:'white',name:''});
 
var p0 = brd.create('point',[0,0],{strokeColor:'black',fillColor:'white',name:''});
 
var p1 = brd.create('point',[4,0],{strokeColor:'black',fillColor:'white',name:''});
 
var p1 = brd.create('point',[4,0],{strokeColor:'black',fillColor:'white',name:''});
−
 
−
// With the help of the rotational transform  'rot' we will compute the vertices
 
−
// of the polygons
 
 
var rot = brd.create('transform', [function() {return Math.PI*2.0/n.Value();},p0], {type:'rotate'});  // angle, rotation center
 
var rot = brd.create('transform', [function() {return Math.PI*2.0/n.Value();},p0], {type:'rotate'});  // angle, rotation center
 
var ptmp = brd.create('point',[0,0],{visible:false,withLabel:false});  // dummy point for the rotation
 
var ptmp = brd.create('point',[0,0],{visible:false,withLabel:false});  // dummy point for the rotation
−
 
−
// Two curves cOut and cIn defining the inner and outer polygon. They both contain dummy paths,
 
−
// the correct paths will be computed later.
 
 
var cOut = brd.create('curve',[[0],[0]],{fillColor:'#5e9abf',highlightFillColor:'#5e9abf',fillOpacity:1,highlightFillOpacity:1,strokeColor:'black',highlightStrokeColor:'black'});
 
var cOut = brd.create('curve',[[0],[0]],{fillColor:'#5e9abf',highlightFillColor:'#5e9abf',fillOpacity:1,highlightFillOpacity:1,strokeColor:'black',highlightStrokeColor:'black'});
−
 
−
// Construction of the circle
 
 
var circ = brd.create('circle',[p0,p1],{fillColor:'#fefd4c',highlightFillColor:'#fefd4c',fillOpacity:0.5,highlightFillOpacity:0.5,strokeColor:'black',highlightStrokeColor:'black'});
 
var circ = brd.create('circle',[p0,p1],{fillColor:'#fefd4c',highlightFillColor:'#fefd4c',fillOpacity:0.5,highlightFillOpacity:0.5,strokeColor:'black',highlightStrokeColor:'black'});
−
var cIn = brd.create('curve',[[0],[0]],{fillColor:'#d769a3',highlightFillColor:'#d769a3',fillOpacity:1,highlightFillOpacity:1,strokeColor:'black',highlightStrokeColor:'black'});
+
var cIn = brd.create('curve',[[0,1,2],[0,1,2]],{fillColor:'#d769a3',highlightFillColor:'#d769a3',fillOpacity:1,highlightFillOpacity:1,strokeColor:'black',highlightStrokeColor:'black'});
  
−
// Construction of the text
 
 
var tCirc = brd.create('text',[-5,-4.0,function(){
 
var tCirc = brd.create('text',[-5,-4.0,function(){
 
     return 'Area of the circle = ' + (0.0625*circ.getRadius()*circ.getRadius()*Math.PI).toFixed(5);
 
     return 'Area of the circle = ' + (0.0625*circ.getRadius()*circ.getRadius()*Math.PI).toFixed(5);
Line 85: Line 73:
 
   }],{fontSize:20});
 
   }],{fontSize:20});
  
−
// In the updateDataArray methods of the curves cIn and cOut the correct paths are computed.
 
−
// updateDataArray() is called during the update of the curve. By default, this method
 
−
// is empty, but it can be overwritten.
 
−
//
 
−
// What is done in these methods? We set the dummy point ptmp to the position of one vertex of the
 
−
// regular polygon. Then we apply n-times the rotational transform to this point. In every step we read the new
 
−
// coordinates of the points and add them to the path of the curve.
 
 
cIn.updateDataArray = function() {
 
cIn.updateDataArray = function() {
 
   var i, len = n.Value();
 
   var i, len = n.Value();
 
   this.dataX = [p0.X()+circ.getRadius()];
 
   this.dataX = [p0.X()+circ.getRadius()];
 
   this.dataY = [p0.Y()];
 
   this.dataY = [p0.Y()];
−
   ptmp.setPositionDirectly(JXG.COORDS_BY_USER,p0.X()+circ.getRadius(),p0.Y());
+
   ptmp.setPositionDirectly(JXG.COORDS_BY_USER, [p0.X()+circ.getRadius(), p0.Y()]);
 
   for (i=0;i<len;i++) {
 
   for (i=0;i<len;i++) {
 
     rot.applyOnce(ptmp);
 
     rot.applyOnce(ptmp);
Line 109: Line 90:
 
   this.dataX = [p0.X()+s];
 
   this.dataX = [p0.X()+s];
 
   this.dataY = [p0.Y()];
 
   this.dataY = [p0.Y()];
−
   ptmp.setPositionDirectly(JXG.COORDS_BY_USER, p0.X()+s,p0.Y());
+
   ptmp.setPositionDirectly(JXG.COORDS_BY_USER, [p0.X()+s,p0.Y()]);
 
   for (i=0;i<len;i++) {
 
   for (i=0;i<len;i++) {
 
     rot.applyOnce(ptmp);
 
     rot.applyOnce(ptmp);
Line 118: Line 99:
  
 
brd.update();
 
brd.update();
 +
 
</source>
 
</source>
  

Latest revision as of 15:32, 3 March 2021

The JavaScript code

var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-6, 6, 6, -6], grid: true});
var n = brd.create('slider',[[-5,5],[4.5,5],[3,4,96]],{name:'n',snapWidth:1});

var p0 = brd.create('point',[0,0],{strokeColor:'black',fillColor:'white',name:''});
var p1 = brd.create('point',[4,0],{strokeColor:'black',fillColor:'white',name:''});
var rot = brd.create('transform', [function() {return Math.PI*2.0/n.Value();},p0], {type:'rotate'});  // angle, rotation center
var ptmp = brd.create('point',[0,0],{visible:false,withLabel:false});  // dummy point for the rotation
var cOut = brd.create('curve',[[0],[0]],{fillColor:'#5e9abf',highlightFillColor:'#5e9abf',fillOpacity:1,highlightFillOpacity:1,strokeColor:'black',highlightStrokeColor:'black'});
var circ = brd.create('circle',[p0,p1],{fillColor:'#fefd4c',highlightFillColor:'#fefd4c',fillOpacity:0.5,highlightFillOpacity:0.5,strokeColor:'black',highlightStrokeColor:'black'});
var cIn = brd.create('curve',[[0,1,2],[0,1,2]],{fillColor:'#d769a3',highlightFillColor:'#d769a3',fillOpacity:1,highlightFillOpacity:1,strokeColor:'black',highlightStrokeColor:'black'});

var tCirc = brd.create('text',[-5,-4.0,function(){
    return 'Area of the circle = ' + (0.0625*circ.getRadius()*circ.getRadius()*Math.PI).toFixed(5);
  }],{fontSize:20});
var tIn = brd.create('text',[-5,-4.5,function(){
    return 'Area of the inscribed ' +n.Value().toFixed(0)+ '-polygon = ' + (0.0625*n.Value()*circ.getRadius()*circ.getRadius()*Math.sin(Math.PI/n.Value())).toFixed(5);
  }],{fontSize:20});
var tOut = brd.create('text',[-5,-5,function(){
    return 'Area of the circumscribed  ' +n.Value().toFixed(0)+ '-polygon = ' + (0.0625*n.Value()*circ.getRadius()*circ.getRadius()*Math.tan(Math.PI/n.Value())).toFixed(5);
  }],{fontSize:20});

cIn.updateDataArray = function() {
  var i, len = n.Value();
  this.dataX = [p0.X()+circ.getRadius()];
  this.dataY = [p0.Y()];
  ptmp.setPositionDirectly(JXG.COORDS_BY_USER, [p0.X()+circ.getRadius(), p0.Y()]);
  for (i=0;i<len;i++) {
    rot.applyOnce(ptmp);
    this.dataX.push(ptmp.X());
    this.dataY.push(ptmp.Y());
  }
}

cOut.updateDataArray = function() {
  var i, len = n.Value();
  var s = circ.getRadius()/Math.cos(Math.PI/n.Value());
  this.dataX = [p0.X()+s];
  this.dataY = [p0.Y()];
  ptmp.setPositionDirectly(JXG.COORDS_BY_USER, [p0.X()+s,p0.Y()]);
  for (i=0;i<len;i++) {
    rot.applyOnce(ptmp);
    this.dataX.push(ptmp.X());
    this.dataY.push(ptmp.Y());
  }
}

brd.update();
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