/** * @author mrdoob / http://mrdoob.com/ * @author *kile / http://kile.stravaganza.org/ * @author philogb / http://blog.thejit.org/ * @author mikael emtinger / http://gomo.se/ * @author egraether / http://egraether.com/ * @author WestLangley / http://github.com/WestLangley */ THREE.Vector3 = function ( x, y, z ) { this.x = x || 0; this.y = y || 0; this.z = z || 0; }; THREE.Vector3.prototype = { constructor: THREE.Vector3, set: function ( x, y, z ) { this.x = x; this.y = y; this.z = z; return this; }, setX: function ( x ) { this.x = x; return this; }, setY: function ( y ) { this.y = y; return this; }, setZ: function ( z ) { this.z = z; return this; }, copy: function ( v ) { this.x = v.x; this.y = v.y; this.z = v.z; return this; }, add: function ( a, b ) { this.x = a.x + b.x; this.y = a.y + b.y; this.z = a.z + b.z; return this; }, addSelf: function ( v ) { this.x += v.x; this.y += v.y; this.z += v.z; return this; }, addScalar: function ( s ) { this.x += s; this.y += s; this.z += s; return this; }, sub: function ( a, b ) { this.x = a.x - b.x; this.y = a.y - b.y; this.z = a.z - b.z; return this; }, subSelf: function ( v ) { this.x -= v.x; this.y -= v.y; this.z -= v.z; return this; }, multiply: function ( a, b ) { this.x = a.x * b.x; this.y = a.y * b.y; this.z = a.z * b.z; return this; }, multiplySelf: function ( v ) { this.x *= v.x; this.y *= v.y; this.z *= v.z; return this; }, multiplyScalar: function ( s ) { this.x *= s; this.y *= s; this.z *= s; return this; }, divideSelf: function ( v ) { this.x /= v.x; this.y /= v.y; this.z /= v.z; return this; }, divideScalar: function ( s ) { if ( s ) { this.x /= s; this.y /= s; this.z /= s; } else { this.x = 0; this.y = 0; this.z = 0; } return this; }, minSelf: function ( v ) { if ( this.x > v.x ) { this.x = v.x; } if ( this.y > v.y ) { this.y = v.y; } if ( this.z > v.z ) { this.z = v.z; } return this; }, maxSelf: function ( v ) { if ( this.x < v.x ) { this.x = v.x; } if ( this.y < v.y ) { this.y = v.y; } if ( this.z < v.z ) { this.z = v.z; } return this; }, clampSelf: function ( min, max ) { // This function assumes min < max, if this assumption isn't true it will not operate correctly if ( this.x < min.x ) { this.x = min.x; } else if ( this.x > max.x ) { this.x = max.x; } if ( this.y < min.y ) { this.y = min.y; } else if ( this.y > max.y ) { this.y = max.y; } if ( this.z < min.z ) { this.z = min.z; } else if ( this.z > max.z ) { this.z = max.z; } return this; }, negate: function() { return this.multiplyScalar( - 1 ); }, dot: function ( v ) { return this.x * v.x + this.y * v.y + this.z * v.z; }, lengthSq: function () { return this.x * this.x + this.y * this.y + this.z * this.z; }, length: function () { return Math.sqrt( this.lengthSq() ); }, lengthManhattan: function () { return Math.abs( this.x ) + Math.abs( this.y ) + Math.abs( this.z ); }, normalize: function () { return this.divideScalar( this.length() ); }, setLength: function ( l ) { return this.normalize().multiplyScalar( l ); }, lerpSelf: function ( v, alpha ) { this.x += ( v.x - this.x ) * alpha; this.y += ( v.y - this.y ) * alpha; this.z += ( v.z - this.z ) * alpha; return this; }, cross: function ( a, b ) { this.x = a.y * b.z - a.z * b.y; this.y = a.z * b.x - a.x * b.z; this.z = a.x * b.y - a.y * b.x; return this; }, crossSelf: function ( v ) { var x = this.x, y = this.y, z = this.z; this.x = y * v.z - z * v.y; this.y = z * v.x - x * v.z; this.z = x * v.y - y * v.x; return this; }, angleTo: function ( v ) { return Math.acos( this.dot( v ) / this.length() / v.length() ); }, distanceTo: function ( v ) { return Math.sqrt( this.distanceToSquared( v ) ); }, distanceToSquared: function ( v ) { var dx = this.x - v.x; var dy = this.y - v.y; var dz = this.z - v.z; return dx * dx + dy * dy + dz * dz; }, getPositionFromMatrix: function ( m ) { this.x = m.elements[12]; this.y = m.elements[13]; this.z = m.elements[14]; return this; }, setEulerFromRotationMatrix: function ( m, order ) { // assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled) // clamp, to handle numerical problems function clamp( x ) { return Math.min( Math.max( x, -1 ), 1 ); } var te = m.elements; var m11 = te[0], m12 = te[4], m13 = te[8]; var m21 = te[1], m22 = te[5], m23 = te[9]; var m31 = te[2], m32 = te[6], m33 = te[10]; if ( order === undefined || order === 'XYZ' ) { this.y = Math.asin( clamp( m13 ) ); if ( Math.abs( m13 ) < 0.99999 ) { this.x = Math.atan2( - m23, m33 ); this.z = Math.atan2( - m12, m11 ); } else { this.x = Math.atan2( m32, m22 ); this.z = 0; } } else if ( order === 'YXZ' ) { this.x = Math.asin( - clamp( m23 ) ); if ( Math.abs( m23 ) < 0.99999 ) { this.y = Math.atan2( m13, m33 ); this.z = Math.atan2( m21, m22 ); } else { this.y = Math.atan2( - m31, m11 ); this.z = 0; } } else if ( order === 'ZXY' ) { this.x = Math.asin( clamp( m32 ) ); if ( Math.abs( m32 ) < 0.99999 ) { this.y = Math.atan2( - m31, m33 ); this.z = Math.atan2( - m12, m22 ); } else { this.y = 0; this.z = Math.atan2( m21, m11 ); } } else if ( order === 'ZYX' ) { this.y = Math.asin( - clamp( m31 ) ); if ( Math.abs( m31 ) < 0.99999 ) { this.x = Math.atan2( m32, m33 ); this.z = Math.atan2( m21, m11 ); } else { this.x = 0; this.z = Math.atan2( - m12, m22 ); } } else if ( order === 'YZX' ) { this.z = Math.asin( clamp( m21 ) ); if ( Math.abs( m21 ) < 0.99999 ) { this.x = Math.atan2( - m23, m22 ); this.y = Math.atan2( - m31, m11 ); } else { this.x = 0; this.y = Math.atan2( m13, m33 ); } } else if ( order === 'XZY' ) { this.z = Math.asin( - clamp( m12 ) ); if ( Math.abs( m12 ) < 0.99999 ) { this.x = Math.atan2( m32, m22 ); this.y = Math.atan2( m13, m11 ); } else { this.x = Math.atan2( - m23, m33 ); this.y = 0; } } return this; }, setEulerFromQuaternion: function ( q, order ) { // q is assumed to be normalized // clamp, to handle numerical problems function clamp( x ) { return Math.min( Math.max( x, -1 ), 1 ); } // http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm-euler-angles-quaternions-and-euler-vectors/content/SpinCalc.m var sqx = q.x * q.x; var sqy = q.y * q.y; var sqz = q.z * q.z; var sqw = q.w * q.w; if ( order === undefined || order === 'XYZ' ) { this.x = Math.atan2( 2 * ( q.x * q.w - q.y * q.z ), ( sqw - sqx - sqy + sqz ) ); this.y = Math.asin( clamp( 2 * ( q.x * q.z + q.y * q.w ) ) ); this.z = Math.atan2( 2 * ( q.z * q.w - q.x * q.y ), ( sqw + sqx - sqy - sqz ) ); } else if ( order === 'YXZ' ) { this.x = Math.asin( clamp( 2 * ( q.x * q.w - q.y * q.z ) ) ); this.y = Math.atan2( 2 * ( q.x * q.z + q.y * q.w ), ( sqw - sqx - sqy + sqz ) ); this.z = Math.atan2( 2 * ( q.x * q.y + q.z * q.w ), ( sqw - sqx + sqy - sqz ) ); } else if ( order === 'ZXY' ) { this.x = Math.asin( clamp( 2 * ( q.x * q.w + q.y * q.z ) ) ); this.y = Math.atan2( 2 * ( q.y * q.w - q.z * q.x ), ( sqw - sqx - sqy + sqz ) ); this.z = Math.atan2( 2 * ( q.z * q.w - q.x * q.y ), ( sqw - sqx + sqy - sqz ) ); } else if ( order === 'ZYX' ) { this.x = Math.atan2( 2 * ( q.x * q.w + q.z * q.y ), ( sqw - sqx - sqy + sqz ) ); this.y = Math.asin( clamp( 2 * ( q.y * q.w - q.x * q.z ) ) ); this.z = Math.atan2( 2 * ( q.x * q.y + q.z * q.w ), ( sqw + sqx - sqy - sqz ) ); } else if ( order === 'YZX' ) { this.x = Math.atan2( 2 * ( q.x * q.w - q.z * q.y ), ( sqw - sqx + sqy - sqz ) ); this.y = Math.atan2( 2 * ( q.y * q.w - q.x * q.z ), ( sqw + sqx - sqy - sqz ) ); this.z = Math.asin( clamp( 2 * ( q.x * q.y + q.z * q.w ) ) ); } else if ( order === 'XZY' ) { this.x = Math.atan2( 2 * ( q.x * q.w + q.y * q.z ), ( sqw - sqx + sqy - sqz ) ); this.y = Math.atan2( 2 * ( q.x * q.z + q.y * q.w ), ( sqw + sqx - sqy - sqz ) ); this.z = Math.asin( clamp( 2 * ( q.z * q.w - q.x * q.y ) ) ); } return this; }, getScaleFromMatrix: function ( m ) { var sx = this.set( m.elements[0], m.elements[1], m.elements[2] ).length(); var sy = this.set( m.elements[4], m.elements[5], m.elements[6] ).length(); var sz = this.set( m.elements[8], m.elements[9], m.elements[10] ).length(); this.x = sx; this.y = sy; this.z = sz; return this; }, equals: function ( v ) { return ( ( v.x === this.x ) && ( v.y === this.y ) && ( v.z === this.z ) ); }, clone: function () { return new THREE.Vector3( this.x, this.y, this.z ); } };