Difference between revisions of "Bezier curves II"

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Line 10: Line 10:
 
brd.suspendUpdate();
 
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();
 
brd.unsuspendUpdate();
 
</jsxgraph>
 
</jsxgraph>
Line 43: Line 43:
 
===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 brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-4,4,4,-4],keepaspectratio:true,axis:true});
  
Line 49: Line 50:
 
brd.suspendUpdate();
 
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();
 
brd.unsuspendUpdate();
 +
 
</source>
 
</source>
  

Latest revision as of 11:18, 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();