scratchfoundation/paper.js
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Intersect rewrite in progress..

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hkrish 2013-05-10 20:46:07 +02:00
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fatline/Intersect.js
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@ -3,7 +3,7 @@
var EPSILON = 10e-12;
var TOLERANCE = 10e-6;
var _tolerence = EPSILON;
var _tolerence = TOLERANCE;
function getIntersections2( path1, path2 ){
var locations = [];
@ -11,43 +11,119 @@ function getIntersections2( path1, path2 ){
}
paper.Curve.getIntersections2 = function( v1, v2, curve1, curve2, locations, _t1, _t2, _u1, _u2 ) {
_t1 = _t1 || 0; _t2 = _t2 || 1;
_u1 = _u1 || 0; _u2 = _u2 || 1;
var loc = { parameter: null, tvalue: null };
var ret = _clipFatLine( v1, v2, 0, 1, 0, 1, true, curve1, curve2, loc );
if( ret === 1 ){
var parameter;
if( locations.tvalue ){
parameter = _t1 + loc.parameter * ( _t2 - _t1 );
locations.push( new CurveLocation( curve1, parameter, curve1.getPoint(parameter), curve2 ) );
} else {
parameter = _u1 + loc.parameter * ( _u2 - _u1 );
locations.push( new CurveLocation( curve2, parameter, curve2.getPoint(parameter), curve1 ) );
paper.Curve.getIntersections2 = function( v1, v2, curve1, curve2, locations, _v1t, _v2t ) {
// cache the original parameter range.
_v1t = _v1t || { t1: 0, t2: 1 };
_v2t = _v2t || { t1: 0, t2: 1 };
var v1t = { t1: _v1t.t1, t2: _v1t.t2 };
var v2t = { t1: _v2t.t1, t2: _v2t.t2 };
// 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 );
// markPoint( new Point( _v1[0], _v1[1] ), ' ', '#f0f' )
// markPoint( new Point( _v1[6], _v1[7] ), ' ', '#f0f' )
// markPoint( new Point( _v2[0], _v2[1] ), ' ', '#0ff' )
// markPoint( new Point( _v2[6], _v2[7] ), ' ', '#0ff' )
// 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
// 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) ){
// First we clip v2 with v1's fat-line
tmpt.t1 = v2t.t1; tmpt.t2 = v2t.t2;
var intersects1 = _clipBezierFatLine( _v1, _v2, tmpt );
// Stop if there are no possible intersections
if( intersects1 === 0 ){
return;
} else if( intersects1 > 0 ){
// Get the clipped parts from the original v2, to avoid cumulative errors
v2t.t1 = tmpt.t1; v2t.t2 = tmpt.t2;
_v2 = Curve.getPart( v2, v2t.t1, v2t.t2 );
}
} else if( ret < 0) {
// We need to subdivide one of the curves
// Better if we can subdivide the longest curve
var v1lx = v1[6] - v1[0];
var v1ly = v1[7] - v1[1];
var v2lx = v2[6] - v2[0];
var v2ly = v2[7] - v2[1];
var sqrDist1 = v1lx * v1lx + v1ly * v1ly;
var sqrDist2 = v2lx * v2lx + v2ly * v2ly;
var parts;
// A quick and dirty way to determine which curve to subdivide
if( sqrDist1 > sqrDist2 ){
parts = Curve.subdivide( v1 );
nuT = ( _t1 + _t2 ) / 2;
Curve.getIntersections2( parts[0], v2, curve1, curve2, locations, _t1, nuT, _u1, _u2 );
Curve.getIntersections2( parts[1], v2, curve1, curve2, locations, nuT, _t2, _u1, _u2 );
// Next we clip v1 with nuv2's fat-line
tmpt.t1 = v1t.t1; tmpt.t2 = v1t.t2;
var intersects2 = _clipBezierFatLine( _v2, _v1, tmpt );
// Stop if there are no possible intersections
if( intersects2 === 0 ){
return;
}else if( intersects1 > 0 ){
// Get the clipped parts from the original v2, to avoid cumulative errors
v1t.t1 = tmpt.t1; v1t.t2 = tmpt.t2;
_v1 = Curve.getPart( v1, v1t.t1, v1t.t2 );
}
// markCurve( _v1, '#f0f', true );
// markCurve( _v2, '#0ff', false );
// 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;
}
}
// Check to see if both parameter ranges have converged or else,
// see if both curves are flat enough to be treated as lines, either
// because they have no control points at all, or are "flat enough"
// If the curve was flat in a previous iteration, we don't need to
// recalculate since it does not need further subdivision then.
if( Math.abs(v1t.t2 - v1t.t1) <= _tolerence && Math.abs(v2t.t2 - v2t.t1) <= _tolerence ){
locations.push(new CurveLocation(curve1, v1t.t1, null, curve2));
return;
} else {
parts = Curve.subdivide( v2 );
nuU = ( _u1 + _u2 ) / 2;
Curve.getIntersections2( v1, parts[0], curve1, curve2, locations, _t1, _t2, _u1, nuU );
Curve.getIntersections2( v1, parts[1], curve1, curve2, locations, _t1, _t2, nuU, _u2 );
//!code from: paperjs#Curve.getIntersections method
if ((Curve.isLinear(_v1)
|| Curve.isFlatEnough(_v1, _tolerence))
&& (Curve.isLinear(_v2)
|| 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);
if (point) {
point = new Point( point );
// Avoid duplicates when hitting segments (closed paths too)
var first = locations[0],
last = locations[locations.length - 1];
if ((!first || !point.equals(first._point))
&& (!last || !point.equals(last._point)))
// Passing null for parameter leads to lazy determination
// of parameter values in CurveLocation#getParameter()
// only once they are requested.
locations.push(new CurveLocation(curve1, null, point, curve2));
// This method can find only one intersection at a time and we just found it.
return;
}
}
}
}
// // We didn't find and intersection yet and one of the parameter ranges has converged to a point
// if( v1t.t1 >= v1t.t2 - _tolerence && v1t.t1 <= v1t.t2 + _tolerence ){
// } else {
// }
};
function _clipFatLine( v1, v2, t1, t2, u1, u2, tvalue, curve1, curve2, location ){
@ -160,19 +236,112 @@ function _clipFatLine( v1, v2, t1, t2, u1, u2, tvalue, curve1, curve2, location
/**
* Clip curve values V2 with fat-line of v1 and vice versa
* @param {Array} v - Section of the first curve, for which we will make a fat-line
* @param {Number} t1 - start parameter for v in vOrg
* @param {Number} t2 - end parameter for v in vOrg
* @param {Array} v2 - Section of the second curve; we will clip this curve with the fat-line of v
* @param {Number} u1 - start parameter for v2 in v2Org
* @param {Number} u2 - end parameter for v2 in v2Org
* @param {Array} vOrg - The original curve values for v
* @param {Array} v2Org - The original curve values for v2
* @return {[type]}
* Clip curve V2 with fat-line of v1
* @param {Array} v1 - Section of the first curve, for which we will make a fat-line
* @param {Array} v2 - Section of the second curve; we will clip this curve with the fat-line of v1
* @param {Object} v2t - The parameter range of v2
* @return {number} -> 0 -no Intersection, 1 -one intersection, -1 -more than one intersection
*/
function _clipBezFatLine( v1, t1, t2, v2, u1, u2, vOrg, v2Org ){
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
var d1 = _getSignedDist( p0x, p0y, p3x, p3y, p1x, p1y );
var d2 = _getSignedDist( p0x, p0y, p3x, p3y, p2x, p2y );
var dmin, dmax;
if( d1 * d2 > 0){
// 3/4 * min{0, d1, d2}
dmin = 0.75 * Math.min( 0, d1, d2 );
dmax = 0.75 * Math.max( 0, d1, d2 );
} else {
// 4/9 * min{0, d1, d2}
dmin = 4 * Math.min( 0, d1, d2 ) / 9.0;
dmax = 4 * Math.max( 0, d1, d2 ) / 9.0;
}
// The convex hull for the non-parametric bezier curve D(ti, di(t))
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.
// 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
// for the coorresponding t values (tmin, tmax):
// Portions of curve v2 before tmin and after tmax can safely be clipped away
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];
for (i = 0, len = Dt.length; i < len; i++) {
var Dtl = Dt[i];
// ixd = Dtl.intersect( vecdmin );
ixd = _intersectLines( Dtl, dmina);
if( ixd ){
ixdx = ixd[0];
tmindmin = ( ixdx < tmindmin )? ixdx : tmindmin;
tmaxdmin = ( ixdx > tmaxdmin )? ixdx : tmaxdmin;
}
// ixd = Dtl.intersect( vecdmax );
ixd = _intersectLines( Dtl, dmaxa);
if( ixd ){
ixdx = ixd[0];
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.
if( tmindmin === Infinity && tmaxdmin === -Infinity &&
tmindmax === Infinity && tmaxdmax === -Infinity ) {
return 0;
}
// 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;
// Return the parameter values for v2 for which we can be sure that the
// intersection with v1 lies within.
var tmin = Math.min( tmindmin, tmaxdmin, tmindmax, tmaxdmax );
var tmax = Math.max( tmindmin, tmaxdmin, tmindmax, tmaxdmax );
// plotD_vs_t( 500, 110, Dt, [dq0, dq1, dq2, dq3], dmin, dmax, tmin, tmax, 0.5 )
// 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,
// possibly we have multiple intersections. We need to subdivide one of the curves.
if( (tdiff - ( v2t.t2 - v2t.t1 ))/tdiff < 0.2 ){
return -1;
}
return 1;
}
function _convexhull( dq0, dq1, dq2, dq3 ){
@ -278,29 +447,40 @@ function drawFatline( v1 ) {
ll.style.strokeColor = new Color( 0,0,0.9);
}
function plotD_vs_t( x, y, arr, dmin, dmax, tmin, tmax, yscale, tvalue ){
function plotD_vs_t( x, y, arr, arr2, dmin, dmax, tmin, tmax, yscale, tvalue ){
yscale = yscale || 1;
new Path.Line( x, y-100, x, y+100 ).style.strokeColor = '#aaa';
new Path.Line( x, y, x + 200, y ).style.strokeColor = '#aaa';
var clr = (tvalue)? '#a00' : '#00a';
if( window.__p3 ) window.__p3.map(function(a){a.remove();});
new Path.Line( x, y + dmin * yscale, x + 200, y + dmin * yscale ).style.strokeColor = '#000';
new Path.Line( x, y + dmax * yscale, x + 200, y + dmax * yscale ).style.strokeColor = '#000';
new Path.Line( x + tmin * 190, y-100, x + tmin * 190, y+100 ).style.strokeColor = clr;
new Path.Line( x + tmax * 190, y-100, x + tmax * 190, y+100 ).style.strokeColor = clr;
window.__p3 = [];
window.__p3.push( new Path.Line( x, y + dmin * yscale, x + 200, y + dmin * yscale ) );
window.__p3[window.__p3.length-1].style.strokeColor = '#000'
window.__p3.push( new Path.Line( x, y + dmax * yscale, x + 200, y + dmax * yscale ) );
window.__p3[window.__p3.length-1].style.strokeColor = '#000'
window.__p3.push( new Path.Line( x + tmin * 190, y-100, x + tmin * 190, y+100 ) );
window.__p3[window.__p3.length-1].style.strokeColor = clr
window.__p3.push( new Path.Line( x + tmax * 190, y-100, x + tmax * 190, y+100 ) );
window.__p3[window.__p3.length-1].style.strokeColor = clr
var pnt = [];
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][0] * 190, y + arr[i][1] * yscale ) );
var pth = new Path.Line( new Point( x + arr[i][0] * 190, y + arr[i][1] * yscale ),
new Point( x + arr[i][2] * 190, y + arr[i][3] * yscale ) );
pth.style.strokeColor = '#999';
window.__p3.push( new Path.Line( new Point( x + arr[i][0] * 190, y + arr[i][1] * yscale ),
new Point( x + arr[i][2] * 190, y + arr[i][3] * yscale ) ) );
window.__p3[window.__p3.length-1].style.strokeColor = '#999';
}
var pnt = [];
var arr2x = [ 0.0, 0.333333333, 0.6666666666, 1.0 ];
for (var i = 0; i < arr2.length; i++) {
pnt.push( new Point( x + arr2x[i] * 190, y + arr2[i] * yscale ) );
}
// var pth = new Path( pnt[0], pnt[1], pnt[2], pnt[3] );
// pth.closed = true;
new Path( new Segment(pnt[0], null, pnt[1].subtract(pnt[0])), new Segment( pnt[3], pnt[2].subtract(pnt[3]), null ) ).style.strokeColor = clr;
window.__p3.push( new Path( new Segment(pnt[0], null, pnt[1].subtract(pnt[0])), new Segment( pnt[3], pnt[2].subtract(pnt[3]), null ) ) );
window.__p3[window.__p3.length-1].style.strokeColor = clr
view.draw();
}
function signum(num) {