@matematrolii/sketchbook/src/lib/utils/THREE.quickhull.js

3D matematrolii playground built on three.js and cannon.js

/**

  QuickHull
  ---------

  The MIT License

  Copyright © 2010-2014 three.js authors

  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:

  The above copyright notice and this permission notice shall be included in
  all copies or substantial portions of the Software.

  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN

  THE SOFTWARE.


    @author mark lundin / http://mark-lundin.com

    This is a 3D implementation of the Quick Hull algorithm.
    It is a fast way of computing a convex hull with average complexity
    of O(n log(n)).
    It uses depends on three.js and is supposed to create THREE.Geometry.

    It's also very messy

 */

 import * as THREE from 'three';

export const quickhull = (function(){


  var faces     = [],
    faceStack   = [],
    i, NUM_POINTS, extremes,
    max     = 0,
    dcur, current, j, v0, v1, v2, v3,
    N, D;

  var ab, ac, ax,
    suba, subb, normal,
    diff, subaA, subaB, subC;

  function reset(){

    ab    = new THREE.Vector3(),
    ac    = new THREE.Vector3(),
    ax    = new THREE.Vector3(),
    suba  = new THREE.Vector3(),
    subb  = new THREE.Vector3(),
    normal  = new THREE.Vector3(),
    diff  = new THREE.Vector3(),
    subaA = new THREE.Vector3(),
    subaB = new THREE.Vector3(),
    subC  = new THREE.Vector3();

  }

  //temporary vectors

  function process( points ){

    // Iterate through all the faces and remove
    while( faceStack.length > 0  ){
      cull( faceStack.shift(), points );
    }
  }


  var norm = function(){

    var ca = new THREE.Vector3(),
      ba = new THREE.Vector3(),
      N = new THREE.Vector3();

    return function( a, b, c ){

      ca.subVectors( c, a );
      ba.subVectors( b, a );

      N.crossVectors( ca, ba );

      return N.normalize();
    }

  }();


  function getNormal( face, points ){

    if( face.normal !== undefined ) return face.normal;

    var p0 = points[face[0]],
      p1 = points[face[1]],
      p2 = points[face[2]];

    ab.subVectors( p1, p0 );
    ac.subVectors( p2, p0 );
    normal.crossVectors( ac, ab );
    normal.normalize();

    return face.normal = normal.clone();

  }


  function assignPoints( face, pointset, points ){

    // ASSIGNING POINTS TO FACE
    var p0 = points[face[0]],
      dots = [], apex,
      norm = getNormal( face, points );


    // Sory all the points by there distance from the plane
    pointset.sort( function( aItem, bItem ){


      dots[aItem.x/3] = dots[aItem.x/3] !== undefined ? dots[aItem.x/3] : norm.dot( suba.subVectors( aItem, p0 ));
      dots[bItem.x/3] = dots[bItem.x/3] !== undefined ? dots[bItem.x/3] : norm.dot( subb.subVectors( bItem, p0 ));

      return dots[aItem.x/3] - dots[bItem.x/3] ;
    });

    //TODO :: Must be a faster way of finding and index in this array
    var index = pointset.length;

    if( index === 1 ) dots[pointset[0].x/3] = norm.dot( suba.subVectors( pointset[0], p0 ));
    while( index-- > 0 && dots[pointset[index].x/3] > 0 )

    var point;
    if( index + 1 < pointset.length && dots[pointset[index+1].x/3] > 0 ){

      face.visiblePoints  = pointset.splice( index + 1 );
    }
  }




  function cull( face, points ){

    var i = faces.length,
      dot, visibleFace, currentFace,
      visibleFaces = [face];

    var apex = points.indexOf( face.visiblePoints.pop() );

    // Iterate through all other faces...
    while( i-- > 0 ){
      currentFace = faces[i];
      if( currentFace !== face ){
        // ...and check if they're pointing in the same direction
        dot = getNormal( currentFace, points ).dot( diff.subVectors( points[apex], points[currentFace[0]] ));
        if( dot > 0 ){
          visibleFaces.push( currentFace );
        }
      }
    }

    var index, neighbouringIndex, vertex;

    // Determine Perimeter - Creates a bounded horizon

    // 1. Pick an edge A out of all possible edges
    // 2. Check if A is shared by any other face. a->b === b->a
      // 2.1 for each edge in each triangle, isShared = ( f1.a == f2.a && f1.b == f2.b ) || ( f1.a == f2.b && f1.b == f2.a )
    // 3. If not shared, then add to convex horizon set,
        //pick an end point (N) of the current edge A and choose a new edge NA connected to A.
        //Restart from 1.
    // 4. If A is shared, it is not an horizon edge, therefore flag both faces that share this edge as candidates for culling
    // 5. If candidate geometry is a degenrate triangle (ie. the tangent space normal cannot be computed) then remove that triangle from all further processing


    var j = i = visibleFaces.length;
    var isDistinct = false,
      hasOneVisibleFace = i === 1,
      cull = [],
      perimeter = [],
      edgeIndex = 0, compareFace, nextIndex,
      a, b;

    var allPoints = [];
    var originFace = [visibleFaces[0][0], visibleFaces[0][1], visibleFaces[0][1], visibleFaces[0][2], visibleFaces[0][2], visibleFaces[0][0]];


    if( visibleFaces.length === 1 ){
      currentFace = visibleFaces[0];

      perimeter = [currentFace[0], currentFace[1], currentFace[1], currentFace[2], currentFace[2], currentFace[0]];
      // remove visible face from list of faces
      if( faceStack.indexOf( currentFace ) > -1 ){
        faceStack.splice( faceStack.indexOf( currentFace ), 1 );
      }


      if( currentFace.visiblePoints ) allPoints = allPoints.concat( currentFace.visiblePoints );
      faces.splice( faces.indexOf( currentFace ), 1 );

    }else{

      while( i-- > 0  ){  // for each visible face

        currentFace = visibleFaces[i];

        // remove visible face from list of faces
        if( faceStack.indexOf( currentFace ) > -1 ){
          faceStack.splice( faceStack.indexOf( currentFace ), 1 );
        }

        if( currentFace.visiblePoints ) allPoints = allPoints.concat( currentFace.visiblePoints );
        faces.splice( faces.indexOf( currentFace ), 1 );


        var isSharedEdge;
        cEdgeIndex = 0;

        while( cEdgeIndex < 3 ){ // Iterate through it's edges

          isSharedEdge = false;
          j = visibleFaces.length;
          a = currentFace[cEdgeIndex]
          b = currentFace[(cEdgeIndex+1)%3];


          while( j-- > 0 && !isSharedEdge ){ // find another visible faces

            compareFace = visibleFaces[j];
            edgeIndex = 0;

            // isSharedEdge = compareFace == currentFace;
            if( compareFace !== currentFace ){

              while( edgeIndex < 3 && !isSharedEdge ){ //Check all it's indices

                nextIndex = ( edgeIndex + 1 );
                isSharedEdge = ( compareFace[edgeIndex] === a && compareFace[nextIndex%3] === b ) ||
                         ( compareFace[edgeIndex] === b && compareFace[nextIndex%3] === a );

                edgeIndex++;
              }
            }
          }

          if( !isSharedEdge || hasOneVisibleFace ){
            perimeter.push( a );
            perimeter.push( b );
          }

          cEdgeIndex++;
        }
      }
    }

    // create new face for all pairs around edge
    i = 0;
    var l = perimeter.length/2;
    var f;

    while( i < l ){
      f = [ perimeter[i*2+1], apex, perimeter[i*2] ];
      assignPoints( f, allPoints, points );
      faces.push( f )
      if( f.visiblePoints !== undefined  )faceStack.push( f );
      i++;
    }

  }

  var distSqPointSegment = function(){

    var ab = new THREE.Vector3(),
      ac = new THREE.Vector3(),
      bc = new THREE.Vector3();

    return function( a, b, c ){

        ab.subVectors( b, a );
        ac.subVectors( c, a );
        bc.subVectors( c, b );

        var e = ac.dot(ab);
        if (e < 0.0) return ac.dot( ac );
        var f = ab.dot( ab );
        if (e >= f) return bc.dot(  bc );
        return ac.dot( ac ) - e * e / f;

      }

  }();





  return function( geometry ){

    reset();


    points    = geometry.vertices;
    faces     = [],
    faceStack   = [],
    i       = NUM_POINTS = points.length,
    extremes  = points.slice( 0, 6 ),
    max     = 0;



    /*
     *  FIND EXTREMETIES
     */
    while( i-- > 0 ){
      if( points[i].x < extremes[0].x ) extremes[0] = points[i];
      if( points[i].x > extremes[1].x ) extremes[1] = points[i];

      if( points[i].y < extremes[2].y ) extremes[2] = points[i];
      if( points[i].y < extremes[3].y ) extremes[3] = points[i];

      if( points[i].z < extremes[4].z ) extremes[4] = points[i];
      if( points[i].z < extremes[5].z ) extremes[5] = points[i];
    }


    /*
     *  Find the longest line between the extremeties
     */

    j = i = 6;
    while( i-- > 0 ){
      j = i - 1;
      while( j-- > 0 ){
          if( max < (dcur = extremes[i].distanceToSquared( extremes[j] )) ){
        max = dcur;
        v0 = extremes[ i ];
        v1 = extremes[ j ];

          }
        }
      }


      // 3. Find the most distant point to the line segment, this creates a plane
      i = 6;
      max = 0;
    while( i-- > 0 ){
      dcur = distSqPointSegment( v0, v1, extremes[i]);
      if( max < dcur ){
        max = dcur;
            v2 = extremes[ i ];
          }
    }


      // 4. Find the most distant point to the plane.

      N = norm(v0, v1, v2);
      D = N.dot( v0 );


      max = 0;
      i = NUM_POINTS;
      while( i-- > 0 ){
        dcur = Math.abs( points[i].dot( N ) - D );
          if( max < dcur ){
            max = dcur;
            v3 = points[i];
      }
      }



      var v0Index = points.indexOf( v0 ),
      v1Index = points.indexOf( v1 ),
      v2Index = points.indexOf( v2 ),
      v3Index = points.indexOf( v3 );


    //  We now have a tetrahedron as the base geometry.
    //  Now we must subdivide the

      var tetrahedron =[
        [ v2Index, v1Index, v0Index ],
        [ v1Index, v3Index, v0Index ],
        [ v2Index, v3Index, v1Index ],
        [ v0Index, v3Index, v2Index ],
    ];



    subaA.subVectors( v1, v0 ).normalize();
    subaB.subVectors( v2, v0 ).normalize();
    subC.subVectors ( v3, v0 ).normalize();
    var sign  = subC.dot( new THREE.Vector3().crossVectors( subaB, subaA ));


    // Reverse the winding if negative sign
    if( sign < 0 ){
      tetrahedron[0].reverse();
      tetrahedron[1].reverse();
      tetrahedron[2].reverse();
      tetrahedron[3].reverse();
    }


    //One for each face of the pyramid
    var pointsCloned = points.slice();
    pointsCloned.splice( pointsCloned.indexOf( v0 ), 1 );
    pointsCloned.splice( pointsCloned.indexOf( v1 ), 1 );
    pointsCloned.splice( pointsCloned.indexOf( v2 ), 1 );
    pointsCloned.splice( pointsCloned.indexOf( v3 ), 1 );


    var i = tetrahedron.length;
    while( i-- > 0 ){
      assignPoints( tetrahedron[i], pointsCloned, points );
      if( tetrahedron[i].visiblePoints !== undefined ){
        faceStack.push( tetrahedron[i] );
      }
      faces.push( tetrahedron[i] );
    }

    process( points );


    //  Assign to our geometry object

    var ll = faces.length;
    while( ll-- > 0 ){
      geometry.faces[ll] = new THREE.Face3( faces[ll][2], faces[ll][1], faces[ll][0], faces[ll].normal )
    }

    geometry.normalsNeedUpdate = true;

    return geometry;

  }

}())