Bezier curves II: Difference between revisions
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The red points are connected by a cubic Bezier curve. The blue points are the control points. | 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. | |||
<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 = []; | 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.createElement('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.createElement('point',[0.75,2.5],{strokeColor:col,fillColor:col})); // control point | ||
p.push(brd.createElement('point',[- | p.push(brd.createElement('point',[-1.5,2.4],{strokeColor:col,fillColor:col})); // control point | ||
col = 'red'; | col = 'red'; | ||
Line 15: | Line 19: | ||
l.push(brd.createElement('segment',[p[0],p[1]],{strokeOpacity:0.5})); | 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}); | var c = brd.createElement('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"> | ||
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(); | |||
</source> | </source> | ||
[[Category:Examples]] | [[Category:Examples]] | ||
[[Category:Curves]] | [[Category:Curves]] | ||
[[Category:Interpolation]] |
Revision as of 12:35, 7 July 2011
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();