Bezier curves II

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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

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.createElement('point',[2,1],{strokeColor:col,fillColor:col}));        // data point
col = 'blue'; 
p.push(brd.createElement('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

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

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

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

l.push(brd.createElement('segment',[m[3],m[4]],{strokeOpacity:0.5}));
m.push(brd.createElement('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}); 
brd.unsuspendUpdate();