index.js

'use strict';
	
	var ThreeBSP,
		EPSILON = 1e-5,
		COPLANAR = 0,
		FRONT = 1,
		BACK = 2,
		SPANNING = 3;
	
  module.exports = function( THREE ) {
    var ThreeBSP = function( geometry ) {
      // Convert THREE.Geometry to ThreeBSP
      var i, _length_i,
        face, vertex, faceVertexUvs, uvs,
        polygon,
        polygons = [],
        tree;
    
      if ( geometry instanceof THREE.Geometry ) {
        this.matrix = new THREE.Matrix4;
      } else if ( geometry instanceof THREE.Mesh ) {
        // #todo: add hierarchy support
        geometry.updateMatrix();
        this.matrix = geometry.matrix.clone();
        geometry = geometry.geometry;
      } else if ( geometry instanceof ThreeBSP.Node ) {
        this.tree = geometry;
        this.matrix = new THREE.Matrix4;
        return this;
      } else {
        throw 'ThreeBSP: Given geometry is unsupported';
      }
    
      for ( i = 0, _length_i = geometry.faces.length; i < _length_i; i++ ) {
        face = geometry.faces[i];
        faceVertexUvs = geometry.faceVertexUvs[0][i];
        polygon = new ThreeBSP.Polygon;
        
        if ( face instanceof THREE.Face3 ) {
          vertex = geometry.vertices[ face.a ];
                                  uvs = faceVertexUvs ? new THREE.Vector2( faceVertexUvs[0].x, faceVertexUvs[0].y ) : null;
                                  vertex = new ThreeBSP.Vertex( vertex.x, vertex.y, vertex.z, face.vertexNormals[0], uvs );
          vertex.applyMatrix4(this.matrix);
          polygon.vertices.push( vertex );
          
          vertex = geometry.vertices[ face.b ];
                                  uvs = faceVertexUvs ? new THREE.Vector2( faceVertexUvs[1].x, faceVertexUvs[1].y ) : null;
                                  vertex = new ThreeBSP.Vertex( vertex.x, vertex.y, vertex.z, face.vertexNormals[2], uvs );
          vertex.applyMatrix4(this.matrix);
          polygon.vertices.push( vertex );
          
          vertex = geometry.vertices[ face.c ];
                                  uvs = faceVertexUvs ? new THREE.Vector2( faceVertexUvs[2].x, faceVertexUvs[2].y ) : null;
                                  vertex = new ThreeBSP.Vertex( vertex.x, vertex.y, vertex.z, face.vertexNormals[2], uvs );
          vertex.applyMatrix4(this.matrix);
          polygon.vertices.push( vertex );
        } else if ( typeof THREE.Face4 ) {
          vertex = geometry.vertices[ face.a ];
                                  uvs = faceVertexUvs ? new THREE.Vector2( faceVertexUvs[0].x, faceVertexUvs[0].y ) : null;
                                  vertex = new ThreeBSP.Vertex( vertex.x, vertex.y, vertex.z, face.vertexNormals[0], uvs );
          vertex.applyMatrix4(this.matrix);
          polygon.vertices.push( vertex );
          
          vertex = geometry.vertices[ face.b ];
                                  uvs = faceVertexUvs ? new THREE.Vector2( faceVertexUvs[1].x, faceVertexUvs[1].y ) : null;
                                  vertex = new ThreeBSP.Vertex( vertex.x, vertex.y, vertex.z, face.vertexNormals[1], uvs );
          vertex.applyMatrix4(this.matrix);
          polygon.vertices.push( vertex );
          
          vertex = geometry.vertices[ face.c ];
                                  uvs = faceVertexUvs ? new THREE.Vector2( faceVertexUvs[2].x, faceVertexUvs[2].y ) : null;
                                  vertex = new ThreeBSP.Vertex( vertex.x, vertex.y, vertex.z, face.vertexNormals[2], uvs );
          vertex.applyMatrix4(this.matrix);
          polygon.vertices.push( vertex );
          
          vertex = geometry.vertices[ face.d ];
                                  uvs = faceVertexUvs ? new THREE.Vector2( faceVertexUvs[3].x, faceVertexUvs[3].y ) : null;
                                  vertex = new ThreeBSP.Vertex( vertex.x, vertex.y, vertex.z, face.vertexNormals[3], uvs );
          vertex.applyMatrix4(this.matrix);
          polygon.vertices.push( vertex );
        } else {
          throw 'Invalid face type at index ' + i;
        }
        
        polygon.calculateProperties();
        polygons.push( polygon );
      };
    
      this.tree = new ThreeBSP.Node( polygons );
    };
    ThreeBSP.prototype.subtract = function( other_tree ) {
      var a = this.tree.clone(),
        b = other_tree.tree.clone();
      
      a.invert();
      a.clipTo( b );
      b.clipTo( a );
      b.invert();
      b.clipTo( a );
      b.invert();
      a.build( b.allPolygons() );
      a.invert();
      a = new ThreeBSP( a );
      a.matrix = this.matrix;
      return a;
    };
    ThreeBSP.prototype.union = function( other_tree ) {
      var a = this.tree.clone(),
        b = other_tree.tree.clone();
      
      a.clipTo( b );
      b.clipTo( a );
      b.invert();
      b.clipTo( a );
      b.invert();
      a.build( b.allPolygons() );
      a = new ThreeBSP( a );
      a.matrix = this.matrix;
      return a;
    };
    ThreeBSP.prototype.intersect = function( other_tree ) {
      var a = this.tree.clone(),
        b = other_tree.tree.clone();
      
      a.invert();
      b.clipTo( a );
      b.invert();
      a.clipTo( b );
      b.clipTo( a );
      a.build( b.allPolygons() );
      a.invert();
      a = new ThreeBSP( a );
      a.matrix = this.matrix;
      return a;
    };
    ThreeBSP.prototype.toGeometry = function() {
      var i, j,
        matrix = new THREE.Matrix4().getInverse( this.matrix ),
        geometry = new THREE.Geometry(),
        polygons = this.tree.allPolygons(),
        polygon_count = polygons.length,
        polygon, polygon_vertice_count,
        vertice_dict = {},
        vertex_idx_a, vertex_idx_b, vertex_idx_c,
        vertex, face,
        verticeUvs;
    
      for ( i = 0; i < polygon_count; i++ ) {
        polygon = polygons[i];
        polygon_vertice_count = polygon.vertices.length;
        
        for ( j = 2; j < polygon_vertice_count; j++ ) {
          verticeUvs = [];
          
          vertex = polygon.vertices[0];
          verticeUvs.push( new THREE.Vector2( vertex.uv.x, vertex.uv.y ) );
          vertex = new THREE.Vector3( vertex.x, vertex.y, vertex.z );
          vertex.applyMatrix4(matrix);
          
          if ( typeof vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ] !== 'undefined' ) {
            vertex_idx_a = vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ];
          } else {
            geometry.vertices.push( vertex );
            vertex_idx_a = vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ] = geometry.vertices.length - 1;
          }
          
          vertex = polygon.vertices[j-1];
          verticeUvs.push( new THREE.Vector2( vertex.uv.x, vertex.uv.y ) );
          vertex = new THREE.Vector3( vertex.x, vertex.y, vertex.z );
          vertex.applyMatrix4(matrix);
          if ( typeof vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ] !== 'undefined' ) {
            vertex_idx_b = vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ];
          } else {
            geometry.vertices.push( vertex );
            vertex_idx_b = vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ] = geometry.vertices.length - 1;
          }
          
          vertex = polygon.vertices[j];
          verticeUvs.push( new THREE.Vector2( vertex.uv.x, vertex.uv.y ) );
          vertex = new THREE.Vector3( vertex.x, vertex.y, vertex.z );
          vertex.applyMatrix4(matrix);
          if ( typeof vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ] !== 'undefined' ) {
            vertex_idx_c = vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ];
          } else {
            geometry.vertices.push( vertex );
            vertex_idx_c = vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ] = geometry.vertices.length - 1;
          }
          
          face = new THREE.Face3(
            vertex_idx_a,
            vertex_idx_b,
            vertex_idx_c,
            new THREE.Vector3( polygon.normal.x, polygon.normal.y, polygon.normal.z )
          );
          
          geometry.faces.push( face );
          geometry.faceVertexUvs[0].push( verticeUvs );
        }
        
      }
      return geometry;
    };
    ThreeBSP.prototype.toMesh = function( material ) {
      var geometry = this.toGeometry(),
        mesh = new THREE.Mesh( geometry, material );
      
      mesh.position.setFromMatrixPosition( this.matrix );
      mesh.rotation.setFromRotationMatrix( this.matrix );
      
      return mesh;
    };
    
    
    ThreeBSP.Polygon = function( vertices, normal, w ) {
      if ( !( vertices instanceof Array ) ) {
        vertices = [];
      }
      
      this.vertices = vertices;
      if ( vertices.length > 0 ) {
        this.calculateProperties();
      } else {
        this.normal = this.w = undefined;
      }
    };
    ThreeBSP.Polygon.prototype.calculateProperties = function() {
      var a = this.vertices[0],
        b = this.vertices[1],
        c = this.vertices[2];
        
      this.normal = b.clone().subtract( a ).cross(
        c.clone().subtract( a )
      ).normalize();
      
      this.w = this.normal.clone().dot( a );
      
      return this;
    };
    ThreeBSP.Polygon.prototype.clone = function() {
      var i, vertice_count,
        polygon = new ThreeBSP.Polygon;
      
      for ( i = 0, vertice_count = this.vertices.length; i < vertice_count; i++ ) {
        polygon.vertices.push( this.vertices[i].clone() );
      };
      polygon.calculateProperties();
      
      return polygon;
    };
    
    ThreeBSP.Polygon.prototype.flip = function() {
      var i, vertices = [];
      
      this.normal.multiplyScalar( -1 );
      this.w *= -1;
      
      for ( i = this.vertices.length - 1; i >= 0; i-- ) {
        vertices.push( this.vertices[i] );
      };
      this.vertices = vertices;
      
      return this;
    };
    ThreeBSP.Polygon.prototype.classifyVertex = function( vertex ) {  
      var side_value = this.normal.dot( vertex ) - this.w;
      
      if ( side_value < -EPSILON ) {
        return BACK;
      } else if ( side_value > EPSILON ) {
        return FRONT;
      } else {
        return COPLANAR;
      }
    };
    ThreeBSP.Polygon.prototype.classifySide = function( polygon ) {
      var i, vertex, classification,
        num_positive = 0,
        num_negative = 0,
        vertice_count = polygon.vertices.length;
      
      for ( i = 0; i < vertice_count; i++ ) {
        vertex = polygon.vertices[i];
        classification = this.classifyVertex( vertex );
        if ( classification === FRONT ) {
          num_positive++;
        } else if ( classification === BACK ) {
          num_negative++;
        }
      }
      
      if ( num_positive > 0 && num_negative === 0 ) {
        return FRONT;
      } else if ( num_positive === 0 && num_negative > 0 ) {
        return BACK;
      } else if ( num_positive === 0 && num_negative === 0 ) {
        return COPLANAR;
      } else {
        return SPANNING;
      }
    };
    ThreeBSP.Polygon.prototype.splitPolygon = function( polygon, coplanar_front, coplanar_back, front, back ) {
      var classification = this.classifySide( polygon );
      
      if ( classification === COPLANAR ) {
        
        ( this.normal.dot( polygon.normal ) > 0 ? coplanar_front : coplanar_back ).push( polygon );
        
      } else if ( classification === FRONT ) {
        
        front.push( polygon );
        
      } else if ( classification === BACK ) {
        
        back.push( polygon );
        
      } else {
        
        var vertice_count,
          i, j, ti, tj, vi, vj,
          t, v,
          f = [],
          b = [];
        
        for ( i = 0, vertice_count = polygon.vertices.length; i < vertice_count; i++ ) {
          
          j = (i + 1) % vertice_count;
          vi = polygon.vertices[i];
          vj = polygon.vertices[j];
          ti = this.classifyVertex( vi );
          tj = this.classifyVertex( vj );
          
          if ( ti != BACK ) f.push( vi );
          if ( ti != FRONT ) b.push( vi );
          if ( (ti | tj) === SPANNING ) {
            t = ( this.w - this.normal.dot( vi ) ) / this.normal.dot( vj.clone().subtract( vi ) );
            v = vi.interpolate( vj, t );
            f.push( v );
            b.push( v );
          }
        }
        
        
        if ( f.length >= 3 ) front.push( new ThreeBSP.Polygon( f ).calculateProperties() );
        if ( b.length >= 3 ) back.push( new ThreeBSP.Polygon( b ).calculateProperties() );
      }
    };
    
    ThreeBSP.Vertex = function( x, y, z, normal, uv ) {
      this.x = x;
      this.y = y;
      this.z = z;
      this.normal = normal || new THREE.Vector3;
      this.uv = uv || new THREE.Vector2;
    };
    ThreeBSP.Vertex.prototype.clone = function() {
      return new ThreeBSP.Vertex( this.x, this.y, this.z, this.normal.clone(), this.uv.clone() );
    };
    ThreeBSP.Vertex.prototype.add = function( vertex ) {
      this.x += vertex.x;
      this.y += vertex.y;
      this.z += vertex.z;
      return this;
    };
    ThreeBSP.Vertex.prototype.subtract = function( vertex ) {
      this.x -= vertex.x;
      this.y -= vertex.y;
      this.z -= vertex.z;
      return this;
    };
    ThreeBSP.Vertex.prototype.multiplyScalar = function( scalar ) {
      this.x *= scalar;
      this.y *= scalar;
      this.z *= scalar;
      return this;
    };
    ThreeBSP.Vertex.prototype.cross = function( vertex ) {
      var x = this.x,
        y = this.y,
        z = this.z;

      this.x = y * vertex.z - z * vertex.y;
      this.y = z * vertex.x - x * vertex.z;
      this.z = x * vertex.y - y * vertex.x;
      
      return this;
    };
    ThreeBSP.Vertex.prototype.normalize = function() {
      var length = Math.sqrt( this.x * this.x + this.y * this.y + this.z * this.z );
      
      this.x /= length;
      this.y /= length;
      this.z /= length;
      
      return this;
    };
    ThreeBSP.Vertex.prototype.dot = function( vertex ) {
      return this.x * vertex.x + this.y * vertex.y + this.z * vertex.z;
    };
    ThreeBSP.Vertex.prototype.lerp = function( a, t ) {
      this.add(
        a.clone().subtract( this ).multiplyScalar( t )
      );
      
      this.normal.add(
        a.normal.clone().sub( this.normal ).multiplyScalar( t )
      );
      
      this.uv.add(
        a.uv.clone().sub( this.uv ).multiplyScalar( t )
      );
      
      return this;
    };
    ThreeBSP.Vertex.prototype.interpolate = function( other, t ) {
      return this.clone().lerp( other, t );
    };
    ThreeBSP.Vertex.prototype.applyMatrix4 = function ( m ) {

      // input: THREE.Matrix4 affine matrix

      var x = this.x, y = this.y, z = this.z;

      var e = m.elements;

      this.x = e[0] * x + e[4] * y + e[8]  * z + e[12];
      this.y = e[1] * x + e[5] * y + e[9]  * z + e[13];
      this.z = e[2] * x + e[6] * y + e[10] * z + e[14];

      return this;

    }
    
    
    ThreeBSP.Node = function( polygons ) {
      var i, polygon_count,
        front = [],
        back = [];

      this.polygons = [];
      this.front = this.back = undefined;
      
      if ( !(polygons instanceof Array) || polygons.length === 0 ) return;

      this.divider = polygons[0].clone();
      
      for ( i = 0, polygon_count = polygons.length; i < polygon_count; i++ ) {
        this.divider.splitPolygon( polygons[i], this.polygons, this.polygons, front, back );
      }   
      
      if ( front.length > 0 ) {
        this.front = new ThreeBSP.Node( front );
      }
      
      if ( back.length > 0 ) {
        this.back = new ThreeBSP.Node( back );
      }
    };
    ThreeBSP.Node.isConvex = function( polygons ) {
      var i, j;
      for ( i = 0; i < polygons.length; i++ ) {
        for ( j = 0; j < polygons.length; j++ ) {
          if ( i !== j && polygons[i].classifySide( polygons[j] ) !== BACK ) {
            return false;
          }
        }
      }
      return true;
    };
    ThreeBSP.Node.prototype.build = function( polygons ) {
      var i, polygon_count,
        front = [],
        back = [];
      
      if ( !this.divider ) {
        this.divider = polygons[0].clone();
      }

      for ( i = 0, polygon_count = polygons.length; i < polygon_count; i++ ) {
        this.divider.splitPolygon( polygons[i], this.polygons, this.polygons, front, back );
      }   
      
      if ( front.length > 0 ) {
        if ( !this.front ) this.front = new ThreeBSP.Node();
        this.front.build( front );
      }
      
      if ( back.length > 0 ) {
        if ( !this.back ) this.back = new ThreeBSP.Node();
        this.back.build( back );
      }
    };
    ThreeBSP.Node.prototype.allPolygons = function() {
      var polygons = this.polygons.slice();
      if ( this.front ) polygons = polygons.concat( this.front.allPolygons() );
      if ( this.back ) polygons = polygons.concat( this.back.allPolygons() );
      return polygons;
    };
    ThreeBSP.Node.prototype.clone = function() {
      var node = new ThreeBSP.Node();
      
      node.divider = this.divider.clone();
      node.polygons = this.polygons.map( function( polygon ) { return polygon.clone(); } );
      node.front = this.front && this.front.clone();
      node.back = this.back && this.back.clone();
      
      return node;
    };
    ThreeBSP.Node.prototype.invert = function() {
      var i, polygon_count, temp;
      
      for ( i = 0, polygon_count = this.polygons.length; i < polygon_count; i++ ) {
        this.polygons[i].flip();
      }
      
      this.divider.flip();
      if ( this.front ) this.front.invert();
      if ( this.back ) this.back.invert();
      
      temp = this.front;
      this.front = this.back;
      this.back = temp;
      
      return this;
    };
    ThreeBSP.Node.prototype.clipPolygons = function( polygons ) {
      var i, polygon_count,
        front, back;

      if ( !this.divider ) return polygons.slice();
      
      front = [], back = [];
      
      for ( i = 0, polygon_count = polygons.length; i < polygon_count; i++ ) {
        this.divider.splitPolygon( polygons[i], front, back, front, back );
      }

      if ( this.front ) front = this.front.clipPolygons( front );
      if ( this.back ) back = this.back.clipPolygons( back );
      else back = [];

      return front.concat( back );
    };
    
    ThreeBSP.Node.prototype.clipTo = function( node ) {
      this.polygons = node.clipPolygons( this.polygons );
      if ( this.front ) this.front.clipTo( node );
      if ( this.back ) this.back.clipTo( node );
    };
    
    
    return ThreeBSP;
  }