geometry

geometry.js

var rad2deg = 180/Math.PI
var deg2rad = Math.PI/180

function rad(x){return x * deg2rad}
function deg(x){return x * rad2deg}

// distance between 2 coordinates in 2D
function distance(p0,p1){
  return Math.sqrt(Math.pow(p0[0]-p1[0],2) + Math.pow(p0[1]-p1[1],2));
}

// map float from one range to another
function mapval(value,istart,istop,ostart,ostop){
    return ostart + (ostop - ostart) * ((value - istart)*1.0 / (istop - istart))
}

// sigmoid curve
function sigmoid(x,k){
  k = (k != undefined) ? k : 10
  return 1/(1+Math.exp(-k*(x-0.5)))
}

// pseudo bean curve
// x^4 + x^2y^2 + y^4 = ax(x^2 + y^2)
// horizontal tangent (2/3a, +-2/3a)
// vertical tangent (0,0) (a,0)
function bean(x){
  return pow(0.25-pow(x-0.5,2),0.5)*(2.6+2.4*pow(x,1.5))*0.54
}


// interpolate between square and circle
var squircle = function(r,a){
  return function(th){
    while (th > PI/2){
      th -= PI/2
    }
    while (th < 0){
      th += PI/2
    }
    return r*pow(1/(pow(cos(th),a)+pow(sin(th),a)),1/a)
  }
}

// mid-point of an array of points
function midPt(){
  var plist = (arguments.length == 1) ? 
    arguments[0] : Array.apply(null, arguments)
  return plist.reduce(function(acc,v){
    return [v[0]/plist.length+acc[0],
            v[1]/plist.length+acc[1],
            v[2]/plist.length+acc[2]]
  },[0,0,0])
}

// rational bezier curve
function bezmh(P, w){
  w = (w == undefined) ? 1 : w
  if (P.length == 2){
    P = [P[0],midPt(P[0],P[1]),P[1]];
  }
  var plist = [];
  for (var j = 0; j < P.length-2; j++){
    var p0; var p1; var p2;
    if (j == 0){p0 = P[j];}else{p0 = midPt(P[j],P[j+1]);}
    p1 = P[j+1];
    if (j == P.length-3){p2 = P[j+2];}else{p2 = midPt(P[j+1],P[j+2]);}
    var pl = 20;
    for (var i = 0; i < pl+(j==P.length-3); i+= 1){
      var t = i/pl;
      var u = (Math.pow (1 - t, 2) + 2 * t * (1 - t) * w + t * t);
      plist.push([
        (Math.pow(1-t,2)*p0[0]+2*t*(1-t)*p1[0]*w+t*t*p2[0])/u,
        (Math.pow(1-t,2)*p0[1]+2*t*(1-t)*p1[1]*w+t*t*p2[1])/u,
        (Math.pow(1-t,2)*p0[2]+2*t*(1-t)*p1[2]*w+t*t*p2[2])/u]);
    }
  }
  return plist;
}