polynomial line fitting

polyline.js

function translate(tx, ty, func){
  return function(x,y){
    var xprime = x-tx;
    var yprime = y-ty;

    return func(xprime,yprime);
  }
}

function rotate(theta, func){
  return function(x,y){
    var xprime = Math.cos(theta)*x-Math.sin(theta)*y;
    var yprime = Math.sin(theta)*x+Math.cos(theta)*y;

    return func(xprime,yprime);
  }
}

function rotate_list(theta, ary){
  var lambda = function(pt){
    var x=pt[0];
    var y=pt[1];
    var xprime = Math.cos(theta)*x-Math.sin(theta)*y;
    var yprime = Math.sin(theta)*x+Math.cos(theta)*y;

    return [xprime,yprime];
  }
  var ret = [];
  for(var i=0; i<ary.length; i++){
    ret.push( lambda(ary[i]) );
  }
  return ret;
}

function translate_list(tx,ty,ary){
  var ret =[];
  for(var i=0; i<ary.length; i++){
    ret.push( [ary[i][0]+tx,ary[i][1]+ty] );
  }
  return ret;
}

function makecurve(points){
  //translate control points to origin
  var tx = points[0][0];
  var ty = points[0][1];
  points = translate_list( -tx, -ty, points );

  //rotate outer control points to flat
  var lastpt = points[points.length-1];
  var theta = Math.atan2( lastpt[1], lastpt[0] );
  points = rotate_list(-theta, points);

  //solve polynomial fit problem
  var pp = new Polyspec(points);
  var pn = pp.solve();

  var rightmost=points[points.length-1][0];

  // rotate turn into inequality, rotate back, and translate back
  return translate(tx,ty,
    rotate(-theta, 
      function(x,y){
        return (y>pn.eval(x) || (x<0&&y>0) || (x>rightmost&&y>0)) &&!(x>rightmost&&y<0) &&!(x<0&&y<0);    
      }
    )
  )
}

function dist(x,y){
  return Math.pow(x*x+y*y,0.5);
}

function intersection(funcs){
  var metaargs=arguments;
  return function(x,y) {
    var ret=true;
    for(var i=0; i<metaargs.length;i++){
      ret = ret && metaargs[i](x,y);
    }
    return ret;
  }
}

function makecircle(r){
  return function(x,y){
    return Math.pow(x,2) + Math.pow(y,2) < Math.pow(r,2);
  }
}

function maketranscircle( p1,p2 ){
  var r = dist(p1[0]-p2[0],p1[1]-p2[1])*1.3;
  return translate(p1[0],p1[1],makecircle(r) );
}

function xor(func1, func2){
  return function(x,y){
    var f1 = func1(x,y);
    var f2 = func2(x,y);

    return (f1 || f2) && !(f1 && f2)
  }
}

var c1=[231,73];
var c2=[338,293];
var c3=[78,283];

var f1 = makecurve([c3,[126,83],[129,156],[61,234],c1]);
var f2 = makecurve([c1,[372,156],c2] );
var f3 = makecurve([c2,[194,396],c3] );

var f4 = maketranscircle([296,321],[344,225]);

emit( xor( intersection(f1,f2,f3), f4) );