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Curve - line intersection

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hkrish 2013-05-12 15:12:53 +02:00
parent 6064d73379
commit fed2a73903
1 changed files with 42 additions and 0 deletions
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fatline/Intersect.js
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@ -487,3 +487,45 @@ var _getSignedDist = function( a1x, a1y, a2x, a2y, bx, by ){
return side * Math.min( dist, dista1, dista2 );
};
/**
* Intersections between curve and line becomes rather simple here mostly
* because of paperjs Numerical class. We can rotate the curve and line so that
* the line is on X axis, and solve the implicit equations for X axis and the curve
*/
var _getCurveLineIntersection = function( vc, vl, curve1, curve2, locations ){
var i, root, point;
var l1x = vl[0], l1y = vl[1], l2x = vl[6], l2y = vl[7];
// rotate both the curve and line around l1 so that line is on x axis
var lvx = l2x - l1x, lvy = l2y - l1y;
// Angle with x axis (1, 0)
var angle = Math.atan2( -lvy, lvx ), sina = Math.sin( angle ), cosa = Math.cos( angle );
// rotated line and curve values
// (rl1x, rl1y) = (0, 0)
var rl2x = lvx * cosa - lvy * sina, rl2y = lvy * cosa + lvx * sina;
var rvc = [];
for( i=0; i<8; i+=2 ){
var vcx = vc[i] - l1x, vcy = vc[i+1] - l1y;
rvc.push( vcx * cosa - vcy * sina );
rvc.push( vcy * cosa + vcx * sina );
}
var roots = [];
Curve.solveCubic(rvc, 1, 0, roots);
i = roots.length;
while( i-- ){
root = roots[i];
if( root >= 0 && root <= 1 ){
point = Curve.evaluate(rvc, root, true, 0);
// We do have a point on the infinite line. Check if it falls on the line *segment*.
if( point.x >= 0 && point.x <= rl2x ){
// The actual intersection point
point = curve1.getPointAt( root, true );
var first = locations[0],
last = locations[locations.length - 1];
if ((!first || !point.equals(first._point))
&& (!last || !point.equals(last._point)))
locations.push( new CurveLocation( curve1, root, point, curve2 ) );
}
}
}
};