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<html>
<head>
<title>JSXGraph example</title>
<link rel="stylesheet" type="text/css" href="../distrib/jsxgraph.css" />
<script type="text/javascript" src="/javascript/jquery/jquery.min.js"></script>
<script type="text/javascript" src="../distrib/jsxgraphcore.js"></script>
</head>
<body>
<h2>Create a point with simple clicks. Uses jQuery via Google CDN.</h2>
<div style="width:800px">
<div id="jxgbox" class="jxgbox" style="width:800px; height:800px; float:left; background-image:url(medsand.gif);"></div>
</div>
<div id="debug" style="display:block;"></div>
<script type="text/javascript">
/* <![CDATA[ */
(function() {
JXG.Options.renderer = 'canvas';
var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-10, 10, 10, -10], axis:false, grid:true}),
//
// bestFit, the best-fitting circle or line is found by least-squares fitting.
//
bestFit = function(p, testOnly) {
var i, angle, co, si,
delta = 0.8,
isLine = false,
M = [], y = [], MT, B, c, z, n, d, xm, ym, r;
// Having constructed the points, we can fit a circle
// through the point set, consisting of n points.
// The (n times 3) matrix consists of
// x_1, y_1, 1
// x_2, y_2, 1
// ...
// x_n, y_n, 1
// where x_i, y_i is the position of point p_i
// The vector y of length n consists of
// x_i*x_i+y_i*y_i
// for i=1,...n.
n = p.length;
for (i=0;i<n;i++) {
M.push([p[i].length ? p[i][0] : p[i].X(), p[i].length ? p[i][1] : p[i].Y(), 1.0]);
y.push(M[i][0]*M[i][0]+M[i][1]*M[i][1]);
}
// Now, the general linear least-square fitting problem
// min_z || M*z - y||_2^2
// is solved by solving the system of linear equations
// (M^T*M) * z = (M^T*y)
// with Gauss elimination.
MT = JXG.Math.transpose(M);
B = JXG.Math.matMatMult(MT, M);
c = JXG.Math.matVecMult(MT, y);
if (Math.abs(JXG.Math.Numerics.det(B))<Math.sqrt(JXG.Math.eps)) {
isLine = true;
} else {
z = JXG.Math.Numerics.Gauss(B, c);
xm = z[0]*0.5;
ym = z[1]*0.5; // xm, ym : center of the circle
r = Math.sqrt(z[2]+xm*xm+ym*ym); // r: radius
d = JXG.Math.Geometry.distance(points[0], points[points.length-1]);
if (r>20) {
//if (r*Math.sqrt(board.stretchX*board.stretchX+board.stretchY*board.stretchY)>500) {
isLine = true;
}
}
if (isLine) {
if (!testOnly)
board.create('line',[points[0], points[points.length-1]], {strokeColor:'green'});
} else {
if (!testOnly)
board.create('circle', [[xm,ym],r]);
}
return isLine;
}, // End of bestFit
/*
bestFitOld = function(p) {
var i, j, r = [], rbar = [], A = [
[0,0,0],
[0,0,0],
[0,0,0]
], n, d,
eigen, minIndex, minE, ev, c, xm, ym, zm, den, nom, radius;
n = p.length;
for (i = 0; i < n; i++) {
r.push([1.0, p[i].length ? p[i][0] : p[i].X(), p[i].length ? p[i][1] : p[i].Y()]);
d = r[i][0] * r[i][0] + r[i][1] * r[i][1] + r[i][2] * r[i][2];
r[i][0] = 1 - r[i][0] / d;
r[i][1] /= d;
r[i][2] /= d;
}
for (j = 0; j < 3; j++) {
for (i = 0,d = 0; i < n; i++) {
d += r[i][j];
}
d /= n;
rbar[j] = d;
for (i = 0; i < n; i++) {[zm,xm,ym]
r[i][j] -= d;
}
}
for (i = 0; i < n; i++) {
A[0][0] += r[i][0] * r[i][0];
A[0][1] += r[i][0] * r[i][1];
A[0][2] += r[i][0] * r[i][2];
A[1][0] += r[i][1] * r[i][0];
A[1][1] += r[i][1] * r[i][1];
A[1][2] += r[i][1] * r[i][2];
A[2][0] += r[i][2] * r[i][0];
A[2][1] += r[i][2] * r[i][1];
A[2][2] += r[i][2] * r[i][2];
}
eigen = JXG.Math.Numerics.Jacobi(A);
minIndex = 0;
minE = eigen[0][0][0];
for (j = 1; j < 3; j++) {
if (eigen[0][j][j] < minE) {
minIndex = j;
minE = eigen[0][j][j];
}
}
ev = [eigen[1][0][minIndex],eigen[1][1][minIndex],eigen[1][2][minIndex]];
d = Math.sqrt(ev[0]*ev[0] + ev[1]*ev[1] + ev[2]*ev[2]);
ev[0] /= d;
ev[1] /= d;
ev[2] /= d;
c = -(rbar[0] * ev[0] + rbar[1] * ev[1] + rbar[2] * ev[2]);
xm = -ev[1];
ym = -ev[2];
zm = 2.0 * (c + ev[0]);
// If c is close to zero, the best fittting object is a line.
// The best threshold parameter has yet to be determined.
// At the moment it is set to 0.01.
nom = xm * xm + ym * ym - 2.0 * c * zm;
den = zm * zm;
//console.log(c, zm, ev, rbar);
//console.log(nom, 500.0*Math.abs(den));
if (Math.abs(nom) > 500.0*Math.abs(den)) {
board.create('line',[points[0], points[points.length-1]], {strokeColor:'green'});
//board.create('line', [ev[0],xm,ym], {strokeColor:'green'});
} else {
radius = Math.sqrt((xm * xm + ym * ym - 2.0 * c * zm) / (zm * zm));
board.create('circle', [
[zm,xm,ym],
radius
]);
}
}, // end of bestFit()
*/
getMouseCoords = function(e) {
if (!document.all) { // not IE
var em = document.createEvent('MouseEvents'), i = 0;
if(e.targetTouches) { // always false
em.initMouseEvent('mousedown', true, false, this.containerObj, 0,
e.targetTouches[i].screenX, e.targetTouches[i].screenY,
e.targetTouches[i].clientX, e.targetTouches[i].clientY,
false, false, false, false, 0, null);
e = em;
}
}
var cPos = board.getCoordsTopLeftCorner(e),
absPos = JXG.getPosition(e),
dx = absPos[0]-cPos[0],
dy = absPos[1]-cPos[1];
return new JXG.Coords(JXG.COORDS_BY_SCREEN, [dx, dy], board);
},
mousedown,
points = [];
var draftcurve = board.create('curve',[[0],[0]],{curveType:'plot', strokeWidth:14, opacity:0.15});
draftcurve.updateDataArray = function() {
if (points.length<=0) return;
var p = JXG.Math.transpose(points);
this.dataX = p[0];
this.dataY = p[1];
};
draftcurve.highlight = function() {};
draftcurve.noHighlight = function() {};
var down = function(e) {
var coords = getMouseCoords(e),
i;
if(e.shiftKey)
return;
mousedown = true;
for(i in board.objects) {
if(JXG.isPoint(board.objects[i]) && board.objects[i].hasPoint(coords.scrCoords[1], coords.scrCoords[2])) {
mousedown = false;
break;
}
}
if(!mousedown)
return;
points = [];
points.push(coords.usrCoords.slice(1));
draftcurve.prepareUpdate().update().updateRenderer();
// prevent accidental text selection
if (e && e.preventDefault) {
e.preventDefault();
} else {
window.event.returnValue = false;
}
};
var move = function(e, m) {
if(mousedown) {
points.push(getMouseCoords(e).usrCoords.slice(1));
draftcurve.prepareUpdate().update().updateRenderer();
draftcurve.setProperty({strokeColor: (bestFit(points,true))?'green':'blue'});
}
};
var up = function(e){
if((e.fromTouch && points.length==1) || (!e.fromTouch && points.length<=15))
board.create('point', points[0], {fillColor:'#000000', fillOpacity:0.8, strokeWidth:0, size:4 });
else
bestFit(points, false);
mousedown = false;
points = [];
};
board.addHook(down, 'mousedown');
board.addHook(move, 'mousemove');
board.addHook(up, 'mouseup');
})();
/* ]]> */
</script>
</body>
</html>
|
