cat.js

Cat = function(){
    this.threeGroup = new THREE.Group();
    
    var yellowMat = new THREE.MeshLambertMaterial ({
      color: 0xfdd276, 
      shading:THREE.FlatShading
    });
  
    var pinkMat = new THREE.MeshLambertMaterial ({
      color: 0xe0877e, // 0xe0a79f, 
      shading:THREE.FlatShading
    });
  
    var redMat = new THREE.MeshLambertMaterial ({
      color: 0x630d15, 
      shading:THREE.FlatShading
    });
  
    var whiteMat = new THREE.MeshLambertMaterial ({
      color: 0xffffff, 
      shading:THREE.FlatShading
    });
  
    var blackMat = new THREE.MeshLambertMaterial ({
      color: 0x111111, 
      shading:THREE.FlatShading
    });
    var brownMat = new THREE.MeshLambertMaterial ({
      color: 0x2e2019,//0x4b342a, 
      shading:THREE.FlatShading
    });
  
    var lightBrownMat = new THREE.MeshLambertMaterial ({
      color: 0x664f4a, 
      shading:THREE.FlatShading
    });
  
    this.handHeight = 10;
    this.bodyHeight = 80;
    this.armHeight = ((this.bodyHeight * 3/5) - this.handHeight)/2 ;
    this.faceHeight = 30;
    this.shouldersPosition = new THREE.Vector3(0,this.armHeight*2 + this.handHeight, 0);
    this.isAttacking = false;
    this.isFootReplacing = false;
    this.isBlinking = false;
    this.footUsed = "left";
    this.transferPower = {x:0,y:0};
    
    
    // body
  
    this.body = new THREE.Group();
  
    // torso
  
    var torsoGeom = new THREE.CylinderGeometry(0, 26 ,this.bodyHeight,3,1);
    this.torso = new THREE.Mesh(torsoGeom,brownMat);
    this.torso.geometry.applyMatrix(new THREE.Matrix4().makeRotationY(Math.PI/3));
    this.torso.geometry.applyMatrix(new THREE.Matrix4().makeTranslation(0,-this.bodyHeight/2,0));
    
    // chest
  
    var chestGeom = new THREE.CylinderGeometry(6,0, 17, 3);
    chestGeom.applyMatrix(new THREE.Matrix4().makeRotationY(Math.PI/3));
    chestGeom.applyMatrix(new THREE.Matrix4().makeScale(1,1,.3));
    this.chest = new THREE.Mesh(chestGeom, whiteMat);
    this.chest.position.set(0,-30,1);
  
    // head
    this.head = new THREE.Group();
  
    var faceGeom = new THREE.BoxGeometry(30,this.faceHeight,30);
    this.face = new THREE.Mesh(faceGeom,brownMat);
    this.face.geometry.applyMatrix(new THREE.Matrix4().makeTranslation(0,this.faceHeight/2,0));
    this.face.geometry.applyMatrix(new THREE.Matrix4().makeRotationY(Math.PI/4));
  
  
    // scarf
    var scarfGeom = new THREE.CylinderGeometry(10,9,9,10, 1);
    this.scarf1 = new THREE.Mesh(scarfGeom, redMat);
    this.scarf1.material.side = THREE.DoubleSide;
    this.scarf1.position.y = -2;
    this.scarf1.position.z = 0;
    this.scarf1.rotation.z = .4;
    this.scarf1.rotation.y = Math.PI/3;
    
    this.scarf2 = this.scarf1.clone();
    this.scarf2.scale.set(.9,.7,.9);
    this.scarf2.position.y = -17;
    this.scarf2.rotation.z = -.2;
  
    var scarfGeom2 = new THREE.BoxGeometry(50,2,10);
    this.scarf3 = new THREE.Mesh(scarfGeom2, redMat);
    this.scarf3.geometry.applyMatrix(new THREE.Matrix4().makeTranslation(25,0,0));
    this.scarf3.position.set(3,-15,2);
    this.scarf3.rotation.y = 1.2;
    this.scarf3.rotation.z = -1;
  
    
    this.head.add(this.scarf1);
    this.torso.add(this.scarf2);
    this.torso.add(this.scarf3);
    this.torso.add(this.chest);
  
    
    var skewMatrixBody = new THREE.Matrix4();
    skewMatrixBody.set(   1,    0,    0,    0,
                          0,    1,    0,    0,
                          0,    0.20,    1,    0,
                          0,    0,    0,    1  );
    
  
    this.torso.geometry.applyMatrix(skewMatrixBody);
    this.chest.geometry.applyMatrix(skewMatrixBody);
    
  
    this.body.add(this.torso);
    this.body.position.y = this.bodyHeight;
  
    
    // Whiskers
    var whiskerGeom = new THREE.BoxGeometry(16, .2,.2);
  
    this.whisker1 = new THREE.Mesh(whiskerGeom, lightBrownMat);
    this.whisker1.geometry.applyMatrix(new THREE.Matrix4().makeTranslation(-7,0,0));
    this.whisker1.position.set(-6,8,18);
    this.whisker1.rotation.z = Math.PI/12;
  
    this.whisker2 = this.whisker1.clone();
    this.whisker2.position.y = 6;
    
    this.whisker3 = this.whisker1.clone();
    this.whisker3.position.y = 4;
  
    this.whisker4 = this.whisker1.clone();
    this.whisker4.rotation.z = Math.PI - Math.PI/12;
    this.whisker4.position.x = -this.whisker1.position.x;
  
    this.whisker5 = this.whisker4.clone();
    this.whisker5.position.y = this.whisker2.position.y;
  
    this.whisker6 = this.whisker4.clone();
    this.whisker6.position.y = this.whisker3.position.y;
  
    this.head.add(this.whisker1);
    this.head.add(this.whisker2);
    this.head.add(this.whisker3);
    this.head.add(this.whisker4);
    this.head.add(this.whisker5);
    this.head.add(this.whisker6);
  
    // ears
    var rightEarGeom = new THREE.CylinderGeometry(0,8, 8, 3,1);
    rightEarGeom.applyMatrix(new THREE.Matrix4().makeTranslation(0,4,0));
    var leftEarGeom = rightEarGeom.clone();
  
    rightEarGeom.applyMatrix(new THREE.Matrix4().makeRotationY(1));
    rightEarGeom.applyMatrix(new THREE.Matrix4().makeScale(1,1,.7));
  
    leftEarGeom.applyMatrix(new THREE.Matrix4().makeRotationY(-1));
    leftEarGeom.applyMatrix(new THREE.Matrix4().makeScale(1,1,.7));
    
    
    
    var skewMatrixRightEar = new THREE.Matrix4().set(   1,    0.0,     0.0,    0,
                                                        0,    1,        0,    0,
                                                        -0.5,    0.0,     1,    0,
                                                        0,    0,        0,    1 );
  
    
    var skewMatrixLeftEar = new THREE.Matrix4().set(    1,    -.5,     0,    0,
                                                        0,    1,        0,    0,
                                                        0,    0.0,     1,    0,
                                                        0,    0,        0,    1 );
  
    this.rightEar = new THREE.Mesh(rightEarGeom, brownMat);
    this.rightEar.position.y = this.faceHeight;
    this.rightEar.position.x = -14;
    this.rightEar.position.z = -1.7;  
    
    this.leftEar = new THREE.Mesh(leftEarGeom, brownMat);
    this.leftEar.position.x = -this.rightEar.position.x;
    this.leftEar.position.z = this.rightEar.position.z;
    this.leftEar.position.y = this.rightEar.position.y;
  
  
    var rightEarInsideGeom = rightEarGeom.clone();
    rightEarInsideGeom.applyMatrix(new THREE.Matrix4().makeScale(.5, .5, .5));
    this.rightEarInside = new THREE.Mesh(rightEarInsideGeom, pinkMat);
    this.rightEarInside.position.y = .5;
    this.rightEarInside.position.x = 1;
    this.rightEarInside.position.z = 2;
  
    this.rightEar.add(this.rightEarInside);
  
    var LeftEarInsideGeom = leftEarGeom.clone();
    LeftEarInsideGeom.applyMatrix(new THREE.Matrix4().makeScale(.5, .5, .5));
    this.leftEarInside = new THREE.Mesh(LeftEarInsideGeom, pinkMat);
    this.leftEarInside.position.y = .5;
    this.leftEarInside.position.x = -1;
    this.leftEarInside.position.z = 2;
  
    this.leftEar.add(this.leftEarInside);
  
    // Eyes
    var eyeGeom = new THREE.BoxGeometry(12,12, 1);
    this.rightEye = new THREE.Mesh(eyeGeom, whiteMat);
    this.rightEye.position.set(-12,20, 10);
    this.rightEye.rotation.y = -Math.PI/4;
  
    this.leftEye = this.rightEye.clone();
    this.leftEye.position.x = -this.rightEye.position.x;
    this.leftEye.rotation.y = Math.PI/4;
  
    // Iris
    var irisGeom = new THREE.BoxGeometry(4,4,2);
    this.rightIris = new THREE.Mesh(irisGeom, brownMat);
    this.rightIris.position.x = 2;
    this.rightIris.position.y = -2;
    this.rightIris.position.z = .5;
  
    this.leftIris = this.rightIris.clone();
    this.leftIris.position.x = -this.rightIris.position.x;
  
    this.rightEye.add(this.rightIris);
    this.leftEye.add(this.leftIris);
  
    // nose
    var noseGeom = new THREE.CylinderGeometry(3,0,4,4)
    noseGeom.applyMatrix(new THREE.Matrix4().makeTranslation(0,-2,-4));
  
    var skewMatrixNose = new THREE.Matrix4().set(   1,    0,     0,    0,
                                                    0,    1,     0,    0,
                                                    0,    -.7,     1,    1.4,
                                                    0,    0,     0,    1 );
  
    noseGeom.applyMatrix(skewMatrixNose);
    this.nose = new THREE.Mesh(noseGeom, pinkMat);
    this.nose.position.z = 24;
    this.nose.position.y =14.1;
  
  
    // cheeks
    var cheeksGeom = new THREE.CylinderGeometry(8,8,14,4);
    cheeksGeom.applyMatrix(new THREE.Matrix4().makeScale(1,1,1.4));
    this.cheeks = new THREE.Mesh(cheeksGeom, brownMat);
    this.cheeks.position.set(0, 7, 13 );
  
    // mouth
    var mouthGeom = cheeksGeom.clone();//new THREE.BoxGeometry(4,2,4);
    mouthGeom.applyMatrix(new THREE.Matrix4().makeTranslation(0,-4,0));
    mouthGeom.applyMatrix(new THREE.Matrix4().makeScale(.5,.2,.5));
    this.mouth = new THREE.Mesh(mouthGeom, brownMat);
    
  
    // tongue
    var tongueGeom = mouthGeom.clone();
    tongueGeom.applyMatrix(new THREE.Matrix4().makeScale(.8,1,.8));
    this.tongue = new THREE.Mesh(tongueGeom, pinkMat);
    this.tongue.position.set(0, .5, 0); 
    this.mouth.add(this.tongue);
  
    this.mouth.rotation.x = Math.PI/4;
    this.mouth.position.set(0, 1.5, 18); 
  
    
    this.head.add(this.face);
    this.head.add(this.rightEar);
    this.head.add(this.leftEar);
    this.head.add(this.rightEye);
    this.head.add(this.leftEye);
    this.head.add(this.nose);
    this.head.add(this.cheeks);
    this.head.add(this.mouth);
    
    this.head.position.y = this.bodyHeight-15;
    this.head.position.z = -5;
  
  
    // shoulders
    this.rightShoulder = new THREE.Group();
    this.leftShoulder = new THREE.Group();
  
    this.rightShoulder.position.set(-6, this.shouldersPosition.y, 0);
    this.leftShoulder.position.set(6, this.shouldersPosition.y, 0);
  
  
    // arms
    var armGeom = new THREE.CylinderGeometry(4, 6, this.armHeight+5,4);
    armGeom.applyMatrix(new THREE.Matrix4().makeRotationY(Math.PI/4));
    armGeom.applyMatrix(new THREE.Matrix4().makeTranslation(0, -this.armHeight/2, 0));
  
    this.rightArm = new THREE.Mesh(armGeom,brownMat);
    this.rightShoulder.add(this.rightArm);
  
    this.leftArm = this.rightArm.clone();
    this.leftShoulder.add(this.leftArm);
    
    // forearms
  
    var foreArmGeom = new THREE.CylinderGeometry(6, 7, this.armHeight,4);
    foreArmGeom.applyMatrix(new THREE.Matrix4().makeRotationY(Math.PI/4));
    foreArmGeom.applyMatrix(new THREE.Matrix4().makeTranslation(0, -this.armHeight/2, 0));
  
  
    this.rightForeArm = new THREE.Mesh(foreArmGeom,brownMat);
    this.rightForeArm.position.y = -this.armHeight;
    this.rightArm.add(this.rightForeArm);
  
    this.leftForeArm = this.rightForeArm.clone();
    this.leftArm.add(this.leftForeArm);
  
    // foot = front foot
    var footGeom = new THREE.BoxGeometry(10,10,10);
    this.rightFoot = new THREE.Mesh(footGeom, whiteMat);
    this.rightFoot.geometry.applyMatrix(new THREE.Matrix4().makeTranslation(0,0,0));
    this.rightFoot.position.set(0,-this.armHeight-5,0);
    this.rightForeArm.add(this.rightFoot);
    this.leftFoot = this.rightFoot.clone();
    this.leftForeArm.add(this.leftFoot);
  
    //footPad
    var footPadGeom = new THREE.BoxGeometry(8,2,8);
    this.rightFootPad = new THREE.Mesh(footPadGeom, pinkMat);
    this.rightFootPad.position.y = -4.5;
    this.rightFoot.add(this.rightFootPad)
  
    this.leftFootPad = this.rightFootPad.clone();
    this.leftFoot.add(this.leftFootPad)
  
    // knees
    var kneeGeom = new THREE.BoxGeometry(8,30,30);
    kneeGeom.applyMatrix(new THREE.Matrix4().makeTranslation(0,15,0));
    
    this.rightKnee = new THREE.Mesh(kneeGeom, brownMat);
    this.rightKnee.rotation.y = -Math.PI/6;
    this.rightKnee.position.x = -14;
    this.rightKnee.position.z = -12;
  
    this.leftKnee = this.rightKnee.clone();
    this.leftKnee.rotation.y = -this.rightKnee.rotation.y;
    this.leftKnee.position.x = -this.rightKnee.position.x;
  
    // legs = back legs
    var legGeom = new THREE.BoxGeometry(12,6,4);
    this.rightLeg = new THREE.Mesh(legGeom, whiteMat);
    this.rightLeg.position.set(0,3,17);
    this.rightKnee.add(this.rightLeg);
  
    this.leftLeg = this.rightLeg.clone();
    this.leftKnee.add(this.leftLeg);
  
    // tail
  
    this.tail = new THREE.Group();
    this.tail.position.z = -36;
    this.tail.position.y = 5;
  
    var p = this.tail;
    var currentY = 0;
    var curentRot = 0;
    var segHeight = 8;
    var recScale = 1.15;
  
    this.tailNSegs = 8 ;
    this.tailSegements = [];
  
    var tailSegGeom = new THREE.CylinderGeometry(5, 4, segHeight, 4);
    tailSegGeom.applyMatrix(new THREE.Matrix4().makeTranslation(0,segHeight/2,0));
    
    
    for (var i = 0; i<this.tailNSegs ; i++){
      var mat = (i<this.tailNSegs-1)? brownMat : whiteMat;
      var tg = tailSegGeom.clone();
      var s = Math.pow(recScale, i);
      tg.applyMatrix(new THREE.Matrix4().makeScale(s, s, s));
      var t = new THREE.Mesh(tg,mat);
      currentRot = (i==0)? - Math.PI/2 : currentRot/(i*i*i);
      t.position.y = currentY;
      t.rotation.x = currentRot;
      p.add(t);
      p = t;
      currentY = (segHeight-2)*s; 
      currentRot = 
      this.tailSegements.push(t);
    }
  
    // stripes Head
  
    var stripeGeom = new THREE.CylinderGeometry(2,0, 15,4);
    var stripe0 = new THREE.Mesh(stripeGeom, lightBrownMat);
    stripe0.rotation.y = -Math.PI/4;
    stripe0.position.x = -1.5;
    stripe0.position.y = 22;
    stripe0.position.z = 18.5;
  
    var stripe1 = stripe0.clone();
    stripe1.position.x = -stripe0.position.x;
    stripe1.rotation.y = -stripe0.rotation.y;
  
    
  
    var stripeGeom2 = new THREE.BoxGeometry(8,2,10);
    var stripe2 = new THREE.Mesh(stripeGeom2, lightBrownMat);
    stripe2.rotation.y = Math.PI/4;
    stripe2.position.x = 15.6;
    stripe2.position.y = 8;
    stripe2.position.z = -1;
  
    var stripe3 = stripe2.clone();
    stripe3.position.y = 4;
  
    var stripe4 = stripe2.clone();
    stripe4.rotation.y = -Math.PI/4;
    stripe4.position.x = -stripe2.position.x;
  
    var stripe5 = stripe4.clone();
    stripe5.position.y = stripe3.position.y;
  
  
    var stripeGeom3 = new THREE.BoxGeometry(1.6,1,10);
    var stripe6 = new THREE.Mesh(stripeGeom3, lightBrownMat);
    stripe6.position.x = -2.1;
    stripe6.position.z = 15;
    stripe6.position.y = 30;
  
    var stripe7 = stripe6.clone();
    stripe7.position.x = -stripe6.position.x;
  
  
    this.head.add(stripe0);
    this.head.add(stripe1);
    this.head.add(stripe2);
    this.head.add(stripe3);
    this.head.add(stripe4);
    this.head.add(stripe5);
    this.head.add(stripe6);
    this.head.add(stripe7);
  
    
    // stripes Knee
  
    var stripe9 = stripe2.clone();
    //stripe9.scale.y = 2;
    stripe9.rotation.y = 0;
    stripe9.position.y = 16;
    stripe9.position.x = -1;
    stripe9.position.z = 11;
  
    var stripe10 = stripe9.clone();
    stripe10.position.y = 22;
    stripe10.position.x = 1;
  
    var stripe11 = stripe9.clone();
    stripe11.position.y = 28;
  
    this.rightKnee.add(stripe9);
    this.rightKnee.add(stripe10);
    this.rightKnee.add(stripe11);
  
    var stripe12 = stripe9.clone();
    stripe12.position.x = -1;
  
    var stripe13 = stripe12.clone();
    stripe13.position.y = stripe10.position.y;
    stripe13.position.x = 1;
  
    var stripe14 = stripe12.clone();
    stripe14.position.y = stripe11.position.y;
  
    this.leftKnee.add(stripe12);
    this.leftKnee.add(stripe13);
    this.leftKnee.add(stripe14);
  
    this.threeGroup.add(this.body);
    this.threeGroup.add(this.head);
    this.threeGroup.add(this.rightShoulder);
    this.threeGroup.add(this.leftShoulder);
  
    this.threeGroup.add(this.rightKnee);
    this.threeGroup.add(this.leftKnee);
    this.threeGroup.add(this.tail);
  
    
    this.threeGroup.traverse( function ( object ) {
      if ( object instanceof THREE.Mesh ) {
        object.castShadow = true;
        object.receiveShadow = true;
      }
    } );
  }
  
  Cat.prototype.updateTail = function(t){
    
    for (var i=0; i<this.tailNSegs; i++){
      var angleStep = -i*.5;
      var angleAmp = Math.PI/(30/(i+1));
  
      var rotZ = Math.sin(t+angleStep)*angleAmp;
      var st = this.tailSegements[i];
      st.rotation.z = rotZ;//(rotY * i);
    }
  }
  
  Cat.prototype.interactWithBall = function(ballPos){
    var bDir = ballPos.clone().sub(this.shouldersPosition.clone());
    var isInDistance = bDir.length() < (this.armHeight*2 + this.handHeight + 8)*1.3;
  
    this.lookAt(ballPos);
  
    this.transferPower.x *= .8;
    this.transferPower.y *= .8;
  
    if (! this.isAttacking){
      if (! isInDistance){
        if (!this.isFootReplacing ){
          this.isFootReplacing = true;
          this.replaceFoot(this.footUsed);
        }
      }else{
        this.lookAt(ballPos);
        if (Math.random()>.96 ){
          this.isAttacking = true;
          this.isFootReplacing = false;
          this.attack(this.footUsed, ballPos, bDir);
        }else{
          this.isFootReplacing = false;
          var middleVector = this.shouldersPosition.clone().add(bDir.clone().multiplyScalar(.4));
          this.prepareAttack(this.footUsed, middleVector);
        }
      }
    }
  
  
    if (!this.isBlinking && Math.random()>.99){
      this.isBlinking = true;
      this.blink();
    }
  
    if (!this.mouthMoving && Math.random()>.99){
      this.mouthMoving = true;
      this.moveMouth();
    }
  }
  
  Cat.prototype.lookAt = function(v){
    if (!this.oldTargetLookPos)this.oldTargetLookPos = new THREE.Vector3();
    this.newTargetLookPos = v.clone();
    this.lookPos = this.oldTargetLookPos.clone().add(this.newTargetLookPos.sub(this.oldTargetLookPos).multiplyScalar(.15));
    this.head.lookAt(this.lookPos);
    this.oldTargetLookPos = this.lookPos;
  }
  
  Cat.prototype.prepareAttack = function(side, v){
    
    var angles = getAngles(v, this.rightShoulder.position, this.armHeight);
    this.updateArm(side, angles, 1, Back.easeOut, null);
  }
  
  Cat.prototype.attack = function(side, v, direction){
    _this = this;
    var shoulder = (side == "right")? this.rightShoulder : this.leftShoulder;
    var angles = getAngles(v, shoulder.position, this.armHeight);
    this.updateArm(side, angles, .15, Back.easeOut, function (){
      var isInDistance = direction.length() < (_this.armHeight*2 + _this.handHeight + 20);
      if (isInDistance) _this.transferPower = {x:-direction.x*(Math.random()*.5)-.1+Math.random()*.2,y:-direction.y*Math.random()*.5};
      _this.isAttacking = false;
      //console.log("attackComplete");
    });
  }
  
  
  
  Cat.prototype.replaceFoot = function(side){
    _this = this;
    var angles =  {theta:0, alpha:0, beta:0};
    this.updateArm(side, angles, 2, Strong.easeInOut, function (){
      _this.isFootReplacing = false;
      _this.footUsed = (_this.footUsed == "right") ? "left" : "right";
      //console.log("replaceComplete");
    });
  }
  
  Cat.prototype.updateArm = function(side, angles, speed, ease, callBack){
    var shoulder,arm, foreArm, foot;
    if (side == "right"){
      shoulder = this.rightShoulder;
      arm = this.rightArm;
      foreArm = this.rightForeArm;
      foot = this.rightFoot;
    }else{
      shoulder = this.leftShoulder;
      arm = this.leftArm;
      foreArm = this.leftForeArm;
      foot = this.leftFoot;
    }
    var ease = ease || Back.easeOut;
  
    var tFootAngle = Math.min (-angles.beta, Math.PI*1.5) ;
  
    TweenMax.to(shoulder.rotation, speed, {y:angles.theta, ease:ease} );
    TweenMax.to(arm.rotation, speed, {x:angles.alpha, ease:ease} );
    TweenMax.to(foreArm.rotation, speed, {x:angles.beta, ease:ease, onComplete:callBack} );
    TweenMax.to(foot.rotation, speed, {x:tFootAngle, ease:ease} );
  }
  
  Cat.prototype.blink = function(){
    _this = this;
    TweenMax.to (this.rightEye.scale, .07, {y:0, yoyo:true, repeat:1});
    TweenMax.to (this.leftEye.scale, .07, {y:0, yoyo:true, repeat:1, onComplete:function(){
      _this.isBlinking = false;
    }});
  }
  
  Cat.prototype.moveMouth = function(){
    _this = this;
    TweenMax.to (this.mouth.rotation, .2, {x:Math.PI/6, yoyo:true, repeat:1, onComplete:function(){
      _this.mouthMoving = false;
    }});
  }
  
  function getAngles(targetPos, shoulderPos, segmentLength){
    var ah = segmentLength;
    var alpha0, alpha1, alpha2;
    var beta0, beta1;
    var bDir = targetPos.clone().sub(shoulderPos);
    var bDirNorm = bDir.clone().normalize();
    
    var dist = bDir.length()-15 ;
  
    var bTargetDir = bDirNorm.clone().multiplyScalar(dist);
    var bDirMin = (dist < ah*2 ) ? bTargetDir.clone() : bDirNorm.clone().multiplyScalar(ah*2);
  
  
    // IK calculations
    var theta = Math.atan2(bDirMin.x, bDirMin.z); // shoulder orientation on Y axis
    theta = (theta < -Math.PI/2 || theta > Math.PI/2) ? 0 : theta;
    var x2 = Math.sqrt(bDirMin.x*bDirMin.x + bDirMin.z*bDirMin.z); // distance projected to x axis => used to find alpha2
    alpha2 = Math.PI/2 - Math.atan(bDirMin.y/x2);
  
    // cosine rule =>       C^2 = A^2 + B^2 - 2*A*B*cosC
    // =>                   cosC = (A^2 + B^2 - C^2) / 2*A*B
  
    var cosAlpha1 = dist / (2*ah); // in this case A^2 = C^2 = segementLength^2, then we can simplify this formula
    cosAlpha1 = (cosAlpha1>1) ? 1 : (cosAlpha1<-1)? -1 : cosAlpha1;
  
    alpha1 = Math.acos(cosAlpha1);
    alpha0 = (Math.PI) - (alpha1 + alpha2);
    alpha0 = Math.max(0, alpha0);
  
  
    cosBeta1 = (ah*ah + ah*ah - dist*dist) / (2*ah*ah);
    cosBeta1 = (cosBeta1 < -1) ? -1 : (cosBeta1 > 1) ? 1 : cosBeta1;
    beta1 = Math.acos(cosBeta1);
    beta0 = Math.PI - beta1;
    beta0 = Math.min(beta0, Math.PI*2/3);
  
    return {theta:theta, alpha:-alpha0, beta:-beta0};
  }