Circular arc approximation by cubic Bezier curve - Revision history

A WASSERMANN at 20:31, 1 July 2012

2012-07-01T20:31:50Z

← Older revision		Revision as of 20:31, 1 July 2012
Line 1:		Line 1:
	Approximating a circular by a single ~~bezier~~ curve only is sufficiently exakt if the arc is less or equal than a quarter circle.		Approximating a circular by a single Bezier curve only is sufficiently exakt if the arc is less or equal than a quarter circle.
	<jsxgraph width="600" height="600">		<jsxgraph width="600" height="600">
	var brd = JXG.JSXGraph.initBoard('jxgbox',{axis:false,boundingbox:[-2,2,2,-2],keepaspectratio:true});		var brd = JXG.JSXGraph.initBoard('jxgbox',{axis:false,boundingbox:[-2,2,2,-2],keepaspectratio:true});

2012-07-01T12:59:50Z

← Older revision		Revision as of 12:59, 1 July 2012
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	function(){ return A.X()-k(M,A,B)*(A.Y()-M.Y()); },		function(){ return A.X()-k(M,A,B)*(A.Y()-M.Y()); },
	function(){ return A.Y()+k(M,A,B)*(A.X()-M.X()); }		function(){ return A.Y()+k(M,A,B)*(A.X()-M.X()); }
	], {});		], {color:'blue'});
	var P2 = brd.create('point', [		var P2 = brd.create('point', [
	function(){ return B.X()+k(M,A,B)*(B.Y()-M.Y()); },		function(){ return B.X()+k(M,A,B)*(B.Y()-M.Y()); },
	function(){ return B.Y()-k(M,A,B)*(B.X()-M.X()); }		function(){ return B.Y()-k(M,A,B)*(B.X()-M.X()); }
	], {});		], {color:'blue'});

	var b = brd.create('curve', JXG.Math.Numerics.bezier([A,P1,P2,B]),		var b = brd.create('curve', JXG.Math.Numerics.bezier([A,P1,P2,B]),
	{strokecolor:'black', strokeOpacity:1, strokeWidth:3});		{strokecolor:'black', strokeOpacity:1, strokeWidth:3});

			var l1 = brd.create('segment', [A,P1], {dash:2});
			var l2 = brd.create('segment', [B,P2], {dash:2});

	</jsxgraph>		</jsxgraph>

2012-07-01T12:59:05Z

← Older revision		Revision as of 12:59, 1 July 2012
Line 69:		Line 69:
	function(){ return A.X()-k(M,A,B)*(A.Y()-M.Y()); },		function(){ return A.X()-k(M,A,B)*(A.Y()-M.Y()); },
	function(){ return A.Y()+k(M,A,B)*(A.X()-M.X()); }		function(){ return A.Y()+k(M,A,B)*(A.X()-M.X()); }
	], {});		], {color:'blue'});
	var P2 = brd.create('point', [		var P2 = brd.create('point', [
	function(){ return B.X()+k(M,A,B)*(B.Y()-M.Y()); },		function(){ return B.X()+k(M,A,B)*(B.Y()-M.Y()); },
	function(){ return B.Y()-k(M,A,B)*(B.X()-M.X()); }		function(){ return B.Y()-k(M,A,B)*(B.X()-M.X()); }
	], {});		], {color:'blue'});

	var b = brd.create('curve', JXG.Math.Numerics.bezier([A,P1,P2,B]),		var b = brd.create('curve', JXG.Math.Numerics.bezier([A,P1,P2,B]),
	{strokecolor:'black', strokeOpacity:1, strokeWidth:3});		{strokecolor:'black', strokeOpacity:1, strokeWidth:3});


			var l1 = brd.create('segment', [A,P1], {dash:2});
			var l2 = brd.create('segment', [B,P2], {dash:2});
	</source>		</source>
	[[Category:Examples]]		[[Category:Examples]]
	[[Category:Curves]]		[[Category:Curves]]
	[[Category:Interpolation]]		[[Category:Interpolation]]

2012-07-01T12:56:53Z

@@ Line 1: / Line 1: @@
 <jsxgraph width="600" height="600">
 var brd = JXG.JSXGraph.initBoard('jxgbox',{axis:false,boundingbox:[-2,2,2,-2],keepaspectratio:true});
@@ Line 40: / Line 41: @@
 ===The underlying JavaScript code===
 [[Category:Examples]]
 [[Category:Curves]]
 [[Category:Interpolation]]

2012-07-01T12:53:52Z

← Older revision		Revision as of 12:53, 1 July 2012
Line 16:		Line 16:
	r = M.Dist(A);		r = M.Dist(A);
	d = Math.sqrt((ax+bx)(ax+bx) + (ay+by)(ay+by));		d = Math.sqrt((ax+bx)(ax+bx) + (ay+by)(ay+by));
	if (JXG.Math.Geometry.rad(A,M,B)>Math.PI) { d *= 1; }		if (JXG.Math.Geometry.rad(A,M,B)>Math.PI) { d *= -1; }

	if (Math.abs(by-ay)>JXG.Math.eps) {		if (Math.abs(by-ay)>JXG.Math.eps) {

2012-07-01T12:53:20Z

← Older revision		Revision as of 12:53, 1 July 2012
Line 16:		Line 16:
	r = M.Dist(A);		r = M.Dist(A);
	d = Math.sqrt((ax+bx)(ax+bx) + (ay+by)(ay+by));		d = Math.sqrt((ax+bx)(ax+bx) + (ay+by)(ay+by));
	if (JXG.Math.~~Gemetry~~.rad(A,M,B)>Math.PI) { d *= 1; }		if (JXG.Math.Geometry.rad(A,M,B)>Math.PI) { d *= 1; }

	if (Math.abs(by-ay)>JXG.Math.eps) {		if (Math.abs(by-ay)>JXG.Math.eps) {

2012-07-01T12:52:53Z

← Older revision		Revision as of 12:52, 1 July 2012
Line 16:		Line 16:
	r = M.Dist(A);		r = M.Dist(A);
	d = Math.sqrt((ax+bx)(ax+bx) + (ay+by)(ay+by));		d = Math.sqrt((ax+bx)(ax+bx) + (ay+by)(ay+by));
	if (JXG.Math.rad(A,M,B)>Math.PI) { d *= 1; }		if (JXG.Math.Gemetry.rad(A,M,B)>Math.PI) { d *= 1; }

	if (Math.abs(by-ay)>JXG.Math.eps) {		if (Math.abs(by-ay)>JXG.Math.eps) {

2012-07-01T12:51:58Z

← Older revision		Revision as of 12:51, 1 July 2012
Line 16:		Line 16:
	r = M.Dist(A);		r = M.Dist(A);
	d = Math.sqrt((ax+bx)(ax+bx) + (ay+by)(ay+by));		d = Math.sqrt((ax+bx)(ax+bx) + (ay+by)(ay+by));
			if (JXG.Math.rad(A,M,B)>Math.PI) { d *= 1; }

	if (Math.abs(by-ay)>JXG.Math.eps) {		if (Math.abs(by-ay)>JXG.Math.eps) {

2012-07-01T12:41:53Z

← Older revision		Revision as of 12:41, 1 July 2012
Line 16:		Line 16:
	r = M.Dist(A);		r = M.Dist(A);
	d = Math.sqrt((ax+bx)(ax+bx) + (ay+by)(ay+by));		d = Math.sqrt((ax+bx)(ax+bx) + (ay+by)(ay+by));
	~~return 0.5;~~
	if (Math.abs(by-ay)>JXG.Math.eps) {		if (Math.abs(by-ay)>JXG.Math.eps) {
	return (ax+bx)(r/d-0.5)8.0/3.0/(by-ay);		return (ax+bx)(r/d-0.5)8.0/3.0/(by-ay);

2012-07-01T12:40:45Z

← Older revision		Revision as of 12:40, 1 July 2012
Line 16:		Line 16:
	r = M.Dist(A);		r = M.Dist(A);
	d = Math.sqrt((ax+bx)(ax+bx) + (ay+by)(ay+by));		d = Math.sqrt((ax+bx)(ax+bx) + (ay+by)(ay+by));
			return 0.5;
	if (~~false &&~~ Math.abs(by-ay)>JXG.Math.eps) {		if (Math.abs(by-ay)>JXG.Math.eps) {
	return (ax+bx)(r/d-0.5)8.0/3.0/(by-ay);		return (ax+bx)(r/d-0.5)8.0/3.0/(by-ay);
	} else {		} else {