Difference between revisions of "Bezier curves II"

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Here, the Bezier curve together with its scaffolds is shown. The black points are always the midpoints of their line segment.
 
Here, the Bezier curve together with its scaffolds is shown. The black points are always the midpoints of their line segment.
 
<jsxgraph width="600" height="600">
 
<jsxgraph width="600" height="600">
 +
JXG.Options.renderer = "canvas";
 
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-4,4,4,-4],keepaspectratio:true,axis:true});
 
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-4,4,4,-4],keepaspectratio:true,axis:true});
  
 
var p = []; l = [], m= [];
 
var p = []; l = [], m= [];
  
 +
brd.suspendUpdate();
 
col = 'red';  
 
col = 'red';  
p.push(brd.createElement('point',[2,1],{strokeColor:col,fillColor:col}));        // data point
+
p.push(brd.create('point',[2,1],{strokeColor:col,fillColor:col}));        // data point
 
col = 'blue';  
 
col = 'blue';  
p.push(brd.createElement('point',[0.75,2.5],{strokeColor:col,fillColor:col}));  // control point
+
p.push(brd.create('point',[0.75,2.5],{strokeColor:col,fillColor:col}));  // control point
p.push(brd.createElement('point',[-1.5,2.4],{strokeColor:col,fillColor:col}));  // control point
+
p.push(brd.create('point',[-1.5,2.4],{strokeColor:col,fillColor:col}));  // control point
  
 
col = 'red';  
 
col = 'red';  
p.push(brd.createElement('point',[-3,1],{strokeColor:col,fillColor:col}));      // data point
+
p.push(brd.create('point',[-3,1],{strokeColor:col,fillColor:col}));      // data point
  
l.push(brd.createElement('segment',[p[0],p[1]],{strokeOpacity:0.5}));
+
l.push(brd.create('segment',[p[0],p[1]],{strokeOpacity:0.5}));
l.push(brd.createElement('segment',[p[1],p[2]],{strokeOpacity:0.5}));
+
l.push(brd.create('segment',[p[1],p[2]],{strokeOpacity:0.5}));
l.push(brd.createElement('segment',[p[2],p[3]],{strokeOpacity:0.5}));
+
l.push(brd.create('segment',[p[2],p[3]],{strokeOpacity:0.5}));
  
 
col = 'black';  
 
col = 'black';  
m.push(brd.createElement('midpoint',[l[0]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
+
m.push(brd.create('midpoint',[l[0]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
m.push(brd.createElement('midpoint',[l[1]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
+
m.push(brd.create('midpoint',[l[1]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
m.push(brd.createElement('midpoint',[l[2]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
+
m.push(brd.create('midpoint',[l[2]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
  
l.push(brd.createElement('segment',[m[0],m[1]],{strokeOpacity:0.5}));
+
l.push(brd.create('segment',[m[0],m[1]],{strokeOpacity:0.5}));
l.push(brd.createElement('segment',[m[1],m[2]],{strokeOpacity:0.5}));
+
l.push(brd.create('segment',[m[1],m[2]],{strokeOpacity:0.5}));
  
m.push(brd.createElement('midpoint',[l[3]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
+
m.push(brd.create('midpoint',[l[3]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
m.push(brd.createElement('midpoint',[l[4]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
+
m.push(brd.create('midpoint',[l[4]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
  
l.push(brd.createElement('segment',[m[3],m[4]],{strokeOpacity:0.5}));
+
l.push(brd.create('segment',[m[3],m[4]],{strokeOpacity:0.5}));
m.push(brd.createElement('midpoint',[l[5]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
+
m.push(brd.create('midpoint',[l[5]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
  
  
var c = brd.createElement('curve', JXG.Math.Numerics.bezier(p), {strokecolor:'blue', strokeOpacity:0.6, strokeWidth:5});  
+
var c = brd.create('curve', JXG.Math.Numerics.bezier(p), {strokecolor:'blue', strokeOpacity:0.6, strokeWidth:5});
 +
brd.unsuspendUpdate();
 
</jsxgraph>
 
</jsxgraph>
  
 
===The underlying JavaScript code===
 
===The underlying JavaScript code===
 
<source lang="javascript">
 
<source lang="javascript">
 +
JXG.Options.renderer = "canvas";
 +
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-4,4,4,-4],keepaspectratio:true,axis:true});
 +
 +
var p = []; l = [], m= [];
 +
 +
brd.suspendUpdate();
 +
col = 'red';
 +
p.push(brd.create('point',[2,1],{strokeColor:col,fillColor:col}));        // data point
 +
col = 'blue';
 +
p.push(brd.create('point',[0.75,2.5],{strokeColor:col,fillColor:col}));  // control point
 +
p.push(brd.create('point',[-1.5,2.4],{strokeColor:col,fillColor:col}));  // control point
 +
 +
col = 'red';
 +
p.push(brd.create('point',[-3,1],{strokeColor:col,fillColor:col}));      // data point
 +
 +
l.push(brd.create('segment',[p[0],p[1]],{strokeOpacity:0.5}));
 +
l.push(brd.create('segment',[p[1],p[2]],{strokeOpacity:0.5}));
 +
l.push(brd.create('segment',[p[2],p[3]],{strokeOpacity:0.5}));
 +
 +
col = 'black';
 +
m.push(brd.create('midpoint',[l[0]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
 +
m.push(brd.create('midpoint',[l[1]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
 +
m.push(brd.create('midpoint',[l[2]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
 +
 +
l.push(brd.create('segment',[m[0],m[1]],{strokeOpacity:0.5}));
 +
l.push(brd.create('segment',[m[1],m[2]],{strokeOpacity:0.5}));
 +
 +
m.push(brd.create('midpoint',[l[3]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
 +
m.push(brd.create('midpoint',[l[4]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
 +
 +
l.push(brd.create('segment',[m[3],m[4]],{strokeOpacity:0.5}));
 +
m.push(brd.create('midpoint',[l[5]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
 +
 +
 +
var c = brd.create('curve', JXG.Math.Numerics.bezier(p), {strokecolor:'blue', strokeOpacity:0.6, strokeWidth:5});
 +
brd.unsuspendUpdate();
 +
 
</source>
 
</source>
  
 
[[Category:Examples]]
 
[[Category:Examples]]
 
[[Category:Curves]]
 
[[Category:Curves]]
 +
[[Category:Interpolation]]

Latest revision as of 10:18, 18 January 2021

The red points are connected by a cubic Bezier curve. The blue points are the control points.

Here, the Bezier curve together with its scaffolds is shown. The black points are always the midpoints of their line segment.

The underlying JavaScript code

JXG.Options.renderer = "canvas";
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-4,4,4,-4],keepaspectratio:true,axis:true});

var p = []; l = [], m= [];

brd.suspendUpdate();
col = 'red'; 
p.push(brd.create('point',[2,1],{strokeColor:col,fillColor:col}));        // data point
col = 'blue'; 
p.push(brd.create('point',[0.75,2.5],{strokeColor:col,fillColor:col}));   // control point
p.push(brd.create('point',[-1.5,2.4],{strokeColor:col,fillColor:col}));   // control point

col = 'red'; 
p.push(brd.create('point',[-3,1],{strokeColor:col,fillColor:col}));       // data point

l.push(brd.create('segment',[p[0],p[1]],{strokeOpacity:0.5}));
l.push(brd.create('segment',[p[1],p[2]],{strokeOpacity:0.5}));
l.push(brd.create('segment',[p[2],p[3]],{strokeOpacity:0.5}));

col = 'black'; 
m.push(brd.create('midpoint',[l[0]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
m.push(brd.create('midpoint',[l[1]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
m.push(brd.create('midpoint',[l[2]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));

l.push(brd.create('segment',[m[0],m[1]],{strokeOpacity:0.5}));
l.push(brd.create('segment',[m[1],m[2]],{strokeOpacity:0.5}));

m.push(brd.create('midpoint',[l[3]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));
m.push(brd.create('midpoint',[l[4]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));

l.push(brd.create('segment',[m[3],m[4]],{strokeOpacity:0.5}));
m.push(brd.create('midpoint',[l[5]],{face:'o',size:1,strokeColor:col,fillColor:col, name:''}));


var c = brd.create('curve', JXG.Math.Numerics.bezier(p), {strokecolor:'blue', strokeOpacity:0.6, strokeWidth:5}); 
brd.unsuspendUpdate();