gear11.jscad

// Involute spur gear builder jscad script. Licensed under the MIT license (http://opensource.org/licenses/mit-license.php). Copyright 2014 Dr. Rainer Hessmer
// http://hessmer.org/gears/InvoluteSpurGearBuilder.html
var g_ExpandToCAGParams = {
  pathradius: 0.01,
  resolution: 2
};

var GearType = {
  Regular: 0,
  Internal: 1,
  Rack: 2
};

// todo populate from UI
// var paramsset = {
//   circularPitch: 8,
//   pressureAngle: 20,
//   clearance: 0.05,
//   backlash: 0.05,
//   toothCount1: 15,
//   centerHoleDiameter1: 20,
//   profileShift: -0,
//   toothCount2: 50,
//   centerHoleDiameter2: 4,
//   type: 3,
//   resolution: 30,
//   stepsPerToothAngle: 3
// }

function main(params) {

  // Main entry point; here we construct our solid:


  var qualitySettings = {
    resolution: paramsset.resolution,
    stepsPerToothAngle: paramsset.stepsPerToothAngle
  };

  var gear1 = new Gear({
    circularPitch: paramsset.circularPitch,
    pressureAngle: paramsset.pressureAngle,
    clearance: paramsset.clearance,
    backlash: paramsset.backlash,
    toothCount: paramsset.toothCount1,
    centerHoleDiameter: paramsset.centerHoleDiameter1,
    profileShift: -paramsset.profileShift,
    qualitySettings: qualitySettings
  });
  var gear2 = new Gear({
    circularPitch: paramsset.circularPitch,
    pressureAngle: paramsset.pressureAngle,
    clearance: paramsset.clearance,
    backlash: paramsset.backlash,
    toothCount: paramsset.toothCount2,
    centerHoleDiameter: paramsset.centerHoleDiameter2,
    profileShift: -paramsset.profileShift,
    qualitySettings: qualitySettings
  });

  var gearSet = new GearSet(
    gear1,
    gear2,
    paramsset.type);

  // var params = paramsset;
  // var qualitySettings = {
  //   resolution: params.resolution,
  //   stepsPerToothAngle: params.stepsPerToothAngle
  // };
  //
  // var gear1 = new Gear({
  //   circularPitch: params.circularPitch,
  //   pressureAngle: params.pressureAngle,
  //   clearance: params.clearance,
  //   backlash: params.backlash,
  //   toothCount: params.wheel1ToothCount,
  //   centerHoleDiameter: params.wheel1CenterHoleDiamater,
  //   profileShift: -params.profileShift,
  //   qualitySettings: qualitySettings
  // });
  // var gear2 = new Gear({
  //   circularPitch: params.circularPitch,
  //   pressureAngle: params.pressureAngle,
  //   clearance: params.clearance,
  //   backlash: params.backlash,
  //   toothCount: params.wheel2ToothCount,
  //   centerHoleDiameter: params.wheel2CenterHoleDiamater,
  //   profileShift: params.profileShift,
  //   qualitySettings: qualitySettings
  // });
  //
  // var gearSet = new GearSet(
  //   gear1,
  //   gear2,
  //   params.showOption);

  var shape = gearSet.createShape();


  var minx = shape.getBounds()[0].x
  var maxx = shape.getBounds()[1].x;
  var miny = shape.getBounds()[0].y
  var maxy = shape.getBounds()[1].y;

  shape = shape.rotateZ(0).translate([(minx * -1), (miny * -1), 0]);
  OpenJsCad.log("returning gear set shape");
  return shape;
}



// function getParameterDefinitions() {
// 	return [{
// 			name: 'circularPitch',
// 			caption: 'Circular pitch (the circumference of the pitch circle divided by the number of teeth):',
// 			type: 'float',
// 			initial: 8
// 		},
// 		{
// 			name: 'pressureAngle',
// 			caption: 'Pressure Angle (common values are 14.5, 20 and 25 degrees):',
// 			type: 'float',
// 			initial: 20
// 		},
// 		{
// 			name: 'clearance',
// 			caption: 'Clearance (minimal distance between the apex of a tooth and the trough of the other gear):',
// 			type: 'float',
// 			initial: 0.05
// 		},
// 		{
// 			name: 'backlash',
// 			caption: 'Backlash (minimal distance between meshing gears):',
// 			type: 'float',
// 			initial: 0.05
// 		},
// 		{
// 			name: 'profileShift',
// 			caption: 'Profile Shift (indicates what portion of gear one\'s addendum height should be shifted to gear two. E.g., a value of 0.1 means the adddendum of gear two is increased by a factor of 1.1 while the height of the addendum of gear one is reduced to 0.9 of its normal height.):',
// 			type: 'float',
// 			initial: 0.0
// 		},
// 		{
// 			name: 'wheel1ToothCount',
// 			caption: 'Gear 1 Teeth Count (n1 > 0: external gear; n1 = 0: rack; n1 < 0: internal gear):',
// 			type: 'int',
// 			initial: 30
// 		},
// 		{
// 			name: 'wheel1CenterHoleDiamater',
// 			caption: 'Gear 1 Center Hole Diameter (0 for no hole):',
// 			type: 'float',
// 			initial: 20
// 		},
// 		{
// 			name: 'wheel2ToothCount',
// 			caption: 'Gear 2 Teeth Count:',
// 			type: 'int',
// 			initial: 8
// 		},
// 		{
// 			name: 'wheel2CenterHoleDiamater',
// 			caption: 'Gear 2 Center Hole Diameter (0 for no hole):',
// 			type: 'float',
// 			initial: 4
// 		},
// 		{
// 			name: 'showOption',
// 			caption: 'Show:',
// 			type: 'choice',
// 			values: [3, 1, 2],
// 			initial: 3,
// 			captions: ["Gear 1 and Gear 2", "Gear 1 Only", "Gear 2 Only"]
// 		},
// 		{
// 			name: 'stepsPerToothAngle',
// 			caption: 'Rotation steps per tooth angle when assembling the tooth profile (3 = draft, 10 = good quality). Increasing the value will result in smoother profiles at the cost of significantly higher calcucation time. Incease in small increments and check the result by zooming in.',
// 			type: 'int',
// 			initial: 3
// 		},
// 		{
// 			name: 'resolution',
// 			caption: 'Number of segments per 360 degree of rotation (only used for circles and arcs); 90 is plenty:',
// 			type: 'int',
// 			initial: 30
// 		},
// 	];
// }


// Generic support for 'class' inheritance (see TypeScript playground example 'Simple Inheritance' for details (http://www.typescriptlang.org/Playground/)
var __extends = this.__extends || function(d, b) {
  function __() {
    this.constructor = d;
  }
  __.prototype = b.prototype;
  d.prototype = new __();
};
// End generic support for 'class' inheritance

// Start base class Gear
var Gear = (function() {
  function Gear(options) {
    var options = options || {};

    this.toothCount = options.toothCount == null ? 15 : options.toothCount;
    if (this.toothCount > 0) {
      this.gearType = GearType.Regular;
    } else if (this.toothCount < 0) {
      this.gearType = GearType.Internal;
      this.toothCount = -this.toothCount;
    } else {
      // this.toothCount  == 0
      this.gearType = GearType.Rack;
    }

    this.circularPitch = options.circularPitch; // Distance from one face of a tooth to the corresponding face of an adjacent tooth on the same gear, measured along the pitch circle.
    this.diametralPitch = options.diametralPitch; // Ratio of the number of teeth to the pitch diameter
    this.pressureAngle = options.pressureAngle || 20; // Most common stock gears have a 20° pressure angle, with 14½° and 25° pressure angle gears being much less
    // common. Increasing the pressure angle increases the width of the base of the gear tooth, leading to greater strength and load carrying capacity. Decreasing
    // the pressure angle provides lower backlash, smoother operation and less sensitivity to manufacturing errors. (reference: http://en.wikipedia.org/wiki/Involute_gear)

    this.centerHoleDiameter = options.centerHoleDiameter || 0;

    // Given either circular pitch or diametral pitch we calculate the other value
    if (this.circularPitch) {
      // convert circular pitch to diametral pitch
      this.diametralPitch = Math.PI / this.circularPitch;
    } else if (this.circularPitch) {
      // convert diametral pitch to circular pitch
      this.circularPitch = Math.PI / this.diametralPitch;
    } else {
      throw "gear module needs either a diametralPitch or circularPitch";
    }

    this.clearance = options.clearance == null ? 0 : options.clearance;
    this.backlash = options.backlash == null ? 0 : options.backlash;

    this.center = [0, 0]; // center of the gear
    this.angle = 0; // angle in degrees of the complete gear (changes during rotation animation)

    // Pitch diameter: Diameter of pitch circle.
    this.pitchDiameter = this.toothCount / this.diametralPitch;
    this.pitchRadius = this.pitchDiameter / 2;

    // Addendum: Radial distance from pitch circle to outside circle.
    this.addendum = 1 / this.diametralPitch;
    this.profileShift = options.profileShift || 0;

    // Typically no profile shift is used meaning that this.shiftedAddendum = this.addendum
    this.shiftedAddendum = this.addendum * (1 + this.profileShift);

    //Outer Circle
    this.outerRadius = this.pitchRadius + this.shiftedAddendum;
    this.angleToothToTooth = 360 / this.toothCount;
    this.qualitySettings = options.qualitySettings;
    //OpenJsCad.log("qualitySettings.resolution: " + this.qualitySettings.resolution);
    //OpenJsCad.log("qualitySettings.stepsPerToothAngle: " + this.qualitySettings.stepsPerToothAngle);
  }
  Gear.prototype.getZeroedShape = function() {
    // return the gear shape center on the origin and rotation angle 0.
    if (this.zeroedShape == null) {
      this.zeroedShape = this._createZeroedShape();
    }
    return this.zeroedShape;
  }
  Gear.prototype._createZeroedShape = function() {
    if (this.gearType == GearType.Regular) {
      return this._createRegularGearShape();
    } else if (this.gearType == GearType.Internal) {
      return this._createInternalGearShape();
    } else if (this.gearType == GearType.Rack) {
      return this._createRackShape();
    }
  }
  Gear.prototype._createRegularGearShape = function() {
    var tooth = this._createSingleTooth();
    //OpenJsCad.log("-1");

    // we could now take the tooth cutout, rotate it tooth count times and union the various slices together into a complete gear.
    // However, the union operations become more and more complex as the complete gear is built up.
    // So instead we capture the outer path of the tooth and concatenate rotated versions of this path into a complete outer gear path.
    // Concatenating paths is inexpensive resulting in significantly faster execution.
    var outlinePaths = tooth.getOutlinePaths();
    var corners = outlinePaths[0].points;

    // first we need to find the corner that sits at the center
    var centerCornerIndex;
    for (var i = 0; i < corners.length; i++) {
      var corner = corners[i];
      if (corner.lengthSquared() < 0.0000001) {
        centerCornerIndex = i;
        break;
      }
    }
    var outerPoints = [];
    var outerCorners = [];
    var outterPointsCount = corners.length - 2;
    for (var i = 1; i < corners.length - 1; i++) {
      var corner = corners[(i + centerCornerIndex) % corners.length];
      outerCorners.push(corner);
      outerPoints.push([corner.x, corner.y]);
    }

    for (var i = 1; i < this.toothCount; i++) {
      var angle = i * this.angleToothToTooth;
      var roatationMatrix = CSG.Matrix4x4.rotationZ(angle)
      for (var j = 0; j < outerCorners.length; j++) {
        var rotatedCorner = outerCorners[j].transform(roatationMatrix);
        outerPoints.push([rotatedCorner.x, rotatedCorner.y]);
      }
      //OpenJsCad.log(i);
    }

    var gearShape = CAG.fromPointsNoCheck(outerPoints);

    if (this.centerHoleDiameter > 0) {
      var centerhole = CAG.circle({
        center: [-0, -0],
        radius: this.centerHoleDiameter / 2,
        resolution: this.qualitySettings.resolution
      });
      gearShape = gearShape.subtract(centerhole);
    }

    return gearShape.rotateZ(-90);
  }
  Gear.prototype._createSingleTooth = function() {
    // create outer circle sector covering one tooth
    var toothSectorPath = new CSG.Path2D([
      [0, 0]
    ], /* closed = */ false);
    var toothSectorArc = CSG.Path2D.arc({
      center: [0, 0],
      radius: this.outerRadius,
      startangle: 90,
      endangle: 90 - this.angleToothToTooth,
      resolution: this.qualitySettings.resolution,
    });
    toothSectorPath = toothSectorPath.concat(toothSectorArc);
    toothSectorPath = toothSectorPath.close();
    var toothSector = toothSectorPath.innerToCAG();

    var toothCutout = this.createToothCutout(false);
    //OpenJsCad.log("-2");
    var tooth = toothSector.subtract(toothCutout);
    return tooth;
  }
  Gear.prototype.createCutoutDemo = function() {
    // create outer circle
    var outerCirclePath = CSG.Path2D.arc({
      center: [0, 0],
      radius: this.outerRadius,
      startangle: 0,
      endangle: 360,
      resolution: this.qualitySettings.resolution,
    });
    outerCirclePath = outerCirclePath.close();

    var gearShape = new CAG();
    gearShape = gearShape.union(outerCirclePath.expandToCAG(g_ExpandToCAGParams.pathradius, g_ExpandToCAGParams.resolution));

    var firstCutoutHalf = this.createHalfToothCutout(true);
    // for illustration purposes we mirror the cutout and rotate it so that we can see a completely formed tooth
    var secondCutoutHalf = firstCutoutHalf.mirroredX();

    gearShape = gearShape.union(firstCutoutHalf);
    gearShape = gearShape.union(secondCutoutHalf);

    // apply gear rotation
    gearShape = gearShape.rotateZ(this.angle)
    // move to correct center
    gearShape = gearShape.translate(this.center);
    return gearShape;
  }
  Gear.prototype.createToothCutout = function(asPath) {
    var angleToothToTooth = 360 / this.toothCount;
    var angleStepSize = this.angleToothToTooth / this.qualitySettings.stepsPerToothAngle;
    //OpenJsCad.log("angleToothToTooth: " + this.angleToothToTooth);
    //OpenJsCad.log("angleStepSize: " + angleStepSize);
    var toothCutout = new CAG();

    var toothCutter = this.createToothCutter(asPath);
    var toothCutterShape = toothCutter.shape;
    var lowerLeftCorner = toothCutter.lowerLeftCorner;

    // To create the tooth profile we move the (virtual) infinite gear and then turn the resulting cutter position back.
    // For illustration see http://lcamtuf.coredump.cx/gcnc/ch6/, section 'Putting it all together'
    // We continue until the moved tooth cutter's lower left corner is outside of the outer circle of the gear.
    // Going any further will no longer influence the shape of the tooth
    var lowerLeftCornerDistance = 0;
    var stepCounter = 0;
    while (true) {
      var angle = stepCounter * angleStepSize;
      var xTranslation = [angle * Math.PI / 180 * this.pitchRadius, 0];

      var movedLowerLeftCorner = lowerLeftCorner.translate(xTranslation);
      movedLowerLeftCorner = movedLowerLeftCorner.rotateZ(angle);

      lowerLeftCornerDistance = movedLowerLeftCorner.length();
      if (movedLowerLeftCorner.length() > this.outerRadius) {
        // the cutter is now completely outside the gear and no longer influences the shape of the gear tooth
        break;
      }

      // we move in both directions
      var movedToothCutterShape = toothCutterShape.translate(xTranslation);
      var movedToothCutterShape = movedToothCutterShape.rotateZ(angle);
      toothCutout = toothCutout.union(movedToothCutterShape);

      if (xTranslation[0] > 0) {
        //OpenJsCad.log("xTranslation: " + xTranslation);
        movedToothCutterShape = toothCutterShape.translate([-xTranslation[0], xTranslation[1]]);
        movedToothCutterShape = movedToothCutterShape.rotateZ(-angle);
        toothCutout = toothCutout.union(movedToothCutterShape);
      }

      stepCounter++;
    }

    var outlinePaths = toothCutout.getOutlinePaths();
    var corners = outlinePaths[0].points;
    var cleanedUpCorners = this._smoothConcaveCorners(corners);

    var points = [];
    cleanedUpCorners.map(function(corner) {
      points.push([corner.x, corner.y]);
    });

    var toothCutout = CAG.fromPoints(points);
    return toothCutout.rotateZ(-this.angleToothToTooth / 2);
  }
  Gear.prototype.createToothCutter = function(asPath) {
    // we create a trapezoidal cutter as described at http://lcamtuf.coredump.cx/gcnc/ch6/ under the section 'Putting it all together'
    var toothWidth = this.circularPitch / 2;
    //OpenJsCad.log("toothWidth: " + toothWidth);
    OpenJsCad.log("addendum: " + this.addendum);
    OpenJsCad.log("shiftedAddendum: " + this.shiftedAddendum);
    OpenJsCad.log("clearance: " + this.clearance);

    var cutterDepth = this.addendum + this.clearance;
    var cutterOutsideLength = 3 * this.addendum;
    OpenJsCad.log("cutterDepth: " + cutterDepth);
    //OpenJsCad.log("cutterOutsideLength: " + cutterOutsideLength);

    var sinPressureAngle = Math.sin(this.pressureAngle * Math.PI / 180);
    var cosPressureAngle = Math.cos(this.pressureAngle * Math.PI / 180);

    // if a positive backlash is defined then we widen the trapezoid accordingly.
    // Each side of the tooth needs to widened by a fourth of the backlash (vertical to cutter faces).
    var dx = this.backlash / 2 / cosPressureAngle;
    //OpenJsCad.log("backlash: " + this.backlash);
    //OpenJsCad.log("dx: " + dx);

    var lowerRightCorner = [toothWidth / 2 + dx - cutterDepth * sinPressureAngle, this.pitchRadius + this.profileShift * this.addendum - cutterDepth];
    var upperRightCorner = [toothWidth / 2 + dx + cutterOutsideLength * sinPressureAngle, this.pitchRadius + this.profileShift * this.addendum + cutterOutsideLength];
    var upperLeftCorner = [-upperRightCorner[0], upperRightCorner[1]];
    var lowerLeftCorner = [-lowerRightCorner[0], lowerRightCorner[1]];

    //this.logPoints([lowerRightCorner, upperRightCorner, upperLeftCorner, lowerLeftCorner]);

    var cutterPath = new CSG.Path2D(
      [lowerLeftCorner, upperLeftCorner, upperRightCorner, lowerRightCorner],
      /* closed = */
      true
    );

    var cutterShape;
    if (asPath) {
      cutterShape = cutterPath.expandToCAG(g_ExpandToCAGParams.pathradius, g_ExpandToCAGParams.resolution);
    } else {
      cutterShape = cutterPath.innerToCAG();
    }
    return {
      shape: cutterShape,
      lowerLeftCorner: cutterPath.points[0]
    }
  }
  Gear.prototype._createInternalGearShape = function() {
    var singleTooth = this._createInternalToothProfile();
    //return singleTooth;

    var outlinePaths = singleTooth.getOutlinePaths();
    var corners = outlinePaths[0].points;

    // first we need to find the corner that sits at the center
    var centerCornerIndex;
    var radius = this.pitchRadius + (1 + this.profileShift) * this.addendum + this.clearance;

    var delta = 0.0000001;
    for (var i = 0; i < corners.length; i++) {
      var corner = corners[i];
      if (corner.y < delta && (corner.x + radius) < delta) {
        centerCornerIndex = i;
        break;
      }
    }
    var outerCorners = [];
    for (var i = 2; i < corners.length - 2; i++) {
      var corner = corners[(i + centerCornerIndex) % corners.length];
      outerCorners.push(corner);
    }

    outerCorners.reverse();
    var cornersCount = outerCorners.length;

    for (var i = 1; i < this.toothCount; i++) {
      var angle = i * this.angleToothToTooth;
      var roatationMatrix = CSG.Matrix4x4.rotationZ(angle)
      for (var j = 0; j < cornersCount; j++) {
        var rotatedCorner = outerCorners[j].transform(roatationMatrix);
        outerCorners.push(rotatedCorner);
      }
    }

    var outerCorners = this._smoothConcaveCorners(outerCorners);
    var outerPoints = [];
    outerCorners.map(function(corner) {
      outerPoints.push([corner.x, corner.y]);
    });

    var innerRadius = this.pitchRadius + (1 - this.profileShift) * this.addendum + this.clearance;
    var outerRadius = innerRadius + 4 * this.addendum;
    var outerCircle = CAG.circle({
      center: this.center,
      radius: outerRadius,
      resolution: this.qualitySettings.resolution
    });
    //return outerCircle;

    var gearCutout = CAG.fromPointsNoCheck(outerPoints);
    //return gearCutout;
    return outerCircle.subtract(gearCutout);
  }
  Gear.prototype._createInternalToothProfile = function() {
    var radius = this.pitchRadius + (1 - this.profileShift) * this.addendum + this.clearance;
    var angleToothToTooth = 360 / this.toothCount;
    var sin = Math.sin(angleToothToTooth / 2 * Math.PI / 180);
    var cos = Math.cos(angleToothToTooth / 2 * Math.PI / 180);

    var fullSector = CAG.fromPoints(
      [
        [0, 0],
        [-(radius * cos), radius * sin],
        [-radius, 0],
        [-(radius * cos), -radius * sin]
      ]
    );
    var innerCircle = CAG.circle({
      center: this.center,
      radius: radius - (2 * this.addendum + this.clearance),
      resolution: this.qualitySettings.resolution
    });
    var sector = fullSector.subtract(innerCircle);

    var cutterTemplate = this._createInternalToothCutter();

    var pinion = this.connectedGear;
    var angleToothToTooth = 360 / pinion.toothCount;
    var stepsPerTooth = this.qualitySettings.stepsPerToothAngle;
    var angleStepSize = angleToothToTooth / stepsPerTooth;
    //OpenJsCad.log("angleToothToTooth: " + angleToothToTooth);
    //OpenJsCad.log("this.qualitySettings.stepsPerToothAngle: " + this.qualitySettings.stepsPerToothAngle);
    //OpenJsCad.log("count: " + this.qualitySettings.stepsPerToothAngle * this.toothCount / pinion.toothCount);
    //OpenJsCad.log("angleStepSize: " + angleStepSize);
    var toothShape = sector;
    var cutter = cutterTemplate.translate([-this.pitchRadius + this.connectedGear.pitchRadius, 0]);
    toothShape = toothShape.subtract(cutter);

    for (var i = 1; i < stepsPerTooth; i++) {
      //OpenJsCad.log("i: " + i);

      var pinionRotationAngle = i * angleStepSize;
      var pinionCenterRayAngle = -pinionRotationAngle * pinion.toothCount / this.toothCount;
      //OpenJsCad.log("pinionRotationAngle: " + pinionRotationAngle);
      //OpenJsCad.log("pinionCenterRayAngle: " + pinionCenterRayAngle);

      //var cutter = cutterTemplate;
      cutter = cutterTemplate.rotateZ(pinionRotationAngle);
      cutter = cutter.translate([-this.pitchRadius + this.connectedGear.pitchRadius, 0]);
      cutter = cutter.rotateZ(pinionCenterRayAngle);

      toothShape = toothShape.subtract(cutter);

      cutter = cutterTemplate.rotateZ(-pinionRotationAngle);
      cutter = cutter.translate([-this.pitchRadius + this.connectedGear.pitchRadius, 0]);
      cutter = cutter.rotateZ(-pinionCenterRayAngle);

      toothShape = toothShape.subtract(cutter);
    }

    return toothShape;
  }
  Gear.prototype._smoothConvexCorners = function(corners) {
    // removes single convex corners located between concave corners
    return this._smoothCorners(corners, /* removeSingleConvex= */ true);
  }
  Gear.prototype._smoothConcaveCorners = function(corners) {
    // removes single concave corners located between convex corners
    return this._smoothCorners(corners, /* removeSingleConvex= */ false);
  }
  Gear.prototype._smoothCorners = function(corners, removeSingleConvex) {
    var isConvex = [];
    var previousCorner = corners[corners.length - 1];
    var currentCorner = corners[0];
    for (var i = 0; i < corners.length; i++) {
      var nextCorner = corners[(i + 1) % corners.length];

      var v1 = previousCorner.minus(currentCorner);
      var v2 = nextCorner.minus(currentCorner);
      var crossProduct = v1.cross(v2);
      isConvex.push(crossProduct < 0);

      previousCorner = currentCorner;
      currentCorner = nextCorner;
    }
    // we want to remove any concave corners that are located between two convex corners
    var cleanedUpCorners = [];
    var previousIndex = corners.length - 1;
    var currentIndex = 0;
    for (var i = 0; i < corners.length; i++) {
      var corner = corners[currentIndex];
      var nextIndex = (i + 1) % corners.length;

      var isSingleConcave = (!isConvex[currentIndex] && isConvex[previousIndex] && isConvex[nextIndex]);
      var isSingleConvex = (isConvex[currentIndex] && !isConvex[previousIndex] && !isConvex[nextIndex]);

      previousIndex = currentIndex;
      currentIndex = nextIndex;

      if (removeSingleConvex && isSingleConvex) {
        //OpenJsCad.log("skipping single convex: " + currentIndex);
        continue;
      }
      if (!removeSingleConvex && isSingleConcave) {
        //OpenJsCad.log("skipping single concave: " + currentIndex);
        continue;
      }

      cleanedUpCorners.push(corner);
    }

    return cleanedUpCorners;
  }
  Gear.prototype._createInternalToothCutter = function() {
    // To cut the internal gear teeth, the actual pinion comes close but we need to enlarge it so properly cater for clearance and backlash
    var pinion = this.connectedGear;

    var enlargedPinion = new Gear({
      circularPitch: pinion.circularPitch,
      pressureAngle: pinion.pressureAngle,
      clearance: -pinion.clearance,
      backlash: -pinion.backlash,
      toothCount: pinion.toothCount,
      centerHoleDiameter: 0,
      profileShift: pinion.profileShift,
      qualitySettings: pinion.qualitySettings
    });

    var tooth = enlargedPinion._createSingleTooth();
    return tooth.rotateZ(90 + 180 / enlargedPinion.toothCount); // we need a tooth pointing to the left
  }
  Gear.prototype._createRackShape = function() {
    var rack = new CAG();
    var protoTooth = this._createRackTooth();

    // we draw one tooth in the middle and then five on either side
    var toothCount = 41.0;
    for (var i = 0; i < toothCount; i++) {
      var tooth = protoTooth.translate([0, (0.5 + -toothCount / 2 + i) * this.circularPitch]);
      rack = rack.union(tooth);
    }

    // creating the bar backing the teeth
    var rightX = -(this.addendum + this.clearance);
    var width = 4 * this.addendum;
    var halfHeight = toothCount * this.circularPitch / 2;
    var bar = CAG.rectangle({
      corner1: [rightX - width, -halfHeight],
      corner2: [rightX, halfHeight]
    });

    rack = rack.union(bar);
    rack = rack.translate([this.addendum * this.profileShift, 0]);
    return rack;
  }
  Gear.prototype._createRackTooth = function() {
    var toothWidth = this.circularPitch / 2;
    var toothDepth = this.addendum + this.clearance;

    var sinPressureAngle = Math.sin(this.pressureAngle * Math.PI / 180);
    var cosPressureAngle = Math.cos(this.pressureAngle * Math.PI / 180);

    // if a positive backlash is defined then we widen the trapezoid accordingly.
    // Each side of the tooth needs to widened by a fourth of the backlash (vertical to cutter faces).
    var dx = this.backlash / 4 / cosPressureAngle;
    //OpenJsCad.log("backlash: " + this.backlash);
    //OpenJsCad.log("dx: " + dx);

    var leftDepth = this.addendum + this.clearance;
    var upperLeftCorner = [-leftDepth, toothWidth / 2 - dx + (this.addendum + this.clearance) * sinPressureAngle];
    var upperRightCorner = [this.addendum, toothWidth / 2 - dx - this.addendum * sinPressureAngle];
    var lowerRightCorner = [upperRightCorner[0], -upperRightCorner[1]];
    var lowerLeftCorner = [upperLeftCorner[0], -upperLeftCorner[1]];

    return CAG.fromPoints([upperLeftCorner, upperRightCorner, lowerRightCorner, lowerLeftCorner]);
  }
  Gear.prototype.pointsToString = function(points) {
    var result = "[";
    points.map(function(point) {
      result += "[" + point.x + "," + point.y + "],";
    });
    return result + "]";
  }
  return Gear;
})();

// GearSet class
var GearSet = (function() {
  function GearSet(gear1, gear2, showOption) {
    this.gear1 = gear1;
    gear1.connectedGear = gear2;
    this.gear2 = gear2;
    gear2.connectedGear = gear1;
    // in order for the two gears to mesh we need to turn the second one by 'half a tooth'
    //this.gear1.setAngle(0);
    this.gearRatio = this.gear1.toothCount / this.gear1.toothCount;

    var relativePitchRadius1 = (this.gear1.gearType == GearType.Internal) ? -this.gear1.pitchRadius : this.gear1.pitchRadius;
    var relativePitchRadius2 = (this.gear2.gearType == GearType.Internal) ? -this.gear2.pitchRadius : this.gear2.pitchRadius;
    this.gearsDistance = relativePitchRadius1 + relativePitchRadius2;

    this.showOption = showOption;
  }
  GearSet.prototype.createShape = function() {
    var shape = new CAG();
    if ((this.showOption & 1) > 0) {
      // show gear 1
      var gear1Shape = this.gear1.getZeroedShape();
      //var gear1Shape = this.gear1.createCutoutDemo();
      shape = shape.union(gear1Shape);
    }
    if ((this.showOption & 2) > 0) {
      // show gear 2
      var gear2Shape = this.gear2.getZeroedShape();

      if (this.gear2.gearType == GearType.Regular) {
        // we need an angle offset of half a tooth for the two gears to mesh
        var angle = 180 + 180 / this.gear2.toothCount;
        // apply gear rotation
        gear2Shape = gear2Shape.rotateZ(angle);
      } else if (this.gear2.gearType == GearType.Internal) {
        // we need an angle offset of half a tooth for the two gears to mesh
        var angle = 180; // + 180 / this.gear2.toothCount;
        // apply gear rotation
        gear2Shape = gear2Shape.rotateZ(angle);
      } else if (this.gear2.gearType == GearType.Rack) {
        gear2Shape = gear2Shape.rotateZ(180);
        gear2Shape = gear2Shape.translate([0, this.gear2.circularPitch / 2]);
      }

      // move to correct center
      gear2Shape = gear2Shape.translate([this.gearsDistance, 0]);

      //var gear2Shape = this.gear2.createCutoutDemo();
      shape = shape.union(gear2Shape);
    }
    return shape;
  }


  return GearSet;
})();