Bezier curves II: Difference between revisions

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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 09:18, 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();