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@hkrish
hkrish committed May 10, 2013
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127 changes: 41 additions & 86 deletions Intersect.js
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Original file line number Diff line number Diff line change
@@ -1,16 +1,12 @@


var EPSILON = 10e-12;
var TOLERANCE = 10e-6;

var _tolerence = TOLERANCE;

function getIntersections2( path1, path2 ){
var locations = [];
return locations;
}


paper.Curve.getIntersections2 = function( v1, v2, curve1, curve2, locations, _v1t, _v2t ) {
// cache the original parameter range.
_v1t = _v1t || { t1: 0, t2: 1 };
Expand All @@ -20,13 +16,12 @@ paper.Curve.getIntersections2 = function( v1, v2, curve1, curve2, locations, _v1
// Get the clipped parts from the original curve, to avoid cumulative errors
var _v1 = Curve.getPart( v1, v1t.t1, v1t.t2 );
var _v2 = Curve.getPart( v2, v2t.t1, v2t.t2 );
// markCurve( _v1, '#f0f', true );
// markCurve( _v2, '#0ff', false );
// markCurve( _v1, '#f0f', true );
// markCurve( _v2, '#0ff', false );
var nuT, parts, tmpt = { t1:null, t2:null };
// Loop until one of the parameter range converges. We have to handle the degenerate case
// Loop until both parameter range converge. We have to handle the degenerate case
// seperately, where fat-line clipping can become numerically unstable when one of the
// curves has converged to a point and the other hasn't.
// TODO: May be it is a good idea to limit the loop by say 100 times?!
while( Math.abs(v1t.t2 - v1t.t1) > _tolerence || Math.abs(v2t.t2 - v2t.t1) > _tolerence ){
// while( !(v1t.t1 >= v1t.t2 - _tolerence && v1t.t1 <= v1t.t2 + _tolerence) ||
// !(v2t.t1 >= v2t.t2 - _tolerence && v2t.t1 <= v2t.t2 + _tolerence) ){
Expand All @@ -41,7 +36,7 @@ paper.Curve.getIntersections2 = function( v1, v2, curve1, curve2, locations, _v1
v2t.t1 = tmpt.t1; v2t.t2 = tmpt.t2;
_v2 = Curve.getPart( v2, v2t.t1, v2t.t2 );
}
// markCurve( _v2, '#0ff', false );
// markCurve( _v2, '#0ff', false );
// Next we clip v1 with nuv2's fat-line
tmpt.t1 = v1t.t1; tmpt.t2 = v1t.t2;
var intersects2 = _clipBezierFatLine( _v2, _v1, tmpt );
Expand All @@ -53,25 +48,21 @@ paper.Curve.getIntersections2 = function( v1, v2, curve1, curve2, locations, _v1
v1t.t1 = tmpt.t1; v1t.t2 = tmpt.t2;
_v1 = Curve.getPart( v1, v1t.t1, v1t.t2 );
}
// markCurve( _v1, '#f0f', true );
// markCurve( _v1, '#f0f', true );
// Get the clipped parts from the original v1
// Check if there could be multiple intersections
if( intersects1 < 0 || intersects2 < 0 ){
// console.log("subdiv")
// Subdivide the curve which has converged the least from the original range [0,1],
// which would be the curve with the largest parameter range after clipping
if( v1t.t2 - v1t.t1 > v2t.t2 - v2t.t1 ){
// subdivide _v1 and recurse
// nuT = ( v1t.t1 + v1t.t2 ) / 2.0;
nuT = ( _v1t.t1 + _v1t.t2 ) / 2.0;
// parts = Curve.subdivide( _v1, nuT );
Curve.getIntersections2( v1, v2, curve1, curve2, locations, { t1: _v1t.t1, t2: nuT }, _v2t );
Curve.getIntersections2( v1, v2, curve1, curve2, locations, { t1: nuT, t2: _v1t.t2 }, _v2t );
return;
} else {
// subdivide _v2 and recurse
nuT = ( _v2t.t1 + _v2t.t2 ) / 2.0;
// parts = Curve.subdivide( _v2, nuT );
Curve.getIntersections2( v1, v2, curve1, curve2, locations, _v1t, { t1: _v2t.t1, t2: nuT } );
Curve.getIntersections2( v1, v2, curve1, curve2, locations, _v1t, { t1: nuT, t2: _v2t.t2 } );
return;
Expand All @@ -89,11 +80,6 @@ paper.Curve.getIntersections2 = function( v1, v2, curve1, curve2, locations, _v1
//!code from: paperjs#Curve.getIntersections method
if ( Curve.isFlatEnough(_v1, _tolerence)
&& Curve.isFlatEnough(_v2, _tolerence) ) {
// var point = _intersectLines(
// [_v1[0], _v1[1], _v1[6], _v1[7]],
// [_v2[0], _v2[1], _v2[6], _v2[7]]);
// DEBUG: @jlehni - Line.intersect returns undefined when the
// lines are very close to tolerence but still larger than tolerence
var point = Line.intersect(
_v1[0], _v1[1], _v1[6], _v1[7],
_v2[0], _v2[1], _v2[6], _v2[7], false);
Expand Down Expand Up @@ -124,15 +110,14 @@ paper.Curve.getIntersections2 = function( v1, v2, curve1, curve2, locations, _v1
* @return {number} -> 0 -no Intersection, 1 -one intersection, -1 -more than one intersection
*/
function _clipBezierFatLine( v1, v2, v2t ){
var p0x = v1[0], p0y = v1[1];
var p3x = v1[6], p3y = v1[7];
var p1x = v1[2], p1y = v1[3];
var p2x = v1[4], p2y = v1[5];
var q0x = v2[0], q0y = v2[1];
var q3x = v2[6], q3y = v2[7];
var q1x = v2[2], q1y = v2[3];
var q2x = v2[4], q2y = v2[5];
// Calculate the fat-line L
// first curve, P
var p0x = v1[0], p0y = v1[1], p3x = v1[6], p3y = v1[7];
var p1x = v1[2], p1y = v1[3], p2x = v1[4], p2y = v1[5];
// second curve, Q
var q0x = v2[0], q0y = v2[1], q3x = v2[6], q3y = v2[7];
var q1x = v2[2], q1y = v2[3], q2x = v2[4], q2y = v2[5];
// Calculate the fat-line L for P is the baseline l and two
// offsets which completely encloses the curve P.
var d1 = _getSignedDist( p0x, p0y, p3x, p3y, p1x, p1y );
var d2 = _getSignedDist( p0x, p0y, p3x, p3y, p2x, p2y );
var dmin, dmax;
Expand All @@ -145,26 +130,21 @@ function _clipBezierFatLine( v1, v2, v2t ){
dmin = 0.4444444444444444 * Math.min( 0, d1, d2 );
dmax = 0.4444444444444444 * Math.max( 0, d1, d2 );
}
// The convex hull for the non-parametric bezier curve D(ti, di(t))
// Calculate non-parametric bezier curve D(ti, di(t)) -
// di(t) is the distance of Q from the baseline l of the fat-line,
// ti is equally spaced in [0,1]
var dq0 = _getSignedDist( p0x, p0y, p3x, p3y, q0x, q0y );
var dq1 = _getSignedDist( p0x, p0y, p3x, p3y, q1x, q1y );
var dq2 = _getSignedDist( p0x, p0y, p3x, p3y, q2x, q2y );
var dq3 = _getSignedDist( p0x, p0y, p3x, p3y, q3x, q3y );
// Find the minimum and maximum distances from L',
// this is useful for checking whether the curves intersect wit each other or not.
// Find the minimum and maximum distances from l,
// this is useful for checking whether the curves intersect with each other or not.
var mindist = Math.min( dq0, dq1, dq2, dq3 );
var maxdist = Math.max( dq0, dq1, dq2, dq3 );
// If the fatlines don't overlap, we have no intersections!
// TODO: check if this is better or trying out intersections with the convex hull is better
if( dmin > maxdist || dmax < mindist ){
return 0;
}
// if non-paramertic curve has a negative slope, swap dmin and dmax
// if( dq3 < dq0 ){
// d1 = dmin;
// dmin = dmax;
// dmax = d1;
// }
// Calculate the convex hull for non-parametric bezier curve D(ti, di(t))
var Dt = _convexhull( dq0, dq1, dq2, dq3 );
// Now we clip the convex hulls for D(ti, di(t)) with dmin and dmax
Expand All @@ -173,36 +153,29 @@ function _clipBezierFatLine( v1, v2, v2t ){
// TODO: try to calculate tmin and tmax directly here
var tmindmin = Infinity, tmaxdmin = -Infinity,
tmindmax = Infinity, tmaxdmax = -Infinity, ixd, ixdx, i, len;
var dmina = [0, dmin, 2, dmin];
var dmaxa = [0, dmax, 2, dmax];
// var dmina = [0, dmin, 2, dmin];
// var dmaxa = [0, dmax, 2, dmax];
for (i = 0, len = Dt.length; i < len; i++) {
var Dtl = Dt[i];
// ixd = Dtl.intersect( vecdmin );
ixd = _intersectLines( Dtl, dmina);
// ixd = _intersectLines( Dtl, dmina);
ixd = Line.intersect( Dtl[0], Dtl[1], Dtl[2], Dtl[3], 0, dmin, 2, dmin, false);
if( ixd ){
ixdx = ixd[0];
ixdx = ixd.x;
tmindmin = ( ixdx < tmindmin )? ixdx : tmindmin;
tmaxdmin = ( ixdx > tmaxdmin )? ixdx : tmaxdmin;
}
// ixd = Dtl.intersect( vecdmax );
ixd = _intersectLines( Dtl, dmaxa);
// ixd = _intersectLines( Dtl, dmaxa);
ixd = Line.intersect( Dtl[0], Dtl[1], Dtl[2], Dtl[3], 0, dmax, 2, dmax, false);
if( ixd ){
ixdx = ixd[0];
ixdx = ixd.x;
tmindmax = ( ixdx < tmindmax )? ixdx : tmindmax;
tmaxdmax = ( ixdx > tmaxdmax )? ixdx : tmaxdmax;
}
}
// // If dmin AND dmax did not intersect with the convexhull,
// // it's time for us to stop. There are no intersections in this case.
// // DEBUG: If dmin, dmax completely enclose the hull, we may need to subdivide!
// if( tmindmin === Infinity && tmaxdmin === -Infinity &&
// tmindmax === Infinity && tmaxdmax === -Infinity ) {
// return 0;
// }
// if dmin doesnot intersect with the convexhull, reset it to 0
// if dmin doesnot intersect with the convexhull, reset the parameter limits to 0
tmindmin = ( tmindmin === Infinity )? 0 : tmindmin;
tmaxdmin = ( tmaxdmin === -Infinity )? 0 : tmaxdmin;
// if dmax doesnot intersect with the convexhull, reset it to 1
// if dmax doesnot intersect with the convexhull, reset the parameter limits to 1
tmindmax = ( tmindmax === Infinity )? 1 : tmindmax;
tmaxdmax = ( tmaxdmax === -Infinity )? 1 : tmaxdmax;
// Return the parameter values for v2 for which we can be sure that the
Expand All @@ -223,15 +196,12 @@ function _clipBezierFatLine( v1, v2, v2t ){
if( Math.max( tmindmax, tmaxdmax ) > tmax )
tmax = 1;
}
// tmin = Math.min( tmindmin, tmaxdmin, tmindmax, tmaxdmax );
// tmax = Math.max( tmindmin, tmaxdmin, tmindmax, tmaxdmax );
// Debug: Plot the non-parametric graph and hull
// plotD_vs_t( 500, 110, Dt, [dq0, dq1, dq2, dq3], v1, dmin, dmax, tmin, tmax, 1.0 / ( tmax - tmin + 0.3 ) )
// Debug: Plot the non-parametric graph and hull
// plotD_vs_t( 500, 110, Dt, [dq0, dq1, dq2, dq3], v1, dmin, dmax, tmin, tmax, 1.0 / ( tmax - tmin + 0.3 ) )
// tmin and tmax are within the range (0, 1). We need to project it to the original
// parameter range for v2.
var v2tmin = v2t.t1;
var tdiff = ( v2t.t2 - v2tmin );
// Set the new parameter range
v2t.t1 = v2tmin + tmin * tdiff;
v2t.t2 = v2tmin + tmax * tdiff;
// If the new parameter range fails to converge by atleast 20% of the original range,
Expand All @@ -249,7 +219,7 @@ function _convexhull( dq0, dq1, dq2, dq3 ){
// Check if [1/3, dq1] and [2/3, dq2] are on the same side of line [0,dq0, 1,dq3]
if( distq1 * distq2 < 0 ) {
// dq1 and dq2 lie on different sides on [0, q0, 1, q3]
// Convexhull is a quadrilatteral and line [0, q0, 1, q3] is NOT part of the convexhull
// Convexhull is a quadrilateral and line [0, q0, 1, q3] is NOT part of the convexhull
// so we are pretty much done here.
Dt = [
[ 0.0, dq0, 0.3333333333333333, dq1 ],
Expand All @@ -259,9 +229,9 @@ function _convexhull( dq0, dq1, dq2, dq3 ){
];
} else {
// dq1 and dq2 lie on the same sides on [0, q0, 1, q3]
// Convexhull can be a triangle or a quadrilatteral and
// Convexhull can be a triangle or a quadrilateral and
// line [0, q0, 1, q3] is part of the convexhull.
// Check if the hull is a triangle or a quadrilatteral
// Check if the hull is a triangle or a quadrilateral
var dqmin, dqmax, dqapex1, dqapex2;
distq1 = Math.abs(distq1);
distq2 = Math.abs(distq2);
Expand Down Expand Up @@ -300,7 +270,7 @@ function _convexhull( dq0, dq1, dq2, dq3 ){
[ 1.0, dq3, 0.0, dq0 ]
];
} else {
// Convexhull is a quadrilatteral and we need all lines in the correct order where
// Convexhull is a quadrilateral and we need all lines in the correct order where
// line [0, q0, 1, q3] is part of the convex hull
Dt = [
[ 0.0, dq0, 0.3333333333333333, dq1 ],
Expand All @@ -315,6 +285,9 @@ function _convexhull( dq0, dq1, dq2, dq3 ){


function drawFatline( v1 ) {
function signum(num) {
return ( num > 0 )? 1 : ( num < 0 )? -1 : 0;
}
var l = new Line( [v1[0], v1[1]], [v1[6], v1[7]], false );
var p1 = new Point( v1[2], v1[3] ), p2 = new Point( v1[4], v1[5] );
var d1 = l.getSide( p1 ) * l.getDistance( p1 );
Expand Down Expand Up @@ -386,28 +359,10 @@ function plotD_vs_t( x, y, arr, arr2, v, dmin, dmax, tmin, tmax, yscale, tvalue
view.draw();
}

function signum(num) {
return ( num > 0 )? 1 : ( num < 0 )? -1 : 0;
}

var _intersectLines = function(v1, v2) {
var result, a1x, a2x, b1x, b2x, a1y, a2y, b1y, b2y;
a1x = v1[0]; a1y = v1[1];
a2x = v1[2]; a2y = v1[3];
b1x = v2[0]; b1y = v2[1];
b2x = v2[2]; b2y = v2[3];
var ua_t = (b2x - b1x) * (a1y - b1y) - (b2y - b1y) * (a1x - b1x);
var ub_t = (a2x - a1x) * (a1y - b1y) - (a2y - a1y) * (a1x - b1x);
var u_b = (b2y - b1y) * (a2x - a1x) - (b2x - b1x) * (a2y - a1y);
if ( u_b !== 0 ) {
var ua = ua_t / u_b;
var ub = ub_t / u_b;
if ( 0 <= ua && ua <= 1 && 0 <= ub && ub <= 1 ) {
return [a1x + ua * (a2x - a1x), a1y + ua * (a2y - a1y)];
}
}
};

// This is basically an "unrolled" version of two methods from paperjs'
// Line class —#Line.getSide() and #Line.getDistance()
// If we create Point and Line objects, the code slows down significantly!
// May be a static method could be better!
var _getSignedDist = function( a1x, a1y, a2x, a2y, bx, by ){
var vx = a2x - a1x, vy = a2y - a1y;
var bax = bx - a1x, bay = by - a1y;
Expand Down
46 changes: 23 additions & 23 deletions intersectTests.js
View file
Original file line number Diff line number Diff line change
Expand Up @@ -10,31 +10,31 @@ function runTests() {

caption = prepareTest( 'Find Curve Intersections - 10,000 times.', container );

pathA = new Path.Circle(new Point(70, 110), 50);
pathA.rotate( 45 );
pathB = new Path.Circle(new Point(160, 110), 50);
pathB.rotate( 45 );
// pathB.segments[3].point = pathB.segments[3].point.add( [10, -120] );
// pathB.translate( [ -20, -30 ] );
// pathB.segments[0].handleIn = pathB.segments[0].handleIn.add( [-100, 30] );
// pathB.translate( [ 20, -30 ] );
// testIntersection( pathA, pathB, caption );

// pathA = new Path();
// pathA.add( new Segment( [47, 93], [-89, 100], [240, -239] ) );
// pathA.add( new Segment( [173, 44], [-281, 268], [-86, 152] ) );
// pathA.closed = true;
// pathB = pathA.clone();
// pathB.rotate( -90 );
// pathA.translate( [-10,0] );
// pathB.translate( [10,0] );
// pathA = new Path.Circle(new Point(70, 110), 50);
// pathA.rotate( 45 );
// pathB = new Path.Circle(new Point(160, 110), 50);
// pathB.rotate( 45 );
// // pathB.segments[3].point = pathB.segments[3].point.add( [10, -120] );
// // pathB.translate( [ -20, -30 ] );
// // pathB.segments[0].handleIn = pathB.segments[0].handleIn.add( [-100, 30] );
// // pathB.translate( [ 20, -30 ] );
// // testIntersection( pathA, pathB, caption );

pathA = new Path();
pathA.add( new Segment( [47, 93], [-89, 100], [240, -239] ) );
pathA.add( new Segment( [173, 44], [-281, 268], [-86, 152] ) );
pathA.closed = true;
pathB = pathA.clone();
pathB.rotate( -90 );
pathA.translate( [-10,0] );
pathB.translate( [10,0] );

window.a = pathA;
window.b = pathB;

view.draw();

window.setTimeout( function(){doTest( pathA, pathB, 1000 )}, 100 );
window.setTimeout( function(){doTest( pathA, pathB, 100 )}, 100 );

// var v1 = [84.625,79.375,51,130.5,22.5,178,163,44];
// var v2 = [91.81412502271213,92.91643774058434,142.93912502271212,126.54143774058434,190.43912502271212,155.04143774058434,56.43912502271214,14.541437740584342]
Expand Down Expand Up @@ -78,11 +78,11 @@ var pathStyleBoolean = {


function doTest( pathA, pathB, count ){
// var _p1U = new Path( pathA.segments[0], pathA.segments[1] );
var _p1U = new Path( pathA.segments[1], pathA.segments[2] );
var _p1U = new Path( pathA.segments[0], pathA.segments[1] );
// var _p1U = new Path( pathA.segments[1], pathA.segments[2] );
// _p1U.reverse();
// var _p2U = new Path( pathB.segments[0], pathB.segments[1] );
var _p2U = new Path( pathB.segments[3], pathB.segments[0] );
var _p2U = new Path( pathB.segments[0], pathB.segments[1] );
// var _p2U = new Path( pathB.segments[3], pathB.segments[0] );
_p1U.style = _p2U.style = pathStyleBoolean;
// for (var i = 0; i < crvs.length; i++) {
// drawFatline( _p1U.curves[0].getValues() );
Expand Down

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