bezier curve intersections

README.md

The source code is at https://github.com/hnakamur/d3.js-drag-bezier-curves-example/tree/use-kld-intersections

Changed Polynomial.ACCURACY from 6 to 15 at 2015-01-12T01:54-0900 thelonious/kld-intersections#2 (comment)

bundle.js

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m=d[v];m>=0&&1>=m&&x.points.push(f.multiply(m*m).add(y.multiply(m).add(h)))}return x.points.length>0&&(x.status="Intersection"),x},r.intersectBezier2Line=function(t,n,e,a,s){var c,l,f,y,h,x,p,g=a.min(s),d=a.max(s),v=new r("No Intersection");c=n.multiply(-2),f=t.add(c.add(e)),c=t.multiply(-2),l=n.multiply(2),y=c.add(l),h=new i(t.x,t.y),p=new o(a.y-s.y,s.x-a.x),x=a.x*s.y-s.x*a.y,roots=new u(p.dot(f),p.dot(y),p.dot(h)+x).getRoots();for(var m=0;m<roots.length;m++){var M=roots[m];if(M>=0&&1>=M){var w=t.lerp(n,M),b=n.lerp(e,M),_=w.lerp(b,M);a.x==s.x?g.y<=_.y&&_.y<=d.y&&(v.status="Intersection",v.appendPoint(_)):a.y==s.y?g.x<=_.x&&_.x<=d.x&&(v.status="Intersection",v.appendPoint(_)):_.gte(g)&&_.lte(d)&&(v.status="Intersection",v.appendPoint(_))}}return v},r.intersectBezier2Polygon=function(t,n,e,i){for(var o=new r("No Intersection"),u=i.length,a=0;u>a;a++){var s=i[a],c=i[(a+1)%u],l=r.intersectBezier2Line(t,n,e,s,c);o.appendPoints(l.points)}return o.points.length>0&&(o.status="Intersection"),o},r.intersectBezier2Rectangle=function(t,n,e,o,u){var a=o.min(u),s=o.max(u),c=new i(s.x,a.y),l=new i(a.x,s.y),f=r.intersectBezier2Line(t,n,e,a,c),y=r.intersectBezier2Line(t,n,e,c,s),h=r.intersectBezier2Line(t,n,e,s,l),x=r.intersectBezier2Line(t,n,e,l,a),p=new r("No Intersection");return p.appendPoints(f.points),p.appendPoints(y.points),p.appendPoints(h.points),p.appendPoints(x.points),p.points.length>0&&(p.status="Intersection"),p},r.intersectBezier3Bezier3=function(t,n,e,i,a,s,c,l){var f,y,h,x,p,g,d,v,m,M,w,b,_=new r("No Intersection");f=t.multiply(-1),y=n.multiply(3),h=e.multiply(-3),x=f.add(y.add(h.add(i))),p=new o(x.x,x.y),f=t.multiply(3),y=n.multiply(-6),h=e.multiply(3),x=f.add(y.add(h)),g=new o(x.x,x.y),f=t.multiply(-3),y=n.multiply(3),h=f.add(y),d=new o(h.x,h.y),v=new o(t.x,t.y),f=a.multiply(-1),y=s.multiply(3),h=c.multiply(-3),x=f.add(y.add(h.add(l))),m=new o(x.x,x.y),f=a.multiply(3),y=s.multiply(-6),h=c.multiply(3),x=f.add(y.add(h)),M=new o(x.x,x.y),f=a.multiply(-3),y=s.multiply(3),h=f.add(y),w=new o(h.x,h.y),b=new o(a.x,a.y);for(var E=v.x*v.x,S=v.x*v.x*v.x,N=v.y*v.y,k=v.y*v.y*v.y,A=d.x*d.x,C=d.x*d.x*d.x,L=d.y*d.y,P=d.y*d.y*d.y,z=g.x*g.x,q=g.x*g.x*g.x,R=g.y*g.y,I=g.y*g.y*g.y,T=p.x*p.x,D=p.x*p.x*p.x,U=p.y*p.y,j=p.y*p.y*p.y,O=b.x*b.x,F=b.x*b.x*b.x,H=b.y*b.y,B=b.y*b.y*b.y,Y=w.x*w.x,V=w.x*w.x*w.x,Z=w.y*w.y,X=M.x*M.x,$=M.x*M.x*M.x,Q=M.y*M.y,J=m.x*m.x,W=m.x*m.x*m.x,G=m.y*m.y,K=m.y*m.y*m.y,tn=new 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rn=nn[en],on=new u(p.x,g.x,d.x,v.x-b.x-rn*w.x-rn*rn*M.x-rn*rn*rn*m.x).getRoots(),un=new u(p.y,g.y,d.y,v.y-b.y-rn*w.y-rn*rn*M.y-rn*rn*rn*m.y).getRoots();
if(on.length>0&&un.length>0){var an=1e-4;t:for(var sn=0;sn<on.length;sn++){var cn=on[sn];if(cn>=0&&1>=cn)for(var ln=0;ln<un.length;ln++)if(Math.abs(cn-un[ln])<an){_.points.push(m.multiply(rn*rn*rn).add(M.multiply(rn*rn).add(w.multiply(rn).add(b))));break t}}}}return _.points.length>0&&(_.status="Intersection"),_},r.intersectBezier3Circle=function(t,n,e,i,o,u){return r.intersectBezier3Ellipse(t,n,e,i,o,u,u)},r.intersectBezier3Ellipse=function(t,n,e,i,a,s,c){var l,f,y,h,x,p,g,d,v=new r("No Intersection");l=t.multiply(-1),f=n.multiply(3),y=e.multiply(-3),h=l.add(f.add(y.add(i))),x=new o(h.x,h.y),l=t.multiply(3),f=n.multiply(-6),y=e.multiply(3),h=l.add(f.add(y)),p=new o(h.x,h.y),l=t.multiply(-3),f=n.multiply(3),y=l.add(f),g=new o(y.x,y.y),d=new o(t.x,t.y);for(var m=s*s,M=c*c,w=new u(x.x*x.x*M+x.y*x.y*m,2*(x.x*p.x*M+x.y*p.y*m),2*(x.x*g.x*M+x.y*g.y*m)+p.x*p.x*M+p.y*p.y*m,2*x.x*M*(d.x-a.x)+2*x.y*m*(d.y-a.y)+2*(p.x*g.x*M+p.y*g.y*m),2*p.x*M*(d.x-a.x)+2*p.y*m*(d.y-a.y)+g.x*g.x*M+g.y*g.y*m,2*g.x*M*(d.x-a.x)+2*g.y*m*(d.y-a.y),d.x*d.x*M-2*d.y*a.y*m-2*d.x*a.x*M+d.y*d.y*m+a.x*a.x*M+a.y*a.y*m-m*M),b=w.getRootsInInterval(0,1),_=0;_<b.length;_++){var E=b[_];v.points.push(x.multiply(E*E*E).add(p.multiply(E*E).add(g.multiply(E).add(d))))}return v.points.length>0&&(v.status="Intersection"),v},r.intersectBezier3Line=function(t,n,e,i,a,s){var c,l,f,y,h,x,p,g,d,v,m=a.min(s),M=a.max(s),w=new r("No Intersection");c=t.multiply(-1),l=n.multiply(3),f=e.multiply(-3),y=c.add(l.add(f.add(i))),h=new o(y.x,y.y),c=t.multiply(3),l=n.multiply(-6),f=e.multiply(3),y=c.add(l.add(f)),x=new o(y.x,y.y),c=t.multiply(-3),l=n.multiply(3),f=c.add(l),p=new o(f.x,f.y),g=new o(t.x,t.y),v=new o(a.y-s.y,s.x-a.x),d=a.x*s.y-s.x*a.y,roots=new u(v.dot(h),v.dot(x),v.dot(p),v.dot(g)+d).getRoots();for(var b=0;b<roots.length;b++){var _=roots[b];if(_>=0&&1>=_){var E=t.lerp(n,_),S=n.lerp(e,_),N=e.lerp(i,_),k=E.lerp(S,_),A=S.lerp(N,_),C=k.lerp(A,_);a.x==s.x?m.y<=C.y&&C.y<=M.y&&(w.status="Intersection",w.appendPoint(C)):a.y==s.y?m.x<=C.x&&C.x<=M.x&&(w.status="Intersection",w.appendPoint(C)):C.gte(m)&&C.lte(M)&&(w.status="Intersection",w.appendPoint(C))}}return w},r.intersectBezier3Polygon=function(t,n,e,i,o){for(var u=new r("No Intersection"),a=o.length,s=0;a>s;s++){var c=o[s],l=o[(s+1)%a],f=r.intersectBezier3Line(t,n,e,i,c,l);u.appendPoints(f.points)}return u.points.length>0&&(u.status="Intersection"),u},r.intersectBezier3Rectangle=function(t,n,e,o,u,a){var s=u.min(a),c=u.max(a),l=new i(c.x,s.y),f=new i(s.x,c.y),y=r.intersectBezier3Line(t,n,e,o,s,l),h=r.intersectBezier3Line(t,n,e,o,l,c),x=r.intersectBezier3Line(t,n,e,o,c,f),p=r.intersectBezier3Line(t,n,e,o,f,s),g=new r("No Intersection");return g.appendPoints(y.points),g.appendPoints(h.points),g.appendPoints(x.points),g.appendPoints(p.points),g.points.length>0&&(g.status="Intersection"),g},r.intersectCircleCircle=function(t,n,e,o){var u,a=n+o,s=Math.abs(n-o),c=t.distanceFrom(e);if(c>a)u=new r("Outside");else if(s>c)u=new r("Inside");else{u=new r("Intersection");var l=(n*n-o*o+c*c)/(2*c),f=Math.sqrt(n*n-l*l),y=t.lerp(e,l/c),h=f/c;u.points.push(new i(y.x-h*(e.y-t.y),y.y+h*(e.x-t.x))),u.points.push(new i(y.x+h*(e.y-t.y),y.y-h*(e.x-t.x)))}return u},r.intersectCircleEllipse=function(t,n,e,i,o){return r.intersectEllipseEllipse(t,n,n,e,i,o)},r.intersectCircleLine=function(t,n,e,i){var o,u=(i.x-e.x)*(i.x-e.x)+(i.y-e.y)*(i.y-e.y),a=2*((i.x-e.x)*(e.x-t.x)+(i.y-e.y)*(e.y-t.y)),s=t.x*t.x+t.y*t.y+e.x*e.x+e.y*e.y-2*(t.x*e.x+t.y*e.y)-n*n,c=a*a-4*u*s;if(0>c)o=new r("Outside");else if(0==c)o=new r("Tangent");else{var l=Math.sqrt(c),f=(-a+l)/(2*u),y=(-a-l)/(2*u);(0>f||f>1)&&(0>y||y>1)?o=new r(0>f&&0>y||f>1&&y>1?"Outside":"Inside"):(o=new r("Intersection"),f>=0&&1>=f&&o.points.push(e.lerp(i,f)),y>=0&&1>=y&&o.points.push(e.lerp(i,y)))}return o},r.intersectCirclePolygon=function(t,n,e){for(var i,o=new r("No Intersection"),u=e.length,a=0;u>a;a++){var s=e[a],c=e[(a+1)%u];i=r.intersectCircleLine(t,n,s,c),o.appendPoints(i.points)}return o.status=o.points.length>0?"Intersection":i.status,o},r.intersectCircleRectangle=function(t,n,e,o){var u=e.min(o),a=e.max(o),s=new i(a.x,u.y),c=new i(u.x,a.y),l=r.intersectCircleLine(t,n,u,s),f=r.intersectCircleLine(t,n,s,a),y=r.intersectCircleLine(t,n,a,c),h=r.intersectCircleLine(t,n,c,u),x=new r("No Intersection");return x.appendPoints(l.points),x.appendPoints(f.points),x.appendPoints(y.points),x.appendPoints(h.points),x.status=x.points.length>0?"Intersection":l.status,x},r.intersectEllipseEllipse=function(t,n,e,o,a,s){for(var c=[e*e,0,n*n,-2*e*e*t.x,-2*n*n*t.y,e*e*t.x*t.x+n*n*t.y*t.y-n*n*e*e],l=[s*s,0,a*a,-2*s*s*o.x,-2*a*a*o.y,s*s*o.x*o.x+a*a*o.y*o.y-a*a*s*s],f=r.bezout(c,l),y=f.getRoots(),h=.001,x=(c[0]*c[0]+2*c[1]*c[1]+c[2]*c[2])*h,p=(l[0]*l[0]+2*l[1]*l[1]+l[2]*l[2])*h,g=new r("No Intersection"),d=0;d<y.length;d++)for(var v=new u(c[0],c[3]+y[d]*c[1],c[5]+y[d]*(c[4]+y[d]*c[2])),m=v.getRoots(),M=0;M<m.length;M++){var w=(c[0]*m[M]+c[1]*y[d]+c[3])*m[M]+(c[2]*y[d]+c[4])*y[d]+c[5];Math.abs(w)<x&&(w=(l[0]*m[M]+l[1]*y[d]+l[3])*m[M]+(l[2]*y[d]+l[4])*y[d]+l[5],Math.abs(w)<p&&g.appendPoint(new i(m[M],y[d])))}return g.points.length>0&&(g.status="Intersection"),g},r.intersectEllipseLine=function(t,n,e,i,u){var a,s=new o(i.x,i.y),c=o.fromPoints(i,u),l=new o(t.x,t.y),f=s.subtract(l),y=new o(c.x/(n*n),c.y/(e*e)),h=new o(f.x/(n*n),f.y/(e*e)),x=c.dot(y),p=c.dot(h),t=f.dot(h)-1,g=p*p-x*t;if(0>g)a=new r("Outside");else if(g>0){var d=Math.sqrt(g),v=(-p-d)/x,m=(-p+d)/x;(0>v||v>1)&&(0>m||m>1)?a=new r(0>v&&0>m||v>1&&m>1?"Outside":"Inside"):(a=new r("Intersection"),v>=0&&1>=v&&a.appendPoint(i.lerp(u,v)),m>=0&&1>=m&&a.appendPoint(i.lerp(u,m)))}else{var M=-p/x;M>=0&&1>=M?(a=new r("Intersection"),a.appendPoint(i.lerp(u,M))):a=new r("Outside")}return a},r.intersectEllipsePolygon=function(t,n,e,i){for(var o=new r("No Intersection"),u=i.length,a=0;u>a;a++){var s=i[a],c=i[(a+1)%u],l=r.intersectEllipseLine(t,n,e,s,c);o.appendPoints(l.points)}return o.points.length>0&&(o.status="Intersection"),o},r.intersectEllipseRectangle=function(t,n,e,o,u){var a=o.min(u),s=o.max(u),c=new i(s.x,a.y),l=new i(a.x,s.y),f=r.intersectEllipseLine(t,n,e,a,c),y=r.intersectEllipseLine(t,n,e,c,s),h=r.intersectEllipseLine(t,n,e,s,l),x=r.intersectEllipseLine(t,n,e,l,a),p=new r("No Intersection");return p.appendPoints(f.points),p.appendPoints(y.points),p.appendPoints(h.points),p.appendPoints(x.points),p.points.length>0&&(p.status="Intersection"),p},r.intersectLineLine=function(t,n,e,o){var u,a=(o.x-e.x)*(t.y-e.y)-(o.y-e.y)*(t.x-e.x),s=(n.x-t.x)*(t.y-e.y)-(n.y-t.y)*(t.x-e.x),c=(o.y-e.y)*(n.x-t.x)-(o.x-e.x)*(n.y-t.y);if(0!=c){var l=a/c,f=s/c;l>=0&&1>=l&&f>=0&&1>=f?(u=new r("Intersection"),u.points.push(new i(t.x+l*(n.x-t.x),t.y+l*(n.y-t.y)))):u=new r("No Intersection")}else u=new r(0==a||0==s?"Coincident":"Parallel");return u},r.intersectLinePolygon=function(t,n,e){for(var i=new r("No Intersection"),o=e.length,u=0;o>u;u++){var a=e[u],s=e[(u+1)%o],c=r.intersectLineLine(t,n,a,s);i.appendPoints(c.points)}return i.points.length>0&&(i.status="Intersection"),i},r.intersectLineRectangle=function(t,n,e,o){var u=e.min(o),a=e.max(o),s=new i(a.x,u.y),c=new i(u.x,a.y),l=r.intersectLineLine(u,s,t,n),f=r.intersectLineLine(s,a,t,n),y=r.intersectLineLine(a,c,t,n),h=r.intersectLineLine(c,u,t,n),x=new r("No Intersection");return x.appendPoints(l.points),x.appendPoints(f.points),x.appendPoints(y.points),x.appendPoints(h.points),x.points.length>0&&(x.status="Intersection"),x},r.intersectPolygonPolygon=function(t,n){for(var e=new r("No Intersection"),i=t.length,o=0;i>o;o++){var u=t[o],a=t[(o+1)%i],s=r.intersectLinePolygon(u,a,n);e.appendPoints(s.points)}return e.points.length>0&&(e.status="Intersection"),e},r.intersectPolygonRectangle=function(t,n,e){var o=n.min(e),u=n.max(e),a=new i(u.x,o.y),s=new i(o.x,u.y),c=r.intersectLinePolygon(o,a,t),l=r.intersectLinePolygon(a,u,t),f=r.intersectLinePolygon(u,s,t),y=r.intersectLinePolygon(s,o,t),h=new r("No Intersection");return h.appendPoints(c.points),h.appendPoints(l.points),h.appendPoints(f.points),h.appendPoints(y.points),h.points.length>0&&(h.status="Intersection"),h},r.intersectRayRay=function(t,n,e,o){var u,a=(o.x-e.x)*(t.y-e.y)-(o.y-e.y)*(t.x-e.x),s=(n.x-t.x)*(t.y-e.y)-(n.y-t.y)*(t.x-e.x),c=(o.y-e.y)*(n.x-t.x)-(o.x-e.x)*(n.y-t.y);if(0!=c){var l=a/c;u=new 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n(t,n){this.init(t,n)}n.prototype.init=function(t,n){this.name=t,this.params=n},t.exports=n},function(t,n,e){n.Point2D=e(10),n.Vector2D=e(11),n.Matrix2D=e(12)},function(t,n,e){n.Polynomial=e(13),n.SqrtPolynomial=e(14)},function(t){function n(t,n){this.x=t,this.y=n}n.prototype.clone=function(){return new n(this.x,this.y)},n.prototype.add=function(t){return new n(this.x+t.x,this.y+t.y)},n.prototype.addEquals=function(t){return this.x+=t.x,this.y+=t.y,this},n.prototype.rmoveto=function(t,n){this.x+=t,this.y+=n},n.prototype.scalarAdd=function(t){return new n(this.x+t,this.y+t)},n.prototype.scalarAddEquals=function(t){return this.x+=t,this.y+=t,this},n.prototype.subtract=function(t){return new n(this.x-t.x,this.y-t.y)},n.prototype.subtractEquals=function(t){return this.x-=t.x,this.y-=t.y,this},n.prototype.scalarSubtract=function(t){return new n(this.x-t,this.y-t)},n.prototype.scalarSubtractEquals=function(t){return this.x-=t,this.y-=t,this},n.prototype.multiply=function(t){return new 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n(t.a*this.x+t.c*this.y+t.e,t.b*this.x+t.d*this.y+t.f)},n.prototype.toString=function(){return"point("+this.x+","+this.y+")"},n.prototype.setXY=function(t,n){this.x=t,this.y=n},n.prototype.setFromPoint=function(t){this.x=t.x,this.y=t.y},n.prototype.swap=function(t){var n=this.x,e=this.y;this.x=t.x,this.y=t.y,t.x=n,t.y=e},t.exports=n},function(t){function n(t,n){this.x=t,this.y=n}n.prototype.length=function(){return Math.sqrt(this.x*this.x+this.y*this.y)},n.prototype.dot=function(t){return this.x*t.x+this.y*t.y},n.prototype.cross=function(t){return this.x*t.y-this.y*t.x},n.prototype.unit=function(){return this.divide(this.length())},n.prototype.unitEquals=function(){return this.divideEquals(this.length()),this},n.prototype.add=function(t){return new n(this.x+t.x,this.y+t.y)},n.prototype.addEquals=function(t){return this.x+=t.x,this.y+=t.y,this},n.prototype.subtract=function(t){return new n(this.x-t.x,this.y-t.y)},n.prototype.subtractEquals=function(t){return 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n(1,0,0,1,0,0),n.prototype.multiply=function(t){return new n(this.a*t.a+this.c*t.b,this.b*t.a+this.d*t.b,this.a*t.c+this.c*t.d,this.b*t.c+this.d*t.d,this.a*t.e+this.c*t.f+this.e,this.b*t.e+this.d*t.f+this.f)},n.prototype.inverse=function(){var t=this.a*this.d-this.b*this.c;if(0==t)throw"Matrix is not invertible";var e=1/t,r=this.f*this.c-this.e*this.d,i=this.e*this.b-this.f*this.a;return new n(this.d*e,-this.b*e,-this.c*e,this.a*e,r*e,i*e)},n.prototype.translate=function(t,e){return new n(this.a,this.b,this.c,this.d,this.a*t+this.c*e+this.e,this.b*t+this.d*e+this.f)},n.prototype.scale=function(t){return new n(this.a*t,this.b*t,this.c*t,this.d*t,this.e,this.f)},n.prototype.scaleAt=function(t,e){var r=e.x-t*e.x,i=e.y-t*e.y;return new n(this.a*t,this.b*t,this.c*t,this.d*t,this.a*r+this.c*i+this.e,this.b*r+this.d*i+this.f)},n.prototype.scaleNonUniform=function(t,e){return new n(this.a*t,this.b*t,this.c*e,this.d*e,this.e,this.f)},n.prototype.scaleNonUniformAt=function(t,e,r){var i=r.x-t*r.x,o=r.y-e*r.y;return new n(this.a*t,this.b*t,this.c*e,this.d*e,this.a*i+this.c*o+this.e,this.b*i+this.d*o+this.f)},n.prototype.rotate=function(t){var e=Math.cos(t),r=Math.sin(t);return new n(this.a*e+this.c*r,this.b*e+this.d*r,this.a*-r+this.c*e,this.b*-r+this.d*e,this.e,this.f)},n.prototype.rotateAt=function(t,e){var r=Math.cos(t),i=Math.sin(t),o=-e.x+e.x*r-e.y*i,u=-e.y+e.y*r+e.x*i;return new n(this.a*r+this.c*i,this.b*r+this.d*i,this.a*-i+this.c*r,this.b*-i+this.d*r,this.a*o+this.c*u+this.e,this.b*o+this.d*u+this.f)},n.prototype.rotateFromVector=function(t){var e=t.unit(),r=e.x,i=e.y;return new n(this.a*r+this.c*i,this.b*r+this.d*i,this.a*-i+this.c*r,this.b*-i+this.d*r,this.e,this.f)},n.prototype.flipX=function(){return new n(-this.a,-this.b,this.c,this.d,this.e,this.f)},n.prototype.flipY=function(){return new n(this.a,this.b,-this.c,-this.d,this.e,this.f)},n.prototype.skewX=function(t){var e=Math.tan(t);return new n(this.a,this.b,this.a*e+this.c,this.b*e+this.d,this.e,this.f)},n.prototype.skewY=function(){var t=Math.tan(angle);return matrix_new(this.a+this.c*t,this.b+this.d*t,this.c,this.d,this.e,this.f)},n.prototype.isIdentity=function(){return 1===this.a&&0===this.b&&0===this.c&&1===this.d&&0===this.e&&0===this.f},n.prototype.isInvertible=function(){this.a*this.d-this.b*this.c!==0},n.prototype.equals=function(t){return this.a===t.a&&this.b===t.b&&this.c===t.c&&this.d===t.d&&this.e===t.e&&this.f===t.f},n.prototype.getScale=function(){return{scaleX:Math.sqrt(this.a*this.a+this.c*this.c),scaleY:Math.sqrt(this.b*this.b+this.d*this.d)}},n.prototype.toString=function(){return"matrix("+this.a+","+this.b+","+this.c+","+this.d+","+this.e+","+this.f+")"},t.exports=n},function(t){function n(){this.init(arguments)}n.TOLERANCE=1e-6,n.ACCURACY=15,n.interpolate=function(t,n,e,r,i){if(t.constructor!==Array||n.constructor!==Array)throw new Error("Polynomial.interpolate: xs and ys must be arrays");if(isNaN(e)||isNaN(r)||isNaN(i))throw new Error("Polynomial.interpolate: n, offset, and x must be numbers");for(var o,u=0,a=0,s=new Array(e),c=new Array(e),l=0,f=Math.abs(i-t[r]),y=0;e>y;y++){var h=Math.abs(i-t[r+y]);f>h&&(l=y,f=h),s[y]=c[y]=n[r+y]}u=n[r+l],l--;for(var x=1;e>x;x++){for(var y=0;e-x>y;y++){var p=t[r+y]-i,g=t[r+y+x]-i,d=s[y+1]-c[y],v=p-g;if(0==v){o={y:0,dy:0};break}v=d/v,c[y]=g*v,s[y]=p*v}a=e-x>2*(l+1)?s[l+1]:c[l--],u+=a}return{y:u,dy:a}},n.prototype.init=function(t){this.coefs=new Array;for(var n=t.length-1;n>=0;n--)this.coefs.push(t[n]);this._variable="t",this._s=0},n.prototype.eval=function(t){if(isNaN(t))throw new Error("Polynomial.eval: parameter must be a number");for(var n=0,e=this.coefs.length-1;e>=0;e--)n=n*t+this.coefs[e];return n},n.prototype.add=function(t){for(var e=new n,r=this.getDegree(),i=t.getDegree(),o=Math.max(r,i),u=0;o>=u;u++){var a=r>=u?this.coefs[u]:0,s=i>=u?t.coefs[u]:0;e.coefs[u]=a+s}return e},n.prototype.multiply=function(t){for(var e=new n,r=0;r<=this.getDegree()+t.getDegree();r++)e.coefs.push(0);for(var r=0;r<=this.getDegree();r++)for(var i=0;i<=t.getDegree();i++)e.coefs[r+i]+=this.coefs[r]*t.coefs[i];return e},n.prototype.divide_scalar=function(t){for(var n=0;n<this.coefs.length;n++)this.coefs[n]/=t},n.prototype.simplify=function(){for(var t=this.getDegree();t>=0&&Math.abs(this.coefs[t])<=n.TOLERANCE;t--)this.coefs.pop()},n.prototype.bisection=function(t,e){var r,i=this.eval(t),o=this.eval(e);if(Math.abs(i)<=n.TOLERANCE)r=t;else if(Math.abs(o)<=n.TOLERANCE)r=e;else if(0>=i*o)for(var u=Math.log(e-t),a=Math.LN10*n.ACCURACY,s=Math.ceil((u+a)/Math.LN2),c=0;s>c;c++){r=.5*(t+e);var l=this.eval(r);if(Math.abs(l)<=n.TOLERANCE)break;0>l*i?(e=r,o=l):(t=r,i=l)}return r},n.prototype.toString=function(){for(var t=new Array,n=new Array,e=this.coefs.length-1;e>=0;e--){var r=Math.round(1e3*this.coefs[e])/1e3;if(0!=r){var i=0>r?" - ":" + ";r=Math.abs(r),e>0&&(1==r?r=this._variable:r+=this._variable),e>1&&(r+="^"+e),n.push(i),t.push(r)}}n[0]=" + "==n[0]?"":"-";for(var o="",e=0;e<t.length;e++)o+=n[e]+t[e];return o},n.prototype.trapezoid=function(t,n,e){if(isNaN(t)||isNaN(n)||isNaN(e))throw new Error("Polynomial.trapezoid: parameters must be numbers");var r=n-t;if(1==e){var i=this.eval(t),o=this.eval(n);this._s=.5*r*(i+o)}else{for(var u=1<<e-2,a=r/u,s=t+.5*a,c=0,l=0;u>l;l++)c+=this.eval(s),s+=a;this._s=.5*(this._s+r*c/u)}if(isNaN(this._s))throw new Error("Polynomial.trapezoid: this._s is NaN");return this._s},n.prototype.simpson=function(t,n){if(isNaN(t)||isNaN(n))throw new Error("Polynomial.simpson: parameters must be numbers");for(var e=n-t,r=.5*e*(this.eval(t)+this.eval(n)),i=r,o=4*r/3,u=o,a=r,s=1e-7,c=1,l=2;20>=l;l++){for(var f=e/c,y=t+.5*f,h=0,x=1;c>=x;x++)h+=this.eval(y),y+=f;if(i=.5*(i+e*h/c),r=i,o=(4*r-a)/3,Math.abs(o-u)<s*Math.abs(u))break;u=o,a=r,c<<=1}return o},n.prototype.romberg=function(t,e){if(isNaN(t)||isNaN(e))throw new Error("Polynomial.romberg: parameters must be numbers");var r=20,i=3,o=1e-6,u=new Array(r+1),a=new Array(r+1),s={y:0,dy:0};a[0]=1;for(var c=1;r>=c&&(u[c-1]=this.trapezoid(t,e,c),!(c>=i&&(s=n.interpolate(a,u,i,c-i,0),Math.abs(s.dy)<=o*s.y)));c++)u[c]=u[c-1],a[c]=.25*a[c-1];return s.y},n.prototype.getDegree=function(){return this.coefs.length-1},n.prototype.getDerivative=function(){for(var t=new n,e=1;e<this.coefs.length;e++)t.coefs.push(e*this.coefs[e]);return t},n.prototype.getRoots=function(){var t;switch(this.simplify(),this.getDegree()){case 0:t=new Array;break;case 1:t=this.getLinearRoot();break;case 2:t=this.getQuadraticRoots();break;case 3:t=this.getCubicRoots();break;case 4:t=this.getQuarticRoots();break;default:t=new Array}return t},n.prototype.getRootsInInterval=function(t,n){var e,r=new Array;if(1==this.getDegree())e=this.bisection(t,n),null!=e&&r.push(e);else{var o=this.getDerivative(),u=o.getRootsInInterval(t,n);if(u.length>0){for(e=this.bisection(t,u[0]),null!=e&&r.push(e),i=0;i<=u.length-2;i++)e=this.bisection(u[i],u[i+1]),null!=e&&r.push(e);e=this.bisection(u[u.length-1],n),null!=e&&r.push(e)}else e=this.bisection(t,n),null!=e&&r.push(e)}return r},n.prototype.getLinearRoot=function(){var t=new Array,n=this.coefs[1];return 0!=n&&t.push(-this.coefs[0]/n),t},n.prototype.getQuadraticRoots=function(){var t=new Array;if(2==this.getDegree()){var n=this.coefs[2],e=this.coefs[1]/n,r=this.coefs[0]/n,i=e*e-4*r;if(i>0){var o=Math.sqrt(i);t.push(.5*(-e+o)),t.push(.5*(-e-o))}else 0==i&&t.push(.5*-e)}return t},n.prototype.getCubicRoots=function(){var t=new Array;if(3==this.getDegree()){var e=this.coefs[3],r=this.coefs[2]/e,i=this.coefs[1]/e,o=this.coefs[0]/e,u=(3*i-r*r)/3,a=(2*r*r*r-9*i*r+27*o)/27,s=r/3,c=a*a/4+u*u*u/27,l=a/2;if(Math.abs(c)<=n.TOLERANCE&&(c=0),c>0){var f,y,h=Math.sqrt(c);f=-l+h,y=f>=0?Math.pow(f,1/3):-Math.pow(-f,1/3),f=-l-h,f>=0?y+=Math.pow(f,1/3):y-=Math.pow(-f,1/3),t.push(y-s)}else if(0>c){var x=Math.sqrt(-u/3),p=Math.atan2(Math.sqrt(-c),-l)/3,g=Math.cos(p),d=Math.sin(p),v=Math.sqrt(3);t.push(2*x*g-s),t.push(-x*(g+v*d)-s),t.push(-x*(g-v*d)-s)}else{var f;f=l>=0?-Math.pow(l,1/3):Math.pow(-l,1/3),t.push(2*f-s),t.push(-f-s)}}return t},n.prototype.getQuarticRoots=function(){var t=new Array;if(4==this.getDegree()){var e=this.coefs[4],r=this.coefs[3]/e,i=this.coefs[2]/e,o=this.coefs[1]/e,u=this.coefs[0]/e,a=new n(1,-i,r*o-4*u,-r*r*u+4*i*u-o*o).getCubicRoots(),s=a[0],c=r*r/4-i+s;if(Math.abs(c)<=n.TOLERANCE&&(c=0),c>0){var l=Math.sqrt(c),f=3*r*r/4-l*l-2*i,y=(4*r*i-8*o-r*r*r)/(4*l),h=f+y,x=f-y;if(Math.abs(h)<=n.TOLERANCE&&(h=0),Math.abs(x)<=n.TOLERANCE&&(x=0),h>=0){var p=Math.sqrt(h);t.push(-r/4+(l+p)/2),t.push(-r/4+(l-p)/2)}if(x>=0){var p=Math.sqrt(x);t.push(-r/4+(p-l)/2),t.push(-r/4-(p+l)/2)}}else if(0>c);else{var y=s*s-4*u;if(y>=-n.TOLERANCE){if(0>y&&(y=0),y=2*Math.sqrt(y),f=3*r*r/4-2*i,f+y>=n.TOLERANCE){var g=Math.sqrt(f+y);t.push(-r/4+g/2),t.push(-r/4-g/2)}if(f-y>=n.TOLERANCE){var g=Math.sqrt(f-y);t.push(-r/4+g/2),t.push(-r/4-g/2)}}}}return t},t.exports=n},function(t,n,e){function r(){this.init(arguments)}var i=e(13);r.VERSION=1,r.prototype=new i,r.prototype.constructor=r,r.superclass=i.prototype,r.prototype.eval=function(t){var n=1e-7,e=r.superclass.eval.call(this,t);if(Math.abs(e)<n&&(e=0),0>e)throw new Error("SqrtPolynomial.eval: cannot take square root of negative number");return Math.sqrt(e)},r.prototype.toString=function(){var t=r.superclass.toString.call(this);return"sqrt("+t+")"},t.exports=r}]);

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