Convert path line to polyline?
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Hello,
anyone here know it's it's possible to convert a path into a polyline?
I need to save SVG (but polyline, not path)
Many thanks!
r.
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Hi
this is not the best way to do that, but all you need to do it better is inside this stuff (i hope).
have a look at the examples at the bottom.
cheers chris
//11:28 12.03.2010
// www.ogebab.de
//-------------------------------------------
//Extension for Illustrator javascript (CS+)
/* ----------------------------------------------
------OBJ---- overview----------
----------------------------------------------
Point()
x, y
many functions...
Line()
many functions...
Bezier()
A, B, C, D
isLine()
more functions...
XpPoint()
lDir, an, rDir | type: Point
isCurvePoint()
Xpath()
pPoints |type: XpPoint
beziers
SetPath()
Xitem()
center
setToCenter()
...
*/
//----------------------------------------------
//---------- little HELPERS----------------------
var fmm = 72 / 25.4;
// ---
function NumSort(a, b) {
return a - b;
}
fibonacci = function(n) {
return Math.round(Math.pow((Math.sqrt(5) + 1) / 2, Math.abs(n))
/ Math.sqrt(5))
* (n < 0 && n % 2 ? -1 : 1);
};
function InVal(tx) {
var inp, pt, t, num, d;
inp = prompt(tx, "5");
if (inp != "" && inp != null) {
t = inp.search(",");
if (t >= 0) {
inp = inp.replace(",", ".");
}
t = inp.search("pt");
if (t >= 0) {
pt = 1;
num = inp.slice(0, t);
} else {
t = inp.search("mm");
if (t >= 0) {
pt = 0;
num = inp.slice(0, t);
} else {
t = inp.search("in");
if (t >= 0) {
pt = 2;
num = inp.slice(0, t);
} else {
pt = 0;
num = inp;
}
}
d = eval(num);
if (pt == 0) {
d = d * 72.0 / 25.4
} else {
if (pt == 2) {
d = d * 72.0
}
}
return (d);
}
return (null);
}
}
function InNum(tx, n) {
var inp = prompt(tx, n), t = inp.search(",");
if (t >= 0) {
inp = inp.replace(",", ".");
}
return eval(inp);
}
function GetSelPaths() {
var pf = app.activeDocument.pathItems, p = new Array();
for ( var i68 = 0; i68 < pf.length; i68++) {
if (pf[i68].selected == true) {
p.push(pf[i68]);
}
}
return p;
}
equate = function(a, b) {
if (b >= 0)
return a - b;
return a + Math.abs(b)
};
Array.prototype.turn1 = function() {
var a = this.shift();
return this.push(a);
};
Array.prototype.insert = function(wert, stelle) {
var a = this.slice(0, stelle), b = this.slice(stelle);
b.unshift(wert);
return (a.concat(b));
};
//--------------------------------------------------------------------------------------------------------------------------------------
//-----------------------OBJECTS---------------------------------------------------------------------------------------------------
////----------intersection section-----
//--------ignore it until you understand the rest
//--usage: Var = new Intersection();
//-- Var.IfIntersect(bezier,bezier); > if bezier is a line(and you know that), use Line.intersect() instead
//-- returns Status and (if) Points/Vector2Ds
//--
//--- a tangent is not a intersection! similar points are SOMETIMES a intersection! ?
//--------KevLinDev.com--------* copyright 2002-2003, Kevin Lindsey-----
Array.prototype.foreach=function(func){for(var i=0;i<this.length;i++)func(this);};
Array.prototype.map=function(func){var result=new Array();for(var i=0;i<this.length;i++)result.push(func(this));return result;};
Array.prototype.min=function(){var min=this[0];for(var i=0;i<this.length;i++)if(this<min)min=this;return min;}
Array.prototype.max=function(){var max=this[0];for(var i=0;i<this.length;i++)if(this>max)max=this;return max;}
Polynomial.TOLERANCE=1e-6;
Polynomial.ACCURACY=6;
function Polynomial(){this.init(arguments);}
Polynomial.prototype.init=function(coefs){this.coefs=new Array();for(var i=coefs.length-1;i>=0;i--)this.coefs.push(coefs);};
Polynomial.prototype.eval=function(x){var result=0;for(var i=this.coefs.length-1;i>=0;i--)result=result*x+this.coefs;return result;};
Polynomial.prototype.multiply=function(that){var result=new Polynomial();for(var i=0;i<=this.getDegree()+that.getDegree();i++)result.coefs.push(0);for(var i=0;i<=this.getDegree();i++)for(var j=0;j<=that.getDegree();j++)result.coefs[i+j]+=this.coefs*that.coefs;return result;};
Polynomial.prototype.divide_scalar=function(scalar){for(var i=0;i<this.coefs.length;i++)this.coefs/=scalar;};
Polynomial.prototype.simplify=function(){for(var i=this.getDegree();i>=0;i--){if(Math.abs(this.coefs)<=Polynomial.TOLERANCE)this.coefs.pop();else break;}};
Polynomial.prototype.bisection=function(min,max){var minValue=this.eval(min);var maxValue=this.eval(max);var result;if(Math.abs(minValue)<=Polynomial.TOLERANCE)result=min;else if(Math.abs(maxValue)<=Polynomial.TOLERANCE)result=max;else if(minValue*maxValue<=0){var tmp1=Math.log(max-min);var tmp2=Math.log(10)*Polynomial.ACCURACY;var iters=Math.ceil((tmp1+tmp2)/Math.log(2));for(var i=0;i<iters;i++){result=0.5*(min+max);var value=this.eval(result);if(Math.abs(value)<=Polynomial.TOLERANCE){break;}if(value*minValue<0){max=result;maxValue=value;}else{min=result;minValue=value;}}}return result;};
Polynomial.prototype.toString=function(){var coefs=new Array();var signs=new Array();for(var i=this.coefs.length-1;i>=0;i--){var value=this.coefs;if(value!=0){var sign=(value<0)?" - ":" + ";value=Math.abs(value);if(i>0)if(value==1)value="x";else value+="x";if(i>1)value+="^"+i;signs.push(sign);coefs.push(value);}}signs[0]=(signs[0]==" + ")?"":"-";var result="";for(var i=0;i<coefs.length;i++)result+=signs+coefs;return result;};
Polynomial.prototype.getDegree=function(){return this.coefs.length-1;};
Polynomial.prototype.getDerivative=function(){var derivative=new Polynomial();for(var i=1;i<this.coefs.length;i++){derivative.coefs.push(i*this.coefs);}return derivative;};
Polynomial.prototype.getRoots=function(){var result;this.simplify();switch(this.getDegree()){case 0:result=new Array();break;case 1:result=this.getLinearRoot();break;case 2:result=this.getQuadraticRoots();break;case 3:result=this.getCubicRoots();break;case 4:result=this.getQuarticRoots();break;default:result=new Array();}return result;};
Polynomial.prototype.getRootsInInterval=function(min,max){var roots=new Array();var root;if(this.getDegree()==1){root=this.bisection(min,max);if(root!=null)roots.push(root);}else{var deriv=this.getDerivative();var droots=deriv.getRootsInInterval(min,max);if(droots.length>0){root=this.bisection(min,droots[0]);if(root!=null)roots.push(root);for(var i=0;i<=droots.length-2;i++){root=this.bisection(droots,droots[i+1]);if(root!=null)roots.push(root);}root=this.bisection(droots[droots.length-1],max);if(root!=null)roots.push(root);}else{root=this.bisection(min,max);if(root!=null)roots.push(root);}}return roots;};
Polynomial.prototype.getLinearRoot=function(){var result=new Array();var a=this.coefs[1];if(a!=0)result.push(-this.coefs[0]/a);return result;};
Polynomial.prototype.getQuadraticRoots=function(){var results=new Array();if(this.getDegree()==2){var a=this.coefs[2];var b=this.coefs[1]/a;var c=this.coefs[0]/a;var d=b*b-4*c;if(d>0){var e=Math.sqrt(d);results.push(0.5*(-b+e));results.push(0.5*(-b-e));}else if(d==0){results.push(0.5*-b);}}return results;};
Polynomial.prototype.getCubicRoots=function(){var results=new Array();if(this.getDegree()==3){var c3=this.coefs[3];var c2=this.coefs[2]/c3;var c1=this.coefs[1]/c3;var c0=this.coefs[0]/c3;var a=(3*c1-c2*c2)/3;var b=(2*c2*c2*c2-9*c1*c2+27*c0)/27;var offset=c2/3;var discrim=b*b/4 + a*a*a/27;var halfB=b/2;if(Math.abs(discrim)<=Polynomial.TOLERANCE)disrim=0;if(discrim>0){var e=Math.sqrt(discrim);var tmp;var root;tmp=-halfB+e;if(tmp>=0)root=Math.pow(tmp,1/3);else root=-Math.pow(-tmp,1/3);tmp=-halfB-e;if(tmp>=0)root+=Math.pow(tmp,1/3);else root-=Math.pow(-tmp,1/3);results.push(root-offset);}else if(discrim<0){var distance=Math.sqrt(-a/3);var angle=Math.atan2(Math.sqrt(-discrim),-halfB)/3;var cos=Math.cos(angle);var sin=Math.sin(angle);var sqrt3=Math.sqrt(3);results.push(2*distance*cos-offset);results.push(-distance*(cos+sqrt3*sin)-offset);results.push(-distance*(cos-sqrt3*sin)-offset);}else{var tmp;if(halfB>=0)tmp=-Math.pow(halfB,1/3);else tmp=Math.pow(-halfB,1/3);results.push(2*tmp-offset);results.push(-tmp-offset);}}return results;};
Polynomial.prototype.getQuarticRoots=function(){var results=new Array();if(this.getDegree()==4){var c4=this.coefs[4];var c3=this.coefs[3]/c4;var c2=this.coefs[2]/c4;var c1=this.coefs[1]/c4;var c0=this.coefs[0]/c4;var resolveRoots=new Polynomial(1,-c2,c3*c1-4*c0,-c3*c3*c0+4*c2*c0-c1*c1).getCubicRoots();var y=resolveRoots[0];var discrim=c3*c3/4-c2+y;if(Math.abs(discrim)<=Polynomial.TOLERANCE)discrim=0;if(discrim>0){var e=Math.sqrt(discrim);var t1=3*c3*c3/4-e*e-2*c2;var t2=(4*c3*c2-8*c1-c3*c3*c3)/(4*e);var plus=t1+t2;var minus=t1-t2;if(Math.abs(plus)<=Polynomial.TOLERANCE)plus=0;if(Math.abs(minus)<=Polynomial.TOLERANCE)minus=0;if(plus>=0){var f=Math.sqrt(plus);results.push(-c3/4 + (e+f)/2);results.push(-c3/4 + (e-f)/2);}if(minus>=0){var f=Math.sqrt(minus);results.push(-c3/4 + (f-e)/2);results.push(-c3/4 - (f+e)/2);}}else if(discrim<0){}else{var t2=y*y-4*c0;if(t2>=-Polynomial.TOLERANCE){if(t2<0)t2=0;t2=2*Math.sqrt(t2);t1=3*c3*c3/4-2*c2;if(t1+t2>=Polynomial.TOLERANCE){var d=Math.sqrt(t1+t2);results.push(-c3/4 + d/2);results.push(-c3/4 - d/2);}if(t1-t2>=Polynomial.TOLERANCE){var d=Math.sqrt(t1-t2);results.push(-c3/4 + d/2);results.push(-c3/4 - d/2);}}}}return results;};
function Vector2D(x,y){if(arguments.length>0){this.init(x,y);}}
Vector2D.prototype.init=function(x,y){this.x=x;this.y=y;};
Vector2D.prototype.length=function(){return Math.sqrt(this.x*this.x+this.y*this.y);};
Vector2D.prototype.dot=function(that){return this.x*that.x+this.y*that.y;};
Vector2D.prototype.cross=function(that){return this.x*that.y-this.y*that.x;}
Vector2D.prototype.unit=function(){return this.divide(this.length());};
Vector2D.prototype.unitEquals=function(){this.divideEquals(this.length());return this;};
Vector2D.prototype.add=function(that){return new Vector2D(this.x+that.x,this.y+that.y);};
Vector2D.prototype.addEquals=function(that){this.x+=that.x;this.y+=that.y;return this;};
Vector2D.prototype.subtract=function(that){return new Vector2D(this.x-that.x,this.y-that.y);};
Vector2D.prototype.subtractEquals=function(that){this.x-=that.x;this.y-=that.y;return this;};
Vector2D.prototype.multiply=function(scalar){return new Vector2D(this.x*scalar,this.y*scalar);};
Vector2D.prototype.multiplyEquals=function(scalar){this.x*=scalar;this.y*=scalar;return this;};
Vector2D.prototype.divide=function(scalar){return new Vector2D(this.x/ scalar, this.y /scalar);};
Vector2D.prototype.divideEquals=function(scalar){this.x/=scalar;this.y/=scalar;return this;};
Vector2D.prototype.perp=function(){return new Vector2D(-this.y,this.x);};
Vector2D.fromPoints=function(p1,p2){return new Vector2D(p2.x-p1.x,p2.y-p1.y);};
Vector2D.prototype.Dot=function (d){
var ell=app.activeDocument.pathItems.ellipse(this.y + d/2 , this.x - d/2 ,d,d);
ell.selected=false; return ell
};
function Intersection(status){if(arguments.length>0){this.init(status);}}
Intersection.prototype.init=function(status){this.status=status;this.points=new Array();};
Intersection.prototype.appendPoint=function(point){this.points.push(point);};
Intersection.prototype.appendPoints=function(points){this.points=this.points.concat(points);};
//-by ogebab---Gibt zurück: IntersectionObjekt (Obj.status / Obj.points / Obj.points.t1 / Obj.points.t2)
Intersection.prototype.IfInterSect=function(seg1,seg2){
var result;
if(seg1.type=="bez"){
if(seg2.type=="line"){
result=Intersection.intersectBezier3Line(seg1,seg2);
}else{
result=Intersection.intersectBezier3Bezier3(seg1,seg2);
}
}else{
if(seg2.type=="bez"){
result=Intersection.intersectBezier3Line(seg2,seg1);
}else{
result=Intersection.intersectLineLine(seg2,seg1);
}
}
if(result.status=="Intersection"){
for(var i=0;i<result.points.length ;i++){
if(seg1.type=="line"){
result.points.t1=getTOfPointOnLine(result.points, seg1);
}else{
result.points.t1=getTOfPointOnCubicCurve(result.points, seg1);
}
if(seg2.type=="line"){
result.points.t2=getTOfPointOnLine(result.points, seg2);
}else{
result.points.t2=getTOfPointOnCubicCurve(result.points, seg2);
}
}
}
return result
};
//--(bez, bez)
Intersection.intersectBezier3Bezier3=function(seg1,seg2){var a,b,c,d;var c13,c12,c11,c10;var c23,c22,c21,c20;var result=new Intersection("No Intersection");a=seg1.A.multiply(-1);b=seg1.B.multiply(3);c=seg1.C.multiply(-3);d=a.add(b.add(c.add(seg1.D)));c13=new Vector2D(d.x,d.y);a=seg1.A.multiply(3);b=seg1.B.multiply(-6);c=seg1.C.multiply(3);d=a.add(b.add(c));c12=new Vector2D(d.x,d.y);a=seg1.A.multiply(-3);b=seg1.B.multiply(3);c=a.add(b);c11=new Vector2D(c.x,c.y);c10=new Vector2D(seg1.A.x,seg1.A.y);a=seg2.A.multiply(-1);b=seg2.B.multiply(3);c=seg2.C.multiply(-3);d=a.add(b.add(c.add(seg2.D)));c23=new Vector2D(d.x,d.y);a=seg2.A.multiply(3);b=seg2.B.multiply(-6);c=seg2.C.multiply(3);d=a.add(b.add(c));c22=new Vector2D(d.x,d.y);a=seg2.A.multiply(-3);b=seg2.B.multiply(3);c=a.add(b);c21=new Vector2D(c.x,c.y);c20=new Vector2D(seg2.A.x,seg2.A.y);var c10x2=c10.x*c10.x;var c10x3=c10.x*c10.x*c10.x;var c10y2=c10.y*c10.y;var c10y3=c10.y*c10.y*c10.y;var c11x2=c11.x*c11.x;var c11x3=c11.x*c11.x*c11.x;var c11y2=c11.y*c11.y;var c11y3=c11.y*c11.y*c11.y;var c12x2=c12.x*c12.x;var c12x3=c12.x*c12.x*c12.x;var c12y2=c12.y*c12.y;var c12y3=c12.y*c12.y*c12.y;var c13x2=c13.x*c13.x;var c13x3=c13.x*c13.x*c13.x;var c13y2=c13.y*c13.y;var c13y3=c13.y*c13.y*c13.y;var c20x2=c20.x*c20.x;var c20x3=c20.x*c20.x*c20.x;var c20y2=c20.y*c20.y;var c20y3=c20.y*c20.y*c20.y;var c21x2=c21.x*c21.x;var c21x3=c21.x*c21.x*c21.x;var c21y2=c21.y*c21.y;var c22x2=c22.x*c22.x;var c22x3=c22.x*c22.x*c22.x;var c22y2=c22.y*c22.y;var c23x2=c23.x*c23.x;var c23x3=c23.x*c23.x*c23.x;var c23y2=c23.y*c23.y;var c23y3=c23.y*c23.y*c23.y;var poly=new Polynomial(-c13x3*c23y3+c13y3*c23x3-3*c13.x*c13y2*c23x2*c23.y+3*c13x2*c13.y*c23.x*c23y2,-6*c13.x*c22.x*c13y2*c23.x*c23.y+6*c13x2*c13.y*c22.y*c23.x*c23.y+3*c22.x*c13y3*c23x2-3*c13x3*c22.y*c23y2-3*c13.x*c13y2*c22.y*c23x2+3*c13x2*c22.x*c13.y*c23y2,-6*c21.x*c13.x*c13y2*c23.x*c23.y-6*c13.x*c22.x*c13y2*c22.y*c23.x+6*c13x2*c22.x*c13.y*c22.y*c23.y+3*c21.x*c13y3*c23x2+3*c22x2*c13y3*c23.x+3*c21.x*c13x2*c13.y*c23y2-3*c13.x*c21.y*c13y2*c23x2-3*c13.x*c22x2*c13y2*c23.y+c13x2*c13.y*c23.x*(6*c21.y*c23.y+3*c22y2)+c13x3*(-c21.y*c23y2-2*c22y2*c23.y-c23.y*(2*c21.y*c23.y+c22y2)),c11.x*c12.y*c13.x*c13.y*c23.x*c23.y-c11.y*c12.x*c13.x*c13.y*c23.x*c23.y+6*c21.x*c22.x*c13y3*c23.x+3*c11.x*c12.x*c13.x*c13.y*c23y2+6*c10.x*c13.x*c13y2*c23.x*c23.y-3*c11.x*c12.x*c13y2*c23.x*c23.y-3*c11.y*c12.y*c13.x*c13.y*c23x2-6*c10.y*c13x2*c13.y*c23.x*c23.y-6*c20.x*c13.x*c13y2*c23.x*c23.y+3*c11.y*c12.y*c13x2*c23.x*c23.y-2*c12.x*c12y2*c13.x*c23.x*c23.y-6*c21.x*c13.x*c22.x*c13y2*c23.y-6*c21.x*c13.x*c13y2*c22.y*c23.x-6*c13.x*c21.y*c22.x*c13y2*c23.x+6*c21.x*c13x2*c13.y*c22.y*c23.y+2*c12x2*c12.y*c13.y*c23.x*c23.y+c22x3*c13y3-3*c10.x*c13y3*c23x2+3*c10.y*c13x3*c23y2+3*c20.x*c13y3*c23x2+c12y3*c13.x*c23x2-c12x3*c13.y*c23y2-3*c10.x*c13x2*c13.y*c23y2+3*c10.y*c13.x*c13y2*c23x2-2*c11.x*c12.y*c13x2*c23y2+c11.x*c12.y*c13y2*c23x2-c11.y*c12.x*c13x2*c23y2+2*c11.y*c12.x*c13y2*c23x2+3*c20.x*c13x2*c13.y*c23y2-c12.x*c12y2*c13.y*c23x2-3*c20.y*c13.x*c13y2*c23x2+c12x2*c12.y*c13.x*c23y2-3*c13.x*c22x2*c13y2*c22.y+c13x2*c13.y*c23.x*(6*c20.y*c23.y+6*c21.y*c22.y)+c13x2*c22.x*c13.y*(6*c21.y*c23.y+3*c22y2)+c13x3*(-2*c21.y*c22.y*c23.y-c20.y*c23y2-c22.y*(2*c21.y*c23.y+c22y2)-c23.y*(2*c20.y*c23.y+2*c21.y*c22.y)),6*c11.x*c12.x*c13.x*c13.y*c22.y*c23.y+c11.x*c12.y*c13.x*c22.x*c13.y*c23.y+c11.x*c12.y*c13.x*c13.y*c22.y*c23.x-c11.y*c12.x*c13.x*c22.x*c13.y*c23.y-c11.y*c12.x*c13.x*c13.y*c22.y*c23.x-6*c11.y*c12.y*c13.x*c22.x*c13.y*c23.x-6*c10.x*c22.x*c13y3*c23.x+6*c20.x*c22.x*c13y3*c23.x+6*c10.y*c13x3*c22.y*c23.y+2*c12y3*c13.x*c22.x*c23.x-2*c12x3*c13.y*c22.y*c23.y+6*c10.x*c13.x*c22.x*c13y2*c23.y+6*c10.x*c13.x*c13y2*c22.y*c23.x+6*c10.y*c13.x*c22.x*c13y2*c23.x-3*c11.x*c12.x*c22.x*c13y2*c23.y-3*c11.x*c12.x*c13y2*c22.y*c23.x+2*c11.x*c12.y*c22.x*c13y2*c23.x+4*c11.y*c12.x*c22.x*c13y2*c23.x-6*c10.x*c13x2*c13.y*c22.y*c23.y-6*c10.y*c13x2*c22.x*c13.y*c23.y-6*c10.y*c13x2*c13.y*c22.y*c23.x-4*c11.x*c12.y*c13x2*c22.y*c23.y-6*c20.x*c13.x*c22.x*c13y2*c23.y-6*c20.x*c13.x*c13y2*c22.y*c23.x-2*c11.y*c12.x*c13x2*c22.y*c23.y+3*c11.y*c12.y*c13x2*c22.x*c23.y+3*c11.y*c12.y*c13x2*c22.y*c23.x-2*c12.x*c12y2*c13.x*c22.x*c23.y-2*c12.x*c12y2*c13.x*c22.y*c23.x-2*c12.x*c12y2*c22.x*c13.y*c23.x-6*c20.y*c13.x*c22.x*c13y2*c23.x-6*c21.x*c13.x*c21.y*c13y2*c23.x-6*c21.x*c13.x*c22.x*c13y2*c22.y+6*c20.x*c13x2*c13.y*c22.y*c23.y+2*c12x2*c12.y*c13.x*c22.y*c23.y+2*c12x2*c12.y*c22.x*c13.y*c23.y+2*c12x2*c12.y*c13.y*c22.y*c23.x+3*c21.x*c22x2*c13y3+3*c21x2*c13y3*c23.x-3*c13.x*c21.y*c22x2*c13y2-3*c21x2*c13.x*c13y2*c23.y+c13x2*c22.x*c13.y*(6*c20.y*c23.y+6*c21.y*c22.y)+c13x2*c13.y*c23.x*(6*c20.y*c22.y+3*c21y2)+c21.x*c13x2*c13.y*(6*c21.y*c23.y+3*c22y2)+c13x3*(-2*c20.y*c22.y*c23.y-c23.y*(2*c20.y*c22.y+c21y2)-c21.y*(2*c21.y*c23.y+c22y2)-c22.y*(2*c20.y*c23.y+2*c21.y*c22.y)),c11.x*c21.x*c12.y*c13.x*c13.y*c23.y+c11.x*c12.y*c13.x*c21.y*c13.y*c23.x+c11.x*c12.y*c13.x*c22.x*c13.y*c22.y-c11.y*c12.x*c21.x*c13.x*c13.y*c23.y-c11.y*c12.x*c13.x*c21.y*c13.y*c23.x-c11.y*c12.x*c13.x*c22.x*c13.y*c22.y-6*c11.y*c21.x*c12.y*c13.x*c13.y*c23.x-6*c10.x*c21.x*c13y3*c23.x+6*c20.x*c21.x*c13y3*c23.x+2*c21.x*c12y3*c13.x*c23.x+6*c10.x*c21.x*c13.x*c13y2*c23.y+6*c10.x*c13.x*c21.y*c13y2*c23.x+6*c10.x*c13.x*c22.x*c13y2*c22.y+6*c10.y*c21.x*c13.x*c13y2*c23.x-3*c11.x*c12.x*c21.x*c13y2*c23.y-3*c11.x*c12.x*c21.y*c13y2*c23.x-3*c11.x*c12.x*c22.x*c13y2*c22.y+2*c11.x*c21.x*c12.y*c13y2*c23.x+4*c11.y*c12.x*c21.x*c13y2*c23.x-6*c10.y*c21.x*c13x2*c13.y*c23.y-6*c10.y*c13x2*c21.y*c13.y*c23.x-6*c10.y*c13x2*c22.x*c13.y*c22.y-6*c20.x*c21.x*c13.x*c13y2*c23.y-6*c20.x*c13.x*c21.y*c13y2*c23.x-6*c20.x*c13.x*c22.x*c13y2*c22.y+3*c11.y*c21.x*c12.y*c13x2*c23.y-3*c11.y*c12.y*c13.x*c22x2*c13.y+3*c11.y*c12.y*c13x2*c21.y*c23.x+3*c11.y*c12.y*c13x2*c22.x*c22.y-2*c12.x*c21.x*c12y2*c13.x*c23.y-2*c12.x*c21.x*c12y2*c13.y*c23.x-2*c12.x*c12y2*c13.x*c21.y*c23.x-2*c12.x*c12y2*c13.x*c22.x*c22.y-6*c20.y*c21.x*c13.x*c13y2*c23.x-6*c21.x*c13.x*c21.y*c22.x*c13y2+6*c20.y*c13x2*c21.y*c13.y*c23.x+2*c12x2*c21.x*c12.y*c13.y*c23.y+2*c12x2*c12.y*c21.y*c13.y*c23.x+2*c12x2*c12.y*c22.x*c13.y*c22.y-3*c10.x*c22x2*c13y3+3*c20.x*c22x2*c13y3+3*c21x2*c22.x*c13y3+c12y3*c13.x*c22x2+3*c10.y*c13.x*c22x2*c13y2+c11.x*c12.y*c22x2*c13y2+2*c11.y*c12.x*c22x2*c13y2-c12.x*c12y2*c22x2*c13.y-3*c20.y*c13.x*c22x2*c13y2-3*c21x2*c13.x*c13y2*c22.y+c12x2*c12.y*c13.x*(2*c21.y*c23.y+c22y2)+c11.x*c12.x*c13.x*c13.y*(6*c21.y*c23.y+3*c22y2)+c21.x*c13x2*c13.y*(6*c20.y*c23.y+6*c21.y*c22.y)+c12x3*c13.y*(-2*c21.y*c23.y-c22y2)+c10.y*c13x3*(6*c21.y*c23.y+3*c22y2)+c11.y*c12.x*c13x2*(-2*c21.y*c23.y-c22y2)+c11.x*c12.y*c13x2*(-4*c21.y*c23.y-2*c22y2)+c10.x*c13x2*c13.y*(-6*c21.y*c23.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*c20.x*c12.x*c13y2*c22.y+2*c11.x*c20.x*c12.y*c22.x*c13y2+c11.x*c11.y*c12y2*c13.x*c22.x-3*c11.x*c12.x*c20.y*c22.x*c13y2-3*c11.x*c12.x*c21.x*c21.y*c13y2+4*c20.x*c11.y*c12.x*c22.x*c13y2-2*c10.x*c12x2*c12.y*c13.y*c22.y-6*c10.y*c20.x*c13x2*c13.y*c22.y-6*c10.y*c20.y*c13x2*c22.x*c13.y-6*c10.y*c21.x*c13x2*c21.y*c13.y-2*c10.y*c12x2*c12.y*c13.x*c22.y-2*c10.y*c12x2*c12.y*c22.x*c13.y-c11.x*c11.y*c12x2*c13.y*c22.y-2*c11.x*c11y2*c13.x*c22.x*c13.y+3*c20.x*c11.y*c12.y*c13x2*c22.y-2*c20.x*c12.x*c12y2*c13.x*c22.y-2*c20.x*c12.x*c12y2*c22.x*c13.y-6*c20.x*c20.y*c13.x*c22.x*c13y2-6*c20.x*c21.x*c13.x*c21.y*c13y2+3*c11.y*c20.y*c12.y*c13x2*c22.x+3*c11.y*c21.x*c12.y*c13x2*c21.y-2*c12.x*c20.y*c12y2*c13.x*c22.x-2*c12.x*c21.x*c12y2*c13.x*c21.y-c11y2*c12.x*c12.y*c13.x*c22.x+2*c20.x*c12x2*c12.y*c13.y*c22.y-3*c11.y*c21x2*c12.y*c13.x*c13.y+6*c20.y*c21.x*c13x2*c21.y*c13.y+2*c11x2*c11.y*c13.x*c13.y*c22.y+c11x2*c12.x*c12.y*c13.y*c22.y+2*c12x2*c20.y*c12.y*c22.x*c13.y+2*c12x2*c21.x*c12.y*c21.y*c13.y-3*c10.x*c21x2*c13y3+3*c20.x*c21x2*c13y3+3*c10x2*c22.x*c13y3-3*c10y2*c13x3*c22.y+3*c20x2*c22.x*c13y3+c21x2*c12y3*c13.x+c11y3*c13x2*c22.x-c11x3*c13y2*c22.y+3*c10.y*c21x2*c13.x*c13y2-c11.x*c11y2*c13x2*c22.y+c11.x*c21x2*c12.y*c13y2+2*c11.y*c12.x*c21x2*c13y2+c11x2*c11.y*c22.x*c13y2-c12.x*c21x2*c12y2*c13.y-3*c20.y*c21x2*c13.x*c13y2-3*c10x2*c13.x*c13y2*c22.y+3*c10y2*c13x2*c22.x*c13.y-c11x2*c12y2*c13.x*c22.y+c11y2*c12x2*c22.x*c13.y-3*c20x2*c13.x*c13y2*c22.y+3*c20y2*c13x2*c22.x*c13.y+c12x2*c12.y*c13.x*(2*c20.y*c22.y+c21y2)+c11.x*c12.x*c13.x*c13.y*(6*c20.y*c22.y+3*c21y2)+c12x3*c13.y*(-2*c20.y*c22.y-c21y2)+c10.y*c13x3*(6*c20.y*c22.y+3*c21y2)+c11.y*c12.x*c13x2*(-2*c20.y*c22.y-c21y2)+c11.x*c12.y*c13x2*(-4*c20.y*c22.y-2*c21y2)+c10.x*c13x2*c13.y*(-6*c20.y*c22.y-3*c21y2)+c20.x*c13x2*c13.y*(6*c20.y*c22.y+3*c21y2)+c13x3*(-2*c20.y*c21y2-c20y2*c22.y-c20.y*(2*c20.y*c22.y+c21y2)),-c10.x*c11.x*c12.y*c13.x*c21.y*c13.y+c10.x*c11.y*c12.x*c13.x*c21.y*c13.y+6*c10.x*c11.y*c21.x*c12.y*c13.x*c13.y-6*c10.y*c11.x*c12.x*c13.x*c21.y*c13.y-c10.y*c11.x*c21.x*c12.y*c13.x*c13.y+c10.y*c11.y*c12.x*c21.x*c13.x*c13.y-c11.x*c11.y*c12.x*c21.x*c12.y*c13.y+c11.x*c11.y*c12.x*c12.y*c13.x*c21.y+c11.x*c20.x*c12.y*c13.x*c21.y*c13.y+6*c11.x*c12.x*c20.y*c13.x*c21.y*c13.y+c11.x*c20.y*c21.x*c12.y*c13.x*c13.y-c20.x*c11.y*c12.x*c13.x*c21.y*c13.y-6*c20.x*c11.y*c21.x*c12.y*c13.x*c13.y-c11.y*c12.x*c20.y*c21.x*c13.x*c13.y-6*c10.x*c20.x*c21.x*c13y3-2*c10.x*c21.x*c12y3*c13.x+6*c10.y*c20.y*c13x3*c21.y+2*c20.x*c21.x*c12y3*c13.x+2*c10.y*c12x3*c21.y*c13.y-2*c12x3*c20.y*c21.y*c13.y-6*c10.x*c10.y*c21.x*c13.x*c13y2+3*c10.x*c11.x*c12.x*c21.y*c13y2-2*c10.x*c11.x*c21.x*c12.y*c13y2-4*c10.x*c11.y*c12.x*c21.x*c13y2+3*c10.y*c11.x*c12.x*c21.x*c13y2+6*c10.x*c10.y*c13x2*c21.y*c13.y+6*c10.x*c20.x*c13.x*c21.y*c13y2-3*c10.x*c11.y*c12.y*c13x2*c21.y+2*c10.x*c12.x*c21.x*c12y2*c13.y+2*c10.x*c12.x*c12y2*c13.x*c21.y+6*c10.x*c20.y*c21.x*c13.x*c13y2+4*c10.y*c11.x*c12.y*c13x2*c21.y+6*c10.y*c20.x*c21.x*c13.x*c13y2+2*c10.y*c11.y*c12.x*c13x2*c21.y-3*c10.y*c11.y*c21.x*c12.y*c13x2+2*c10.y*c12.x*c21.x*c12y2*c13.x-3*c11.x*c20.x*c12.x*c21.y*c13y2+2*c11.x*c20.x*c21.x*c12.y*c13y2+c11.x*c11.y*c21.x*c12y2*c13.x-3*c11.x*c12.x*c20.y*c21.x*c13y2+4*c20.x*c11.y*c12.x*c21.x*c13y2-6*c10.x*c20.y*c13x2*c21.y*c13.y-2*c10.x*c12x2*c12.y*c21.y*c13.y-6*c10.y*c20.x*c13x2*c21.y*c13.y-6*c10.y*c20.y*c21.x*c13x2*c13.y-2*c10.y*c12x2*c21.x*c12.y*c13.y-2*c10.y*c12x2*c12.y*c13.x*c21.y-c11.x*c11.y*c12x2*c21.y*c13.y-4*c11.x*c20.y*c12.y*c13x2*c21.y-2*c11.x*c11y2*c21.x*c13.x*c13.y+3*c20.x*c11.y*c12.y*c13x2*c21.y-2*c20.x*c12.x*c21.x*c12y2*c13.y-2*c20.x*c12.x*c12y2*c13.x*c21.y-6*c20.x*c20.y*c21.x*c13.x*c13y2-2*c11.y*c12.x*c20.y*c13x2*c21.y+3*c11.y*c20.y*c21.x*c12.y*c13x2-2*c12.x*c20.y*c21.x*c12y2*c13.x-c11y2*c12.x*c21.x*c12.y*c13.x+6*c20.x*c20.y*c13x2*c21.y*c13.y+2*c20.x*c12x2*c12.y*c21.y*c13.y+2*c11x2*c11.y*c13.x*c21.y*c13.y+c11x2*c12.x*c12.y*c21.y*c13.y+2*c12x2*c20.y*c21.x*c12.y*c13.y+2*c12x2*c20.y*c12.y*c13.x*c21.y+3*c10x2*c21.x*c13y3-3*c10y2*c13x3*c21.y+3*c20x2*c21.x*c13y3+c11y3*c21.x*c13x2-c11x3*c21.y*c13y2-3*c20y2*c13x3*c21.y-c11.x*c11y2*c13x2*c21.y+c11x2*c11.y*c21.x*c13y2-3*c10x2*c13.x*c21.y*c13y2+3*c10y2*c21.x*c13x2*c13.y-c11x2*c12y2*c13.x*c21.y+c11y2*c12x2*c21.x*c13.y-3*c20x2*c13.x*c21.y*c13y2+3*c20y2*c21.x*c13x2*c13.y,c10.x*c10.y*c11.x*c12.y*c13.x*c13.y-c10.x*c10.y*c11.y*c12.x*c13.x*c13.y+c10.x*c11.x*c11.y*c12.x*c12.y*c13.y-c10.y*c11.x*c11.y*c12.x*c12.y*c13.x-c10.x*c11.x*c20.y*c12.y*c13.x*c13.y+6*c10.x*c20.x*c11.y*c12.y*c13.x*c13.y+c10.x*c11.y*c12.x*c20.y*c13.x*c13.y-c10.y*c11.x*c20.x*c12.y*c13.x*c13.y-6*c10.y*c11.x*c12.x*c20.y*c13.x*c13.y+c10.y*c20.x*c11.y*c12.x*c13.x*c13.y-c11.x*c20.x*c11.y*c12.x*c12.y*c13.y+c11.x*c11.y*c12.x*c20.y*c12.y*c13.x+c11.x*c20.x*c20.y*c12.y*c13.x*c13.y-c20.x*c11.y*c12.x*c20.y*c13.x*c13.y-2*c10.x*c20.x*c12y3*c13.x+2*c10.y*c12x3*c20.y*c13.y-3*c10.x*c10.y*c11.x*c12.x*c13y2-6*c10.x*c10.y*c20.x*c13.x*c13y2+3*c10.x*c10.y*c11.y*c12.y*c13x2-2*c10.x*c10.y*c12.x*c12y2*c13.x-2*c10.x*c11.x*c20.x*c12.y*c13y2-c10.x*c11.x*c11.y*c12y2*c13.x+3*c10.x*c11.x*c12.x*c20.y*c13y2-4*c10.x*c20.x*c11.y*c12.x*c13y2+3*c10.y*c11.x*c20.x*c12.x*c13y2+6*c10.x*c10.y*c20.y*c13x2*c13.y+2*c10.x*c10.y*c12x2*c12.y*c13.y+2*c10.x*c11.x*c11y2*c13.x*c13.y+2*c10.x*c20.x*c12.x*c12y2*c13.y+6*c10.x*c20.x*c20.y*c13.x*c13y2-3*c10.x*c11.y*c20.y*c12.y*c13x2+2*c10.x*c12.x*c20.y*c12y2*c13.x+c10.x*c11y2*c12.x*c12.y*c13.x+c10.y*c11.x*c11.y*c12x2*c13.y+4*c10.y*c11.x*c20.y*c12.y*c13x2-3*c10.y*c20.x*c11.y*c12.y*c13x2+2*c10.y*c20.x*c12.x*c12y2*c13.x+2*c10.y*c11.y*c12.x*c20.y*c13x2+c11.x*c20.x*c11.y*c12y2*c13.x-3*c11.x*c20.x*c12.x*c20.y*c13y2-2*c10.x*c12x2*c20.y*c12.y*c13.y-6*c10.y*c20.x*c20.y*c13x2*c13.y-2*c10.y*c20.x*c12x2*c12.y*c13.y-2*c10.y*c11x2*c11.y*c13.x*c13.y-c10.y*c11x2*c12.x*c12.y*c13.y-2*c10.y*c12x2*c20.y*c12.y*c13.x-2*c11.x*c20.x*c11y2*c13.x*c13.y-c11.x*c11.y*c12x2*c20.y*c13.y+3*c20.x*c11.y*c20.y*c12.y*c13x2-2*c20.x*c12.x*c20.y*c12y2*c13.x-c20.x*c11y2*c12.x*c12.y*c13.x+3*c10y2*c11.x*c12.x*c13.x*c13.y+3*c11.x*c12.x*c20y2*c13.x*c13.y+2*c20.x*c12x2*c20.y*c12.y*c13.y-3*c10x2*c11.y*c12.y*c13.x*c13.y+2*c11x2*c11.y*c20.y*c13.x*c13.y+c11x2*c12.x*c20.y*c12.y*c13.y-3*c20x2*c11.y*c12.y*c13.x*c13.y-c10x3*c13y3+c10y3*c13x3+c20x3*c13y3-c20y3*c13x3-3*c10.x*c20x2*c13y3-c10.x*c11y3*c13x2+3*c10x2*c20.x*c13y3+c10.y*c11x3*c13y2+3*c10.y*c20y2*c13x3+c20.x*c11y3*c13x2+c10x2*c12y3*c13.x-3*c10y2*c20.y*c13x3-c10y2*c12x3*c13.y+c20x2*c12y3*c13.x-c11x3*c20.y*c13y2-c12x3*c20y2*c13.y-c10.x*c11x2*c11.y*c13y2+c10.y*c11.x*c11y2*c13x2-3*c10.x*c10y2*c13x2*c13.y-c10.x*c11y2*c12x2*c13.y+c10.y*c11x2*c12y2*c13.x-c11.x*c11y2*c20.y*c13x2+3*c10x2*c10.y*c13.x*c13y2+c10x2*c11.x*c12.y*c13y2+2*c10x2*c11.y*c12.x*c13y2-2*c10y2*c11.x*c12.y*c13x2-c10y2*c11.y*c12.x*c13x2+c11x2*c20.x*c11.y*c13y2-3*c10.x*c20y2*c13x2*c13.y+3*c10.y*c20x2*c13.x*c13y2+c11.x*c20x2*c12.y*c13y2-2*c11.x*c20y2*c12.y*c13x2+c20.x*c11y2*c12x2*c13.y-c11.y*c12.x*c20y2*c13x2-c10x2*c12.x*c12y2*c13.y-3*c10x2*c20.y*c13.x*c13y2+3*c10y2*c20.x*c13x2*c13.y+c10y2*c12x2*c12.y*c13.x-c11x2*c20.y*c12y2*c13.x+2*c20x2*c11.y*c12.x*c13y2+3*c20.x*c20y2*c13x2*c13.y-c20x2*c12.x*c12y2*c13.y-3*c20x2*c20.y*c13.x*c13y2+c12x2*c20y2*c12.y*c13.x);var roots=poly.getRootsInInterval(0,1);for(var i=0;i<roots.length;i++){var s=roots;var xRoots=new Polynomial(c13.x,c12.x,c11.x,c10.x-c20.x-s*c21.x-s*s*c22.x-s*s*s*c23.x).getRoots();var yRoots=new Polynomial(c13.y,c12.y,c11.y,c10.y-c20.y-s*c21.y-s*s*c22.y-s*s*s*c23.y).getRoots();if(xRoots.length>0&&yRoots.length>0){var TOLERANCE=1e-3;checkRoots:for(var j=0;j<xRoots.length;j++){var xRoot=xRoots;if(0<=xRoot&&xRoot<=1){for(var k=0;k<yRoots.length;k++){if(Math.abs(xRoot-yRoots )<TOLERANCE){result.points.push(c23.multiply(s*s*s).add(c22.multiply(s*s).add(c21.multiply(s).add(c20))));break checkRoots;}}}}}}if(result.points.length>0)result.status="Intersection";return result;};
//--(bez, line) erwartet trotzdem segment
Intersection.intersectBezier3Line=function(seg1,seg2){var a,b,c,d;var c3,c2,c1,c0;var cl;var n;var min=seg2.A.min(seg2.D);var max=seg2.A.max(seg2.D);var result=new Intersection("No Intersection");a=seg1.A.multiply(-1);b=seg1.B.multiply(3);c=seg1.C.multiply(-3);d=a.add(b.add(c.add(seg1.D)));c3=new Vector2D(d.x,d.y);a=seg1.A.multiply(3);b=seg1.B.multiply(-6);c=seg1.C.multiply(3);d=a.add(b.add(c));c2=new Vector2D(d.x,d.y);a=seg1.A.multiply(-3);b=seg1.B.multiply(3);c=a.add(b);c1=new Vector2D(c.x,c.y);c0=new Vector2D(seg1.A.x,seg1.A.y);n=new Vector2D(seg2.A.y-seg2.D.y,seg2.D.x-seg2.A.x);cl=seg2.A.x*seg2.D.y-seg2.D.x*seg2.A.y;roots=new Polynomial(n.dot(c3),n.dot(c2),n.dot(c1),n.dot(c0)+cl).getRoots();for(var i=0;i<roots.length;i++){var t=roots;if(0<=t&&t<=1){var p5=seg1.A.lerp(seg1.B,t);var p6=seg1.B.lerp(seg1.C,t);var p7=seg1.C.lerp(seg1.D,t);var p8=p5.lerp(p6,t);var p9=p6.lerp(p7,t);var pt10=p8.lerp(p9,t);if(seg2.A.x==seg2.D.x){if(min.y<=pt10.y&&pt10.y<=max.y){result.status="Intersection";result.appendPoint(pt10);}}else if(seg2.A.y==seg2.D.y){if(min.x<=pt10.x&&pt10.x<=max.x){result.status="Intersection";result.appendPoint(pt10);}}else if(pt10.gte(min)&&pt10.lte(max)){result.status="Intersection";result.appendPoint(pt10);}}}return result;};
//--(line, line) erwartet trotzdem segment
Intersection.intersectLineLine=function (seg1,seg2){var result;var ua_t=(seg2.D.x-seg2.A.x)*(seg1.A.y-seg2.A.y)-(seg2.D.y-seg2.A.y)*(seg1.A.x-seg2.A.x);var ub_t=(seg1.D.x-seg1.A.x)*(seg1.A.y-seg2.A.y)-(seg1.D.y-seg1.A.y)*(seg1.A.x-seg2.A.x);var u_b=(seg2.D.y-seg2.A.y)*(seg1.D.x-seg1.A.x)-(seg2.D.x-seg2.A.x)*(seg1.D.y-seg1.A.y);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){result=new Intersection("Intersection");result.points.push(new Point(seg1.A.x+ua*(seg1.D.x-seg1.A.x),seg1.A.y+ua*(seg1.D.y-seg1.A.y)));}else{result=new Intersection("No Intersection");}}else{if(ua_t==0||ub_t==0){result=new Intersection("Coincident");}else{result=new Intersection("Parallel");}}return result;};
//------------------------
Intersection.intersectBezier3Circle=function(p1,p2,p3,p4,c,r){return Intersection.intersectBezier3Ellipse(p1,p2,p3,p4,c,r,r);};
Intersection.intersectBezier3Ellipse=function(p1,p2,p3,p4,ec,rx,ry){var a,b,c,d;var c3,c2,c1,c0;var result=new Intersection("No Intersection");a=p1.multiply(-1);b=p2.multiply(3);c=p3.multiply(-3);d=a.add(b.add(c.add(p4)));c3=new Vector2D(d.x,d.y);a=p1.multiply(3);b=p2.multiply(-6);c=p3.multiply(3);d=a.add(b.add(c));c2=new Vector2D(d.x,d.y);a=p1.multiply(-3);b=p2.multiply(3);c=a.add(b);c1=new Vector2D(c.x,c.y);c0=new Vector2D(p1.x,p1.y);var rxrx=rx*rx;var ryry=ry*ry;var poly=new Polynomial(c3.x*c3.x*ryry+c3.y*c3.y*rxrx,2*(c3.x*c2.x*ryry+c3.y*c2.y*rxrx),2*(c3.x*c1.x*ryry+c3.y*c1.y*rxrx)+c2.x*c2.x*ryry+c2.y*c2.y*rxrx,2*c3.x*ryry*(c0.x-ec.x)+2*c3.y*rxrx*(c0.y-ec.y)+2*(c2.x*c1.x*ryry+c2.y*c1.y*rxrx),2*c2.x*ryry*(c0.x-ec.x)+2*c2.y*rxrx*(c0.y-ec.y)+c1.x*c1.x*ryry+c1.y*c1.y*rxrx,2*c1.x*ryry*(c0.x-ec.x)+2*c1.y*rxrx*(c0.y-ec.y),c0.x*c0.x*ryry-2*c0.y*ec.y*rxrx-2*c0.x*ec.x*ryry+c0.y*c0.y*rxrx+ec.x*ec.x*ryry+ec.y*ec.y*rxrx-rxrx*ryry);
var roots1=poly.getRootsInInterval(0,1);for(var i=0;i<roots1.length;i++){var t=roots1;result.points.push(c3.multiply(t*t*t).add(c2.multiply(t*t).add(c1.multiply(t).add(c0))));}if(result.points.length>0)result.status="Intersection";return result;};
Intersection.intersectLinePolygon=function(a1,a2,points){var result=new Intersection("No Intersection");var length=points.length;for(var i=0;i<length;i++){var b1=points;var b2=points[(i+1)%length];var inter=Intersection.intersectLineLine(a1,a2,b1,b2);result.appendPoints(inter.points);}if(result.points.length>0)result.status="Intersection";return result;};
Intersection.intersectPolygonPolygon=function(points1,points2){var result=new Intersection("No Intersection");var length=points1.length;for(var i=0;i<length;i++){var a1=points1;var a2=points1[(i+1)%length];var inter=Intersection.intersectLinePolygon(a1,a2,points2);result.appendPoints(inter.points);}if(result.points.length>0)result.status="Intersection";return result;};
//--------------by Andreas Weber-----------------------
function getTOfPointOnCubicCurve(p0, seg){return getTOfPoint.apply(this, arguments);}
function getTOfPoint(p0,seg){var p1=seg.A,p2=seg.B,p3=seg.C,p4=seg.D;var ax,bx,cx,dx,ay,by,cy,dy,xl,yl,i,j,k,len1,len2,len3,min,r,round,v;var p0x=p0.x,p0y=p0.y,p1x=p1.x,p1y=p1.y,p2x=p2.x,p2y=p2.y,p3x=p3.x,p3y=p3.y;round=10000;var p4x=p4.x,p4y=p4.y;ax=p4x-3*p3x+3*p2x-p1x;bx=3*p3x-6*p2x+3*p1x;cx=3*p2x-3*p1x;dx=p1x-p0x;ay=p4y-3*p3y+3*p2y-p1y;by=3*p3y-6*p2y+3*p1y;cy=3*p2y-3*p1y;dy=p1y-p0y;min=1/round;if(ax<min&&ax>0-min){ax=0} if(bx<min&&bx>0-min){bx=0} if(cx<min&&cx>0-min){cx=0} if(dx<min&&dx>0-min){dx=0} if(ay<min&&ay>0-min){ay=0} if(by<min&&by>0-min){by=0} if(cy<min&&cy>0-min){cy=0} if(dy<min&&dy>0-min){dy=0} xl=solveCubicPolynomial(ax,bx,cx,dx);yl=solveCubicPolynomial(ay,by,cy,dy);for(i=0,len1=xl.length;i<len1;i++){v=xl;if(v!='NAN'){xl=Math.round(v*round)/round;}v=xl;if(v<0||v>1){xl.splice(i,1);len1--;i--;}}for(i=0,len1=yl.length;i<len1;i++){v=yl;if(v!='NAN'){yl=Math.round(v*round)/round;}v=yl;if(v<0||v>1){yl.splice(i,1);len1--;i--;}}if(xl[0]=='NAN'){return yl;}else if(yl[0]=='NAN'){return xl;}else{r=new Array();len1=xl.length;len2=yl.length;for(i=0;i<len1;i++){for(j=0;j<len2;j++){if(xl==yl){for(k=0,len3;k<r.length;k++){if(r ==xl){break;}}r.push(xl);yl.splice(j,1);len2--;}}}if(r.length>0){return r;} return[-1];}}
/*by Aless Lasaruk, adapted by Andreas Weber*/
function solveCubicPolynomial(a, b, c, d) { var p, q, di, pi; if(a==0){ if(b==0){ if(c==0 && d==0){ return ['NAN']; }else if(c != 0){ return [-d/c]; } }else{ di = c*c-4*b*d; if (di < 0){ return []; }else if(di==0) { return [-c/(2*b)]; }else{ return [(-c + Math.sqrt(di))/(2*b), (-c - Math.sqrt(di))/(2*b)]; } } } p = (3*a*c - b*b)/(3*a*a); q = (2*b*b*b-9*a*b*c+27*a*a*d)/(27*a*a*a); di = q*q/4+p*p*p/27; if(di > 0){ return [crt(-q/2+Math.sqrt(di))+crt(-q/2-Math.sqrt(di))-b/(3*a)]; }else if(di==0) { return [crt(q/2)-b/(3*a), -crt(4*q)-b/(3*a)]; }else{ pi = Math.PI; return [2*Math.sqrt(-p/3)*Math.cos(1/3*Math.acos(-q/2*Math.sqrt(-27/(p*p*p))))- b/(3*a), -2*Math.sqrt(-p/3)*Math.cos(1/3*Math.acos(-q/2*Math.sqrt(-27/(p*p*p)))+ pi/3) - b/(3*a), -2*Math.sqrt(-p/3)*Math.cos(1/3*Math.acos(-q/2*Math.sqrt(-27/(p*p*p)))- pi/3) - b/(3*a) ]; } }
function crt(x){return x<0 ? -Math.pow(-x,1/3) : Math.pow(x,1/3);}
//-----------------------------
function getTOfPointOnLine(pt, seg){return seg.A.distanceFrom(pt)/seg.A.distanceFrom(seg.D);}
////----------end of intersection
// POINT OBJ
// point und line: basiert auf code: written by Kevin Lindsey
// (kevin@kevlindev.com)
function Point(x, y) {
this.name = "_point";
if (arguments.length == 1) {
this.x = x[0];
this.y = x[1]
}
if (arguments.length == 2) {
this.x = x;
this.y = y
}
this.arr = [ this.x, this.y ];
}
Point.prototype.lerp = function(that, t) {
return new Point(this.x + (that.x - this.x) * t, this.y + (that.y - this.y)
* t);
};
Point.prototype.distanceFrom = function(that) {
var dx = this.x - that.x;
var dy = this.y - that.y;
return Math.sqrt(dx * dx + dy * dy);
};
Point.prototype.angle = function(p2) {
var w = Math.atan2(p2.y - this.y, p2.x - this.x) * 180 / Math.PI;
if (w < 0) {
w = w + 360
}
return w;
};
Point.prototype.plumb = function(lp1, lp2) {
var x = this.x, y = this.y, x0 = lp1.x, y0 = lp1.y, x1 = lp2.x, y1 = lp2.y;
if (!(x1 - x0))
return new Point(x0, y);
else if (!(y1 - y0))
return new Point(x, y0);
var left, tg = -1 / ((y1 - y0) / (x1 - x0));
var o = {
x : left = (x1 * (x * tg - y + y0) + x0 * (x * -tg + y - y1))
/ (tg * (x1 - x0) + y0 - y1),
y : tg * left - tg * x + y
};
return new Point(o.x, o.y);
};
Point.prototype.isInHull = function(hull) {// hull? handlungsbedarf
// wenn hull=bezier
if (hull.A) {
hull.pPoints.push(hull.A);
hull.pPoints.push(hull.B);
hull.pPoints.push(hull.C);
hull.pPoints.push(hull.D);
}
var w = new Array();
for ( var i1 = 0; i1 < hull.pPoints.length; i1++) {
w[i1] = this.angle(hull.pPoints[i1])
}
w.sort(NumSort);
for ( var i = 0; i < w.length; i++) {
if (i == 0) {
if (w[0] + 360 - w[w.length - 1] > 180) {
return false
}
} else {
if (w - w[i - 1] > 180) {
return false
}
}
}
return true
};
Point.prototype.Dot = function(d) {
var ell = app.activeDocument.pathItems.ellipse(this.y + d / 2, this.x - d
/ 2, d, d);
ell.selected = false;
return ell
};
Point.prototype.Line = function(pt) {
var list = [ [ this.x, this.y ], [ pt.x, pt.y ] ], line = app.activeDocument.pathItems
.add();
line.setEntirePath(list);
return line
};
Point.prototype.add = function(that) {
return new Point(this.x + that.x, this.y + that.y);
};
Point.prototype.addEquals = function(that) {
this.x += that.x;
this.y += that.y;
return this;
};
Point.prototype.scalarAdd = function(scalar) {
return new Point(this.x + scalar, this.y + scalar);
};
Point.prototype.scalarAddEquals = function(scalar) {
this.x += scalar;
this.y += scalar;
return this;
};
Point.prototype.subtract = function(that) {
return new Point(this.x - that.x, this.y - that.y);
};
Point.prototype.subtractEquals = function(that) {
this.x -= that.x;
this.y -= that.y;
return this;
};
Point.prototype.scalarSubtract = function(scalar) {
return new Point(this.x - scalar, this.y - scalar);
};
Point.prototype.scalarSubtractEquals = function(scalar) {
this.x -= scalar;
this.y -= scalar;
return this;
};
Point.prototype.multiply = function(scalar) {
return new Point(this.x * scalar, this.y * scalar);
};
Point.prototype.multiplyEquals = function(scalar) {
this.x *= scalar;
this.y *= scalar;
return this;
};
Point.prototype.divide = function(scalar) {
return new Point(this.x / scalar, this.y / scalar);
};
Point.prototype.divideEquals = function(scalar) {
this.x /= scalar;
this.y /= scalar;
return this;
};
Point.prototype.eq = function(that) {
return (this.x == that.x && this.y == that.y);
};
Point.prototype.lt = function(that) {
return (this.x < that.x && this.y < that.y);
};
Point.prototype.lte = function(that) {
return (this.x <= that.x && this.y <= that.y);
};
Point.prototype.gt = function(that) {
return (this.x > that.x && this.y > that.y);
};
Point.prototype.gte = function(that) {
return (this.x >= that.x && this.y >= that.y);
};
Point.prototype.min = function(that) {
return new Point(Math.min(this.x, that.x), Math.min(this.y, that.y));
};
Point.prototype.max = function(that) {
return new Point(Math.max(this.x, that.x), Math.max(this.y, that.y));
};
Point.prototype.toString = function() {
return this.x + "," + this.y;
};
Point.prototype.setXY = function(x, y) {
this.x = x;
this.y = y;
};
Point.prototype.setFromPoint = function(that) {
this.x = that.x;
this.y = that.y;
};
Point.prototype.swap = function(that) {
var x = this.x;
var y = this.y;
this.x = that.x;
this.y = that.y;
that.x = x;
that.y = y;
};
// LINE OBJ
function Line(p1, p2) {
this.p1 = p1;
this.p2 = p2;
this.type = this.type()
}
Line.prototype.type = function() {
if (this.p1.x == this.p2.x) {
return "vert"
}
if (this.p1.y == this.p2.y) {
return "hori"
}
return "diag"
};
// Steigung
Line.prototype.slope = function() {
var p = this.p2.subtract(this.p1);
return p.y / p.x
};
Line.prototype.YatX0 = function() {
return this.p1.y - this.slope() * this.p1.x
};
Line.prototype.isParallel = function(that) {
if (this.type == "diag" && that.type == "diag") {
if (this.slope() == that.slope()) {
return true
}
return false
}
if (this.type == that.type)
return true;
return false
};
Line.prototype.intersect = function(that) {
var a = this.type, b = that.type, x, y;
if (this.isParallel(that) == false) {
if (a == "hori") {
y = this.p1.y;
if (b == "vert")
return new Point(that.p1.x, y);
if (b == "diag")
return new Point(equate(that.YatX0(), y)
/ equate(this.slope(), that.slope()), y)
}
if (a == "vert") {
x = this.p1.x;
if (b == "hori")
return new Point(x, that.p1.y);
if (b == "diag")
return new Point(x, that.slope() * x + that.YatX0())
}
if (a == "diag") {
if (b == "hori") {
y = that.p1.y;
x = equate(y, this.YatX0())
/ equate(this.slope(), that.slope());
return new Point(x, y)
}
if (b == "vert") {
x = that.p1.x;
y = this.slope() * x + this.YatX0();
return new Point(x, y)
}
if (b == "diag") {
x = equate(that.YatX0(), this.YatX0())
/ equate(this.slope(), that.slope());
y = this.slope() * x + this.YatX0();
return new Point(x, y)
}
}
}
return "parallel"
};
Line.prototype.plumb = function(pt) { // lotrecht
var x = pt.x, y = pt.y, x0 = this.p1.x, y0 = this.p1.y, x1 = this.p2.x, y1 = this.p2.y;
if (!(x1 - x0))
return new Point(x0, y);
else if (!(y1 - y0))
return new Point(x, y0);
var left, tg = -1 / ((y1 - y0) / (x1 - x0));
var o = {
x : left = (x1 * (x * tg - y + y0) + x0 * (x * -tg + y - y1))
/ (tg * (x1 - x0) + y0 - y1),
y : tg * left - tg * x + y
};
return new Point(o.x, o.y);
};
Line.prototype.getT = function(pt) {
return this.p1.distanceFrom(pt) / this.p1.distanceFrom(this.p2);
};
Line.prototype.hasPoint = function(pt) {
var t = this.getT(pt);
if (t < 0 || t > 1)
return t;
return t
};
// BEZIER OBJ
function Bezier(p1, p2) {
this.name = "_bezier";
this.A = p1.an;
this.B = p1.rDir;
this.C = p2.lDir;
this.D = p2.an;
this.type = this.isLine()
}
Bezier.prototype.isLine = function() {
var self = this;
if (self.A.x == self.B.x && self.A.y == self.B.y && self.D.x == self.C.x
&& self.D.y == self.C.y) {
return "line"
}
return "bez"
};
Bezier.prototype.PointsForT = function(ti) {
if (this.type == "bez") {
this.BT = this.A.lerp(this.B, ti); // new B
this.tt = this.B.lerp(this.C, ti); // ???
this.CT = this.C.lerp(this.D, ti); // new C
this.T1 = this.BT.lerp(this.tt, ti);// new point lDir
this.T2 = this.tt.lerp(this.CT, ti);// new point rDir
this.PP = this.T1.lerp(this.T2, ti);// new point an
this.t = ti;
this.normale = function() {
var n = this.PP.subtract(this.T1), n2 = new Point(-n.y, n.x);
return n2.add(this.PP);
}
// tangent is T1 or T2
if (ti <= 0.001) {
this.tang = this.T2.angle(this.PP)
}
if (ti >= 0.999) {
this.tang = this.PP.angle(this.T1)
}
if (ti > 0.001 && ti < 0.999) {
this.tang = this.T2.angle(this.T1)
}
}
if (this.type == "line") {
this.PP = this.A.lerp(this.D, ti);
// return this
}
return this
};
Bezier.prototype.BezLength = function(tolerance) {
var seelf = this, len1 = this.A.distanceFrom(this.D), len2 = 0, result = new Array(
[ this.A, 0 ]);
result.push( [ this.D, 1 ]);
var ri = 1, s = 2, z = 0;
romberg();
function romberg() {
z += 1;
for (ri; ri < s; ri += 2) {
var temp = seelf.PointsForT(ri / s);
result = result.insert( [ temp.PP, temp.t ], ri);//
}
s = s * 2;
ri = 1;
for ( var j = 0; j < result.length; j++) {
result[0][2] = len2;
if (result[0][1] < 1) {
len2 += result[0][0].distanceFrom(result[1][0]);
}
result.turn1();
}
}
while (len2 - len1 > tolerance || z < 5) { //
len1 = len2;
len2 = 0;
romberg();
}
return {
bezLength : len2,
list : result
};
// return len2;
}
Bezier.prototype.getTonLength = function(le, tolerance) {
try {
var dat = this.BezLength(tolerance)
} catch (e) {
return "getLengthFail"
}
var lDiff; // var t;
if (dat.bezLength < le) {
le -= 0.0001
}
if (dat.bezLength < le) {
alert("getTonLength_toShort \n " + le + " " + dat.bezLength);
return "toShort"
}
if (dat.bezLength == le)
return 1;
if (le == 0)
return 0
// if(dat.bezLength>le){alert("getTonLength_toLong \n "+le+"
// "+dat.bezLength);return "toLong"}
// if(dat.bezLength==le){le=le-0.1}
for ( var i = 0; i < dat.list.length; i++) {
if (dat.list[2] > le) {
lDiff = (dat.list[2] - dat.list[i - 1][2])
/ (le - dat.list[i - 1][2]);
// alert();
return dat.list[i - 1][1] + dat.list[1][1] / lDiff;
}
}
}
// EXTENDED PATHPOINT OBJ
function XpPoint(ld, an, rd) {
if (arguments.length < 1)
return null;
this.name = "_pPoint";
if (ld.anchor) { // illustrator pathPoint
this.lDir = new Point(ld.leftDirection);
this.an = new Point(ld.anchor);
this.rDir = new Point(ld.rightDirection);
this.type = ld.pointType;
} else if (ld.an) { // pPoint
this.lDir = ld.lDir;
this.an = ld.an;
this.rDir = ld.rDir;
this.type = ld.type;
} else if (ld.x) { // point('s)
if (an)
this.an = an
else
this.an = ld;
this.lDir = ld;
if (rd)
this.rDir = rd
else
this.rDir = ld;
// this.ai.type=
}
}
// only useful for pathPoints on Beziers, not on rect or line or ....
XpPoint.prototype.isCurvePoint = function() {
if ((Math.round((this.rDir.y - this.an.y) / (this.rDir.x - this.an.x)
* 1000) == Math.round((this.lDir.y - this.an.y)
/ (this.lDir.x - this.an.x) * 1000))
|| (this.rDir.y == this.an.y && this.lDir.y == this.an.y)
|| (this.rDir.x == this.an.x && this.lDir.x == this.an.x)) {
return true
}
return false
};
// EXTENDED PATH OBJ
Xpath.prototype = new Xitem();
Xpath.prototype.constructor = Xpath ;
function Xpath(pfad) {
Xitem.call(this, pfad);
this.name = "_Xpath";
this.ai = pfad;
if (pfad.pathPoints) {
this.pPoints = new Array();
this.pPoints.name = "_pPoints";
for ( var i = 0; i < pfad.pathPoints.length; i++) {
this.pPoints.push(new XpPoint(pfad.pathPoints))
}
}
if (this.pPoints) {
this.beziers = new Array();
this.beziers.name = "_beziers";
var i73 = 0, pts = this.pPoints;
if (pfad.closed == false)
i73++;
for (i73; i73 < pts.length; i73++) {
this.beziers.push(new Bezier(pts[0], pts[1]));
pts.turn1()
}
pts.turn1()
}
}
Xpath.prototype.SetPath = function() {
var ancor = new Array(), p = this.pPoints;
for ( var i1 = 0; i1 < p.length; i1++) {
ancor.push( [ p[i1].an.x, p[i1].an.y ]);
}
var P;
if (this.ai.pathPoints) {
P = this.ai.pathPoints.parent
} else {
P = app.activeDocument.pathItems.add()
}
P.setEntirePath(ancor);
for ( var i = 0; i < p.length; i++) {
P.pathPoints.rightDirection = [ p.rDir.x, p.rDir.y ];
P.pathPoints.leftDirection = [ p.lDir.x, p.lDir.y ];
if (p.type) {
P.pathPoints.pointType = p.type
}
}
};
// EXTENDED ITEM OBJ
function Xitem(obj) {
if (obj) {
this.name = "_Xitem";
this.ai = obj;
Xitem.prototype.center = new Point(this.ai.position[0] + this.ai.width
/ 2, this.ai.position[1] - this.ai.height / 2);
Xitem.prototype.bottomLeft = new Point(this.ai.position[0],
this.ai.position[1] - this.ai.height);
Xitem.prototype.topRight = new Point(this.ai.position[0]
+ this.ai.width, this.ai.position[1]);
}
}
Xitem.prototype.SetToCenter = function(point) {
this.ai.position = [ point.x - this.ai.width / 2,
point.y + this.ai.height / 2 ]
};
Xitem.prototype.SetToBottom = function(point) {
this.ai.position = [ point.x - this.ai.width / 2, point.y + this.ai.height ]
};
Xitem.prototype.SetToTop = function(point) {
this.ai.position = [ point.x - this.ai.width / 2, point.y ]
};
Xitem.prototype.inside = function(pt) {
if (pt.x < this.topRight.x && pt.y < this.topRight.y) {
if (pt.x > this.bottomLeft.x && pt.y > this.bottomLeft.y) {
return true
}
}
return false
};
// Xitem.prototype.duplicate=function (){return new Xitem(this.ai.duplicate())};
// -------------------------------------------------------------------
// ----------END OF
// XTENDAIJS----------------------------------------------------------
function Demo(h) {
alert("we will take its first 4 pathpoints as points for a beziersegment");
var pfad = new Xpath(h);
sel[0].remove();
var a = pfad.pPoints[1].an;
var b = pfad.pPoints[2].an;
var c = pfad.pPoints[3].an;
var d = pfad.pPoints[0].an;
var bez = new Bezier( {
an : a,
rDir : b
}, {
lDir : c,
an : d
}) // ------ (pPoint1 , pPoint2)
// ------{A,B,C,D} are Points ( with properties x,y)
// ----------------------------------------------------------------------------------------------------------------
var p1 = bez.A.Dot(15), p2 = bez.D.Dot(15);
redraw()
alert("These are the anchors");
// ----------------------------------------------------------------------------------------------------------------
// ---------Bezier.Point.function(size)
var p3 = bez.B.Dot(10), p4 = bez.C.Dot(10);
// ---------Bezier.Point.function(Point)
var l1 = bez.A.Line(bez.B), l2 = bez.C.Line(bez.D);
redraw()
alert("These are the handles");
// ----------------------------------------------------------------------------------------------------------------
var t03 = bez.PointsForT(0.3);
t03.PP.Dot(10);
redraw()
alert("This is the Point on the Path at T=0.3...");
// ---------------------------------------------------------------------------------------------------------------
bez.B.Line(bez.C);
t03.BT.Line(t03.tt);
t03.CT.Line(t03.tt);
t03.T1.Line(t03.T2);
redraw()
alert("... and this is how it was calculated");
// ---------------------------------------------------------------------------------------------------------------
bez.PointsForT(0.1).PP.Dot(10);
bez.PointsForT(0.2).PP.Dot(10);
bez.PointsForT(0.5).PP.Dot(10);
bez.PointsForT(0.4).PP.Dot(10);
bez.PointsForT(0.6).PP.Dot(10);
bez.PointsForT(0.7).PP.Dot(10);
bez.PointsForT(0.8).PP.Dot(10);
bez.PointsForT(0.9).PP.Dot(10);
redraw()
alert("Points from T=0.1 to 0.9");
// --------------------------------------------------------------------------------------------------------------
var pa1 = new Xpath(pa.add()); //-------- normally created from existing PathItem...
// -------...then this step is not necessary:
pa1.pPoints = [ new XpPoint(a, a, b), new XpPoint(c, d, d) ];
pa1.SetPath();
redraw()
alert("This is the resulting Path \n try to set a point manually at pos t 0.3\n and observe how the handles change");
}
function Demo3(PagEitem) {
var p = new Xpath(PagEitem);
var pZero = new Point(0, 0);
alert(p.center);
p.SetToCenter(pZero);
redraw();
alert(p.name);
alert(p.ai.typename);
p.SetToCenter( {
x : 20,
y : 20
});
}
function Demo2() {
var pa1 = new Xpath(sel[0]), pa2 = new Xpath(sel[1]);
for ( var i_1 = 0; i_1 < pa1.beziers.length; i_1++) {
for ( var i_2 = 0; i_2 < pa2.beziers.length; i_2++) {
var inters = new Intersection().IfInterSect(pa1.beziers[i_1],
pa2.beziers[i_2]);
if (inters.status == "Intersection") {
for ( var i_3 = 0; i_3 < inters.points.length; i_3++) {
// if you want to know the point...
inters.points[i_3].Dot(7);
// ...to manipulate path 1...
pa1.beziers[i_1].PointsForT(inters.points[i_3].t1).PP
.Dot(15);
// ...path 2
pa2.beziers[i_2].PointsForT(inters.points[i_3].t2).PP
.Dot(20);
}
}
}
}
}
function polyline(){
for(var i =0;i<pa.length;i++){
var polypoints=[];
var pfad= new Xpath(pa);
for(var j =0;j<pfad.beziers.length;j++){
var bez = pfad.beziers;
for(var k=0; k<=1; k+=0.1){
var point = bez.PointsForT(k).PP;
polypoints.push([point.x,point.y]);
}
}
pa.setEntirePath(polypoints);
}
}
//-----Begin Script--------
var ad = app.activeDocument, pa = ad.pathItems;
var sel = GetSelPaths();
//demo1
// if (sel) {
// //sel.selected=false; redraw();
// Demo3(sel[0])
// } else {
// alert("please draw a path with at least 4 ancors, select it and run again");
// }
//demo2 select 2 (overlapping) PathItems and run
// Demo2()
polyline();
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