scratchfoundation/paper.js
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Almost working. And is Super-fast!!!

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hkrish 2013-05-03 22:23:00 +02:00
parent b966aafd0f
commit 6b44c98169
1 changed files with 74 additions and 43 deletions
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117
fatline/Intersect.js
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@ -19,20 +19,22 @@ function _clipFatLine( v1, v2, t1, t2, u1, u2, tdiff, udiff, tvalue, curve1, cur
if( count === undefined ) { count = 0; } if( count === undefined ) { count = 0; }
else { ++count; } else { ++count; }
if( t1 >= t2 - _tolerence && t1 <= t2 + _tolerence && u1 >= u2 - _tolerence && u1 <= u2 + _tolerence ){ if( t1 >= t2 - _tolerence && t1 <= t2 + _tolerence && u1 >= u2 - _tolerence && u1 <= u2 + _tolerence ){
var curve = tvalue ? curve2 : curve1; var loc = tvalue ? new CurveLocation( curve2, t1, null, curve1 ) :
locations.push( new CurveLocation( curve, t1 ) ); new CurveLocation( curve1, u1, null, curve2 );
locations.push( loc );
return; return;
} }
p0x = v1[0]; p0y = v1[1];
var p0 = new Point( v1[0], v1[1] ), p3 = new Point( v1[6], v1[7] ); p3x = v1[6]; p3y = v1[7];
var p1 = new Point( v1[2], v1[3] ), p2 = new Point( v1[4], v1[5] ); p1x = v1[2]; p1y = v1[3];
var q0 = new Point( v2[0], v2[1] ), q3 = new Point( v2[6], v2[7] ); p2x = v1[4]; p2y = v1[5];
var q1 = new Point( v2[2], v2[3] ), q2 = new Point( v2[4], v2[5] ); q0x = v2[0]; q0y = v2[1];
q3x = v2[6]; q3y = v2[7];
q1x = v2[2]; q1y = v2[3];
q2x = v2[4]; q2y = v2[5];
// Calculate L // Calculate L
var lp = new Line( p0, p3, false ); var d1 = _getSignedDist( p0x, p0y, p3x, p3y, p1x, p1y );
var d1 = lp.getSide( p1 ) * lp.getDistance( p1 ); var d2 = _getSignedDist( p0x, p0y, p3x, p3y, p2x, p2y );
var d2 = lp.getSide( p2 ) * lp.getDistance( p2 );
var dmin, dmax; var dmin, dmax;
if( d1 * d2 > 0){ if( d1 * d2 > 0){
// 3/4 * min{0, d1, d2} // 3/4 * min{0, d1, d2}
@ -43,58 +45,67 @@ function _clipFatLine( v1, v2, t1, t2, u1, u2, tdiff, udiff, tvalue, curve1, cur
dmin = 4 * Math.min( 0, d1, d2 ) / 9.0; dmin = 4 * Math.min( 0, d1, d2 ) / 9.0;
dmax = 4 * Math.max( 0, d1, d2 ) / 9.0; dmax = 4 * Math.max( 0, d1, d2 ) / 9.0;
} }
// Infinite lines for dmin and dmax for clipping
var vecdmin = new Line( [0, dmin], [1, 0] );
var vecdmax = new Line( [0, dmax], [1, 0] );
// The convex hull for the non-parametric bezier curve D(ti, di(t)) // The convex hull for the non-parametric bezier curve D(ti, di(t))
var dq0 = new Point( 0.0, lp.getSide(q0) * lp.getDistance(q0) ); var dq0 = _getSignedDist( p0x, p0y, p3x, p3y, q0x, q0y );
var dq1 = new Point( 0.3333333333333333, lp.getSide(q1) * lp.getDistance(q1) ); var dq1 = _getSignedDist( p0x, p0y, p3x, p3y, q1x, q1y );
var dq2 = new Point( 0.6666666666666666, lp.getSide(q2) * lp.getDistance(q2) ); var dq2 = _getSignedDist( p0x, p0y, p3x, p3y, q2x, q2y );
var dq3 = new Point( 1.0, lp.getSide(q3) * lp.getDistance(q3) ); var dq3 = _getSignedDist( p0x, p0y, p3x, p3y, q3x, q3y );
var mindist = Math.min( dq0, dq3 );
var maxdist = Math.max( dq0, dq3 );
// If the fatlines don't overlap, we have no intersections!
if( dmin > maxdist || dmax < mindist ){
return;
}
// Ideally we need to calculate the convex hull for D(ti, di(t)) // Ideally we need to calculate the convex hull for D(ti, di(t))
// here we are just checking against all possibilities // here we are just checking against all possibilities
var Dt = [ var Dt = [
new Line( dq0, dq1, false ), [ 0.0, dq0, 0.3333333333333333, dq1 ],
new Line( dq1, dq2, false ), [ 0.3333333333333333, dq1, 0.6666666666666666, dq2 ],
new Line( dq2, dq3, false ), [ 0.6666666666666666, dq2, 1.0, dq3 ],
new Line( dq3, dq0, false ), [ 1.0, dq3, 0.0, dq0 ],
new Line( dq0, dq2, false ), [ 0.0, dq0, 0.6666666666666666, dq2 ],
new Line( dq3, dq1, false ) [ 1.0, dq3, 0.3333333333333333, dq1 ]
]; ];
// Now we clip the convex hulls for D(ti, di(t)) with dmin and dmax // Now we clip the convex hulls for D(ti, di(t)) with dmin and dmax
// for the coorresponding t values // for the coorresponding t values
var tmindmin = Infinity, tmaxdmin = -Infinity, var tmindmin = Infinity, tmaxdmin = -Infinity,
tmindmax = Infinity, tmaxdmax = -Infinity, ixd, ixdx, i; tmindmax = Infinity, tmaxdmax = -Infinity, ixd, ixdx, i;
var dmina = [0, dmin, 2, dmin];
var dmaxa = [0, dmax, 2, dmax];
for (i = 0; i < 6; i++) { for (i = 0; i < 6; i++) {
var Dtl = Dt[i]; var Dtl = Dt[i];
ixd = Dtl.intersect( vecdmin ); // ixd = Dtl.intersect( vecdmin );
ixd = _intersectLines( Dtl, dmina);
if( ixd ){ if( ixd ){
ixdx = ixd.x; ixdx = ixd[0];
tmindmin = ( ixdx < tmindmin )? ixdx : tmindmin; tmindmin = ( ixdx < tmindmin )? ixdx : tmindmin;
tmaxdmin = ( ixdx > tmaxdmin )? ixdx : tmaxdmin; tmaxdmin = ( ixdx > tmaxdmin )? ixdx : tmaxdmin;
} }
ixd = Dtl.intersect( vecdmax ); // ixd = Dtl.intersect( vecdmax );
ixd = _intersectLines( Dtl, dmaxa);
if( ixd ){ if( ixd ){
ixdx = ixd.x; ixdx = ixd[0];
tmindmax = ( ixdx < tmindmax )? ixdx : tmindmax; tmindmax = ( ixdx < tmindmax )? ixdx : tmindmax;
tmaxdmax = ( ixdx > tmaxdmax )? ixdx : tmaxdmax; tmaxdmax = ( ixdx > tmaxdmax )? ixdx : tmaxdmax;
} }
} }
// if dmin doesnot intersect with the convexhull, reset it to 0
tmindmin = ( tmindmin === Infinity )? 0 : tmindmin;
tmaxdmin = ( tmaxdmin === -Infinity )? 0 : tmaxdmin;
// if dmax doesnot intersect with the convexhull, reset it to 1
tmindmax = ( tmindmax === Infinity )? 1 : tmindmax;
tmaxdmax = ( tmaxdmax === -Infinity )? 1 : tmaxdmax;
var tmin = Math.min( tmindmin, tmaxdmin, tmindmax, tmaxdmax ); var tmin = Math.min( tmindmin, tmaxdmin, tmindmax, tmaxdmax );
var tmax = Math.max( tmindmin, tmaxdmin, tmindmax, tmaxdmax ); var tmax = Math.max( tmindmin, tmaxdmin, tmindmax, tmaxdmax);
if( tmin < 0 || tmax > 1 ) {
return;
}
// if( count === 1 ){ // if( count === 1 ){
// // console.log( dmin, dmax, tmin, tmax ) // console.log( dmin, dmax, tmin, tmax, " - ", tmindmin, tmaxdmin, tmindmax, tmaxdmax )
// plotD_vs_t( 250, 110, Dt, dmin, dmax, tmin, tmax, 1, tvalue ); // plotD_vs_t( 250, 110, Dt, dmin, dmax, tmin, tmax, 1, tvalue );
// } // }
// return;
// We need to toggle clipping both curves alternatively // We need to toggle clipping both curves alternatively
// tvalue indicates whether to compare t or u for testing for convergence // tvalue indicates whether to compare t or u for testing for convergence
var nuV2 = Curve.getPart( v2, tmin, tmax ); var nuV2 = Curve.getPart( v2, tmin, tmax );
@ -109,8 +120,6 @@ function _clipFatLine( v1, v2, t1, t2, u1, u2, tdiff, udiff, tvalue, curve1, cur
if( convRate <= 0.2) { if( convRate <= 0.2) {
} }
// console.log( nuT1, nuT2, t1, t2 );
_clipFatLine( nuV2, v1, nuT1, nuT2, u1, u2, (tmax - tmin), udiff, !tvalue, curve1, curve2, locations, count ); _clipFatLine( nuV2, v1, nuT1, nuT2, u1, u2, (tmax - tmin), udiff, !tvalue, curve1, curve2, locations, count );
} else { } else {
nuU1 = u1 + tmin * ( u2 - u1 ); nuU1 = u1 + tmin * ( u2 - u1 );
@ -168,8 +177,8 @@ function plotD_vs_t( x, y, arr, dmin, dmax, tmin, tmax, yscale, tvalue ){
var pnt = []; var pnt = [];
for (var i = 0; i < arr.length; i++) { for (var i = 0; i < arr.length; i++) {
pnt.push( new Point( x + arr[i].point.x * 190, y + arr[i].point.y * yscale ) ); // pnt.push( new Point( x + arr[i].point.x * 190, y + arr[i].point.y * yscale ) );
// pnt.push( new Point( x + arr[i][0] * 190, y + arr[i][1] * yscale ) ); pnt.push( new Point( x + arr[i][0] * 190, y + arr[i][1] * yscale ) );
} }
var pth = new Path( pnt[0], pnt[1], pnt[2], pnt[3] ); var pth = new Path( pnt[0], pnt[1], pnt[2], pnt[3] );
pth.closed = true; pth.closed = true;
@ -186,7 +195,7 @@ var _intersectLines = function(v1, v2) {
a1x = v1[0]; a1y = v1[1]; a1x = v1[0]; a1y = v1[1];
a2x = v1[2]; a2y = v1[3]; a2x = v1[2]; a2y = v1[3];
b1x = v2[0]; b1y = v2[1]; b1x = v2[0]; b1y = v2[1];
b2x = v2[3]; b2y = v2[3]; b2x = v2[2]; b2y = v2[3];
var ua_t = (b2x - b1x) * (a1y - b1y) - (b2y - b1y) * (a1x - b1x); var ua_t = (b2x - b1x) * (a1y - b1y) - (b2y - b1y) * (a1x - b1x);
var ub_t = (a2x - a1x) * (a1y - b1y) - (a2y - a1y) * (a1x - b1x); var ub_t = (a2x - a1x) * (a1y - b1y) - (a2y - a1y) * (a1x - b1x);
var u_b = (b2y - b1y) * (a2x - a1x) - (b2x - b1x) * (a2y - a1y); var u_b = (b2y - b1y) * (a2x - a1x) - (b2x - b1x) * (a2y - a1y);
@ -194,7 +203,29 @@ var _intersectLines = function(v1, v2) {
var ua = ua_t / u_b; var ua = ua_t / u_b;
var ub = ub_t / u_b; var ub = ub_t / u_b;
if ( 0 <= ua && ua <= 1 && 0 <= ub && ub <= 1 ) { if ( 0 <= ua && ua <= 1 && 0 <= ub && ub <= 1 ) {
return new Point(a1x + ua * (a2x - a1x), a1y + ua * (a2y - a1y)); return [a1x + ua * (a2x - a1x), a1y + ua * (a2y - a1y)];
} }
} }
}; };
var _getSignedDist = function( a1x, a1y, a2x, a2y, bx, by ){
var vx = a2x - a1x, vy = a2y - a1y;
var bax = bx - a1x, bay = by - a1y;
var ba2x = bx - a2x, ba2y = by - a2y;
var cvb = bax * vy - bay * vx;
if (cvb === 0) {
cvb = bax * vx + bay * vy;
if (cvb > 0) {
cvb = (bax - vx) * vx + (bay -vy) * vy;
if (cvb < 0){ cvb = 0; }
}
}
var side = cvb < 0 ? -1 : cvb > 0 ? 1 : 0;
// Calculate the distance
var m = vy / vx, b = a1y - ( m * a1x );
var dist = Math.abs( by - ( m * bx ) - b ) / Math.sqrt( m*m + 1 );
var dista1 = Math.sqrt( bax * bax + bay * bay );
var dista2 = Math.sqrt( ba2x * ba2x + ba2y * ba2y );
return side * Math.min( dist, dista1, dista2 );
};