// File:src/Three.js /** * @author mrdoob / http://mrdoob.com/ */ var THREE = { REVISION: '69dev' }; // browserify support if ( typeof module === 'object' ) { module.exports = THREE; } // GL STATE CONSTANTS THREE.CullFaceNone = 0; THREE.CullFaceBack = 1; THREE.CullFaceFront = 2; THREE.CullFaceFrontBack = 3; THREE.FrontFaceDirectionCW = 0; THREE.FrontFaceDirectionCCW = 1; // SHADOWING TYPES THREE.BasicShadowMap = 0; THREE.PCFShadowMap = 1; THREE.PCFSoftShadowMap = 2; // MATERIAL CONSTANTS // side THREE.FrontSide = 0; THREE.BackSide = 1; THREE.DoubleSide = 2; // shading THREE.NoShading = 0; THREE.FlatShading = 1; THREE.SmoothShading = 2; // colors THREE.NoColors = 0; THREE.FaceColors = 1; THREE.VertexColors = 2; // blending modes THREE.NoBlending = 0; THREE.NormalBlending = 1; THREE.AdditiveBlending = 2; THREE.SubtractiveBlending = 3; THREE.MultiplyBlending = 4; THREE.CustomBlending = 5; // custom blending equations // (numbers start from 100 not to clash with other // mappings to OpenGL constants defined in Texture.js) THREE.AddEquation = 100; THREE.SubtractEquation = 101; THREE.ReverseSubtractEquation = 102; // custom blending destination factors THREE.ZeroFactor = 200; THREE.OneFactor = 201; THREE.SrcColorFactor = 202; THREE.OneMinusSrcColorFactor = 203; THREE.SrcAlphaFactor = 204; THREE.OneMinusSrcAlphaFactor = 205; THREE.DstAlphaFactor = 206; THREE.OneMinusDstAlphaFactor = 207; // custom blending source factors //THREE.ZeroFactor = 200; //THREE.OneFactor = 201; //THREE.SrcAlphaFactor = 204; //THREE.OneMinusSrcAlphaFactor = 205; //THREE.DstAlphaFactor = 206; //THREE.OneMinusDstAlphaFactor = 207; THREE.DstColorFactor = 208; THREE.OneMinusDstColorFactor = 209; THREE.SrcAlphaSaturateFactor = 210; // TEXTURE CONSTANTS THREE.MultiplyOperation = 0; THREE.MixOperation = 1; THREE.AddOperation = 2; // Mapping modes THREE.UVMapping = function () {}; THREE.CubeReflectionMapping = function () {}; THREE.CubeRefractionMapping = function () {}; THREE.SphericalReflectionMapping = function () {}; THREE.SphericalRefractionMapping = function () {}; // Wrapping modes THREE.RepeatWrapping = 1000; THREE.ClampToEdgeWrapping = 1001; THREE.MirroredRepeatWrapping = 1002; // Filters THREE.NearestFilter = 1003; THREE.NearestMipMapNearestFilter = 1004; THREE.NearestMipMapLinearFilter = 1005; THREE.LinearFilter = 1006; THREE.LinearMipMapNearestFilter = 1007; THREE.LinearMipMapLinearFilter = 1008; // Data types THREE.UnsignedByteType = 1009; THREE.ByteType = 1010; THREE.ShortType = 1011; THREE.UnsignedShortType = 1012; THREE.IntType = 1013; THREE.UnsignedIntType = 1014; THREE.FloatType = 1015; // Pixel types //THREE.UnsignedByteType = 1009; THREE.UnsignedShort4444Type = 1016; THREE.UnsignedShort5551Type = 1017; THREE.UnsignedShort565Type = 1018; // Pixel formats THREE.AlphaFormat = 1019; THREE.RGBFormat = 1020; THREE.RGBAFormat = 1021; THREE.LuminanceFormat = 1022; THREE.LuminanceAlphaFormat = 1023; // Compressed texture formats THREE.RGB_S3TC_DXT1_Format = 2001; THREE.RGBA_S3TC_DXT1_Format = 2002; THREE.RGBA_S3TC_DXT3_Format = 2003; THREE.RGBA_S3TC_DXT5_Format = 2004; /* // Potential future PVRTC compressed texture formats THREE.RGB_PVRTC_4BPPV1_Format = 2100; THREE.RGB_PVRTC_2BPPV1_Format = 2101; THREE.RGBA_PVRTC_4BPPV1_Format = 2102; THREE.RGBA_PVRTC_2BPPV1_Format = 2103; */ // File:src/math/Color.js /** * @author mrdoob / http://mrdoob.com/ */ THREE.Color = function ( color ) { if ( arguments.length === 3 ) { return this.setRGB( arguments[ 0 ], arguments[ 1 ], arguments[ 2 ] ); } return this.set( color ) }; THREE.Color.prototype = { constructor: THREE.Color, r: 1, g: 1, b: 1, set: function ( value ) { if ( value instanceof THREE.Color ) { this.copy( value ); } else if ( typeof value === 'number' ) { this.setHex( value ); } else if ( typeof value === 'string' ) { this.setStyle( value ); } return this; }, setHex: function ( hex ) { hex = Math.floor( hex ); this.r = ( hex >> 16 & 255 ) / 255; this.g = ( hex >> 8 & 255 ) / 255; this.b = ( hex & 255 ) / 255; return this; }, setRGB: function ( r, g, b ) { this.r = r; this.g = g; this.b = b; return this; }, setHSL: function ( h, s, l ) { // h,s,l ranges are in 0.0 - 1.0 if ( s === 0 ) { this.r = this.g = this.b = l; } else { var hue2rgb = function ( p, q, t ) { if ( t < 0 ) t += 1; if ( t > 1 ) t -= 1; if ( t < 1 / 6 ) return p + ( q - p ) * 6 * t; if ( t < 1 / 2 ) return q; if ( t < 2 / 3 ) return p + ( q - p ) * 6 * ( 2 / 3 - t ); return p; }; var p = l <= 0.5 ? l * ( 1 + s ) : l + s - ( l * s ); var q = ( 2 * l ) - p; this.r = hue2rgb( q, p, h + 1 / 3 ); this.g = hue2rgb( q, p, h ); this.b = hue2rgb( q, p, h - 1 / 3 ); } return this; }, setStyle: function ( style ) { // rgb(255,0,0) if ( /^rgb\((\d+), ?(\d+), ?(\d+)\)$/i.test( style ) ) { var color = /^rgb\((\d+), ?(\d+), ?(\d+)\)$/i.exec( style ); this.r = Math.min( 255, parseInt( color[ 1 ], 10 ) ) / 255; this.g = Math.min( 255, parseInt( color[ 2 ], 10 ) ) / 255; this.b = Math.min( 255, parseInt( color[ 3 ], 10 ) ) / 255; return this; } // rgb(100%,0%,0%) if ( /^rgb\((\d+)\%, ?(\d+)\%, ?(\d+)\%\)$/i.test( style ) ) { var color = /^rgb\((\d+)\%, ?(\d+)\%, ?(\d+)\%\)$/i.exec( style ); this.r = Math.min( 100, parseInt( color[ 1 ], 10 ) ) / 100; this.g = Math.min( 100, parseInt( color[ 2 ], 10 ) ) / 100; this.b = Math.min( 100, parseInt( color[ 3 ], 10 ) ) / 100; return this; } // #ff0000 if ( /^\#([0-9a-f]{6})$/i.test( style ) ) { var color = /^\#([0-9a-f]{6})$/i.exec( style ); this.setHex( parseInt( color[ 1 ], 16 ) ); return this; } // #f00 if ( /^\#([0-9a-f])([0-9a-f])([0-9a-f])$/i.test( style ) ) { var color = /^\#([0-9a-f])([0-9a-f])([0-9a-f])$/i.exec( style ); this.setHex( parseInt( color[ 1 ] + color[ 1 ] + color[ 2 ] + color[ 2 ] + color[ 3 ] + color[ 3 ], 16 ) ); return this; } // red if ( /^(\w+)$/i.test( style ) ) { this.setHex( THREE.ColorKeywords[ style ] ); return this; } }, copy: function ( color ) { this.r = color.r; this.g = color.g; this.b = color.b; return this; }, copyGammaToLinear: function ( color ) { this.r = color.r * color.r; this.g = color.g * color.g; this.b = color.b * color.b; return this; }, copyLinearToGamma: function ( color ) { this.r = Math.sqrt( color.r ); this.g = Math.sqrt( color.g ); this.b = Math.sqrt( color.b ); return this; }, convertGammaToLinear: function () { var r = this.r, g = this.g, b = this.b; this.r = r * r; this.g = g * g; this.b = b * b; return this; }, convertLinearToGamma: function () { this.r = Math.sqrt( this.r ); this.g = Math.sqrt( this.g ); this.b = Math.sqrt( this.b ); return this; }, getHex: function () { return ( this.r * 255 ) << 16 ^ ( this.g * 255 ) << 8 ^ ( this.b * 255 ) << 0; }, getHexString: function () { return ( '000000' + this.getHex().toString( 16 ) ).slice( - 6 ); }, getHSL: function ( optionalTarget ) { // h,s,l ranges are in 0.0 - 1.0 var hsl = optionalTarget || { h: 0, s: 0, l: 0 }; var r = this.r, g = this.g, b = this.b; var max = Math.max( r, g, b ); var min = Math.min( r, g, b ); var hue, saturation; var lightness = ( min + max ) / 2.0; if ( min === max ) { hue = 0; saturation = 0; } else { var delta = max - min; saturation = lightness <= 0.5 ? delta / ( max + min ) : delta / ( 2 - max - min ); switch ( max ) { case r: hue = ( g - b ) / delta + ( g < b ? 6 : 0 ); break; case g: hue = ( b - r ) / delta + 2; break; case b: hue = ( r - g ) / delta + 4; break; } hue /= 6; } hsl.h = hue; hsl.s = saturation; hsl.l = lightness; return hsl; }, getStyle: function () { return 'rgb(' + ( ( this.r * 255 ) | 0 ) + ',' + ( ( this.g * 255 ) | 0 ) + ',' + ( ( this.b * 255 ) | 0 ) + ')'; }, offsetHSL: function ( h, s, l ) { var hsl = this.getHSL(); hsl.h += h; hsl.s += s; hsl.l += l; this.setHSL( hsl.h, hsl.s, hsl.l ); return this; }, add: function ( color ) { this.r += color.r; this.g += color.g; this.b += color.b; return this; }, addColors: function ( color1, color2 ) { this.r = color1.r + color2.r; this.g = color1.g + color2.g; this.b = color1.b + color2.b; return this; }, addScalar: function ( s ) { this.r += s; this.g += s; this.b += s; return this; }, multiply: function ( color ) { this.r *= color.r; this.g *= color.g; this.b *= color.b; return this; }, multiplyScalar: function ( s ) { this.r *= s; this.g *= s; this.b *= s; return this; }, lerp: function ( color, alpha ) { this.r += ( color.r - this.r ) * alpha; this.g += ( color.g - this.g ) * alpha; this.b += ( color.b - this.b ) * alpha; return this; }, equals: function ( c ) { return ( c.r === this.r ) && ( c.g === this.g ) && ( c.b === this.b ); }, fromArray: function ( array ) { this.r = array[ 0 ]; this.g = array[ 1 ]; this.b = array[ 2 ]; return this; }, toArray: function () { return [ this.r, this.g, this.b ]; }, clone: function () { return new THREE.Color().setRGB( this.r, this.g, this.b ); } }; THREE.ColorKeywords = { 'aliceblue': 0xF0F8FF, 'antiquewhite': 0xFAEBD7, 'aqua': 0x00FFFF, 'aquamarine': 0x7FFFD4, 'azure': 0xF0FFFF, 'beige': 0xF5F5DC, 'bisque': 0xFFE4C4, 'black': 0x000000, 'blanchedalmond': 0xFFEBCD, 'blue': 0x0000FF, 'blueviolet': 0x8A2BE2, 'brown': 0xA52A2A, 'burlywood': 0xDEB887, 'cadetblue': 0x5F9EA0, 'chartreuse': 0x7FFF00, 'chocolate': 0xD2691E, 'coral': 0xFF7F50, 'cornflowerblue': 0x6495ED, 'cornsilk': 0xFFF8DC, 'crimson': 0xDC143C, 'cyan': 0x00FFFF, 'darkblue': 0x00008B, 'darkcyan': 0x008B8B, 'darkgoldenrod': 0xB8860B, 'darkgray': 0xA9A9A9, 'darkgreen': 0x006400, 'darkgrey': 0xA9A9A9, 'darkkhaki': 0xBDB76B, 'darkmagenta': 0x8B008B, 'darkolivegreen': 0x556B2F, 'darkorange': 0xFF8C00, 'darkorchid': 0x9932CC, 'darkred': 0x8B0000, 'darksalmon': 0xE9967A, 'darkseagreen': 0x8FBC8F, 'darkslateblue': 0x483D8B, 'darkslategray': 0x2F4F4F, 'darkslategrey': 0x2F4F4F, 'darkturquoise': 0x00CED1, 'darkviolet': 0x9400D3, 'deeppink': 0xFF1493, 'deepskyblue': 0x00BFFF, 'dimgray': 0x696969, 'dimgrey': 0x696969, 'dodgerblue': 0x1E90FF, 'firebrick': 0xB22222, 'floralwhite': 0xFFFAF0, 'forestgreen': 0x228B22, 'fuchsia': 0xFF00FF, 'gainsboro': 0xDCDCDC, 'ghostwhite': 0xF8F8FF, 'gold': 0xFFD700, 'goldenrod': 0xDAA520, 'gray': 0x808080, 'green': 0x008000, 'greenyellow': 0xADFF2F, 'grey': 0x808080, 'honeydew': 0xF0FFF0, 'hotpink': 0xFF69B4, 'indianred': 0xCD5C5C, 'indigo': 0x4B0082, 'ivory': 0xFFFFF0, 'khaki': 0xF0E68C, 'lavender': 0xE6E6FA, 'lavenderblush': 0xFFF0F5, 'lawngreen': 0x7CFC00, 'lemonchiffon': 0xFFFACD, 'lightblue': 0xADD8E6, 'lightcoral': 0xF08080, 'lightcyan': 0xE0FFFF, 'lightgoldenrodyellow': 0xFAFAD2, 'lightgray': 0xD3D3D3, 'lightgreen': 0x90EE90, 'lightgrey': 0xD3D3D3, 'lightpink': 0xFFB6C1, 'lightsalmon': 0xFFA07A, 'lightseagreen': 0x20B2AA, 'lightskyblue': 0x87CEFA, 'lightslategray': 0x778899, 'lightslategrey': 0x778899, 'lightsteelblue': 0xB0C4DE, 'lightyellow': 0xFFFFE0, 'lime': 0x00FF00, 'limegreen': 0x32CD32, 'linen': 0xFAF0E6, 'magenta': 0xFF00FF, 'maroon': 0x800000, 'mediumaquamarine': 0x66CDAA, 'mediumblue': 0x0000CD, 'mediumorchid': 0xBA55D3, 'mediumpurple': 0x9370DB, 'mediumseagreen': 0x3CB371, 'mediumslateblue': 0x7B68EE, 'mediumspringgreen': 0x00FA9A, 'mediumturquoise': 0x48D1CC, 'mediumvioletred': 0xC71585, 'midnightblue': 0x191970, 'mintcream': 0xF5FFFA, 'mistyrose': 0xFFE4E1, 'moccasin': 0xFFE4B5, 'navajowhite': 0xFFDEAD, 'navy': 0x000080, 'oldlace': 0xFDF5E6, 'olive': 0x808000, 'olivedrab': 0x6B8E23, 'orange': 0xFFA500, 'orangered': 0xFF4500, 'orchid': 0xDA70D6, 'palegoldenrod': 0xEEE8AA, 'palegreen': 0x98FB98, 'paleturquoise': 0xAFEEEE, 'palevioletred': 0xDB7093, 'papayawhip': 0xFFEFD5, 'peachpuff': 0xFFDAB9, 'peru': 0xCD853F, 'pink': 0xFFC0CB, 'plum': 0xDDA0DD, 'powderblue': 0xB0E0E6, 'purple': 0x800080, 'red': 0xFF0000, 'rosybrown': 0xBC8F8F, 'royalblue': 0x4169E1, 'saddlebrown': 0x8B4513, 'salmon': 0xFA8072, 'sandybrown': 0xF4A460, 'seagreen': 0x2E8B57, 'seashell': 0xFFF5EE, 'sienna': 0xA0522D, 'silver': 0xC0C0C0, 'skyblue': 0x87CEEB, 'slateblue': 0x6A5ACD, 'slategray': 0x708090, 'slategrey': 0x708090, 'snow': 0xFFFAFA, 'springgreen': 0x00FF7F, 'steelblue': 0x4682B4, 'tan': 0xD2B48C, 'teal': 0x008080, 'thistle': 0xD8BFD8, 'tomato': 0xFF6347, 'turquoise': 0x40E0D0, 'violet': 0xEE82EE, 'wheat': 0xF5DEB3, 'white': 0xFFFFFF, 'whitesmoke': 0xF5F5F5, 'yellow': 0xFFFF00, 'yellowgreen': 0x9ACD32 }; // File:src/math/Quaternion.js /** * @author mikael emtinger / http://gomo.se/ * @author alteredq / http://alteredqualia.com/ * @author WestLangley / http://github.com/WestLangley * @author bhouston / http://exocortex.com */ THREE.Quaternion = function ( x, y, z, w ) { this._x = x || 0; this._y = y || 0; this._z = z || 0; this._w = ( w !== undefined ) ? w : 1; }; THREE.Quaternion.prototype = { constructor: THREE.Quaternion, _x: 0,_y: 0, _z: 0, _w: 0, get x () { return this._x; }, set x ( value ) { this._x = value; this.onChangeCallback(); }, get y () { return this._y; }, set y ( value ) { this._y = value; this.onChangeCallback(); }, get z () { return this._z; }, set z ( value ) { this._z = value; this.onChangeCallback(); }, get w () { return this._w; }, set w ( value ) { this._w = value; this.onChangeCallback(); }, set: function ( x, y, z, w ) { this._x = x; this._y = y; this._z = z; this._w = w; this.onChangeCallback(); return this; }, copy: function ( quaternion ) { this._x = quaternion.x; this._y = quaternion.y; this._z = quaternion.z; this._w = quaternion.w; this.onChangeCallback(); return this; }, setFromEuler: function ( euler, update ) { if ( euler instanceof THREE.Euler === false ) { throw new Error( 'THREE.Quaternion: .setFromEuler() now expects a Euler rotation rather than a Vector3 and order.' ); } // http://www.mathworks.com/matlabcentral/fileexchange/ // 20696-function-to-convert-between-dcm-euler-angles-quaternions-and-euler-vectors/ // content/SpinCalc.m var c1 = Math.cos( euler._x / 2 ); var c2 = Math.cos( euler._y / 2 ); var c3 = Math.cos( euler._z / 2 ); var s1 = Math.sin( euler._x / 2 ); var s2 = Math.sin( euler._y / 2 ); var s3 = Math.sin( euler._z / 2 ); if ( euler.order === 'XYZ' ) { this._x = s1 * c2 * c3 + c1 * s2 * s3; this._y = c1 * s2 * c3 - s1 * c2 * s3; this._z = c1 * c2 * s3 + s1 * s2 * c3; this._w = c1 * c2 * c3 - s1 * s2 * s3; } else if ( euler.order === 'YXZ' ) { this._x = s1 * c2 * c3 + c1 * s2 * s3; this._y = c1 * s2 * c3 - s1 * c2 * s3; this._z = c1 * c2 * s3 - s1 * s2 * c3; this._w = c1 * c2 * c3 + s1 * s2 * s3; } else if ( euler.order === 'ZXY' ) { this._x = s1 * c2 * c3 - c1 * s2 * s3; this._y = c1 * s2 * c3 + s1 * c2 * s3; this._z = c1 * c2 * s3 + s1 * s2 * c3; this._w = c1 * c2 * c3 - s1 * s2 * s3; } else if ( euler.order === 'ZYX' ) { this._x = s1 * c2 * c3 - c1 * s2 * s3; this._y = c1 * s2 * c3 + s1 * c2 * s3; this._z = c1 * c2 * s3 - s1 * s2 * c3; this._w = c1 * c2 * c3 + s1 * s2 * s3; } else if ( euler.order === 'YZX' ) { this._x = s1 * c2 * c3 + c1 * s2 * s3; this._y = c1 * s2 * c3 + s1 * c2 * s3; this._z = c1 * c2 * s3 - s1 * s2 * c3; this._w = c1 * c2 * c3 - s1 * s2 * s3; } else if ( euler.order === 'XZY' ) { this._x = s1 * c2 * c3 - c1 * s2 * s3; this._y = c1 * s2 * c3 - s1 * c2 * s3; this._z = c1 * c2 * s3 + s1 * s2 * c3; this._w = c1 * c2 * c3 + s1 * s2 * s3; } if ( update !== false ) this.onChangeCallback(); return this; }, setFromAxisAngle: function ( axis, angle ) { // http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/index.htm // assumes axis is normalized var halfAngle = angle / 2, s = Math.sin( halfAngle ); this._x = axis.x * s; this._y = axis.y * s; this._z = axis.z * s; this._w = Math.cos( halfAngle ); this.onChangeCallback(); return this; }, setFromRotationMatrix: function ( m ) { // http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm // assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled) var te = m.elements, m11 = te[ 0 ], m12 = te[ 4 ], m13 = te[ 8 ], m21 = te[ 1 ], m22 = te[ 5 ], m23 = te[ 9 ], m31 = te[ 2 ], m32 = te[ 6 ], m33 = te[ 10 ], trace = m11 + m22 + m33, s; if ( trace > 0 ) { s = 0.5 / Math.sqrt( trace + 1.0 ); this._w = 0.25 / s; this._x = ( m32 - m23 ) * s; this._y = ( m13 - m31 ) * s; this._z = ( m21 - m12 ) * s; } else if ( m11 > m22 && m11 > m33 ) { s = 2.0 * Math.sqrt( 1.0 + m11 - m22 - m33 ); this._w = ( m32 - m23 ) / s; this._x = 0.25 * s; this._y = ( m12 + m21 ) / s; this._z = ( m13 + m31 ) / s; } else if ( m22 > m33 ) { s = 2.0 * Math.sqrt( 1.0 + m22 - m11 - m33 ); this._w = ( m13 - m31 ) / s; this._x = ( m12 + m21 ) / s; this._y = 0.25 * s; this._z = ( m23 + m32 ) / s; } else { s = 2.0 * Math.sqrt( 1.0 + m33 - m11 - m22 ); this._w = ( m21 - m12 ) / s; this._x = ( m13 + m31 ) / s; this._y = ( m23 + m32 ) / s; this._z = 0.25 * s; } this.onChangeCallback(); return this; }, setFromUnitVectors: function () { // http://lolengine.net/blog/2014/02/24/quaternion-from-two-vectors-final // assumes direction vectors vFrom and vTo are normalized var v1, r; var EPS = 0.000001; return function ( vFrom, vTo ) { if ( v1 === undefined ) v1 = new THREE.Vector3(); r = vFrom.dot( vTo ) + 1; if ( r < EPS ) { r = 0; if ( Math.abs( vFrom.x ) > Math.abs( vFrom.z ) ) { v1.set( - vFrom.y, vFrom.x, 0 ); } else { v1.set( 0, - vFrom.z, vFrom.y ); } } else { v1.crossVectors( vFrom, vTo ); } this._x = v1.x; this._y = v1.y; this._z = v1.z; this._w = r; this.normalize(); return this; } }(), inverse: function () { this.conjugate().normalize(); return this; }, conjugate: function () { this._x *= - 1; this._y *= - 1; this._z *= - 1; this.onChangeCallback(); return this; }, dot: function ( v ) { return this._x * v._x + this._y * v._y + this._z * v._z + this._w * v._w; }, lengthSq: function () { return this._x * this._x + this._y * this._y + this._z * this._z + this._w * this._w; }, length: function () { return Math.sqrt( this._x * this._x + this._y * this._y + this._z * this._z + this._w * this._w ); }, normalize: function () { var l = this.length(); if ( l === 0 ) { this._x = 0; this._y = 0; this._z = 0; this._w = 1; } else { l = 1 / l; this._x = this._x * l; this._y = this._y * l; this._z = this._z * l; this._w = this._w * l; } this.onChangeCallback(); return this; }, multiply: function ( q, p ) { if ( p !== undefined ) { console.warn( 'THREE.Quaternion: .multiply() now only accepts one argument. Use .multiplyQuaternions( a, b ) instead.' ); return this.multiplyQuaternions( q, p ); } return this.multiplyQuaternions( this, q ); }, multiplyQuaternions: function ( a, b ) { // from http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/code/index.htm var qax = a._x, qay = a._y, qaz = a._z, qaw = a._w; var qbx = b._x, qby = b._y, qbz = b._z, qbw = b._w; this._x = qax * qbw + qaw * qbx + qay * qbz - qaz * qby; this._y = qay * qbw + qaw * qby + qaz * qbx - qax * qbz; this._z = qaz * qbw + qaw * qbz + qax * qby - qay * qbx; this._w = qaw * qbw - qax * qbx - qay * qby - qaz * qbz; this.onChangeCallback(); return this; }, multiplyVector3: function ( vector ) { console.warn( 'THREE.Quaternion: .multiplyVector3() has been removed. Use is now vector.applyQuaternion( quaternion ) instead.' ); return vector.applyQuaternion( this ); }, slerp: function ( qb, t ) { if ( t === 0 ) return this; if ( t === 1 ) return this.copy( qb ); var x = this._x, y = this._y, z = this._z, w = this._w; // http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/ var cosHalfTheta = w * qb._w + x * qb._x + y * qb._y + z * qb._z; if ( cosHalfTheta < 0 ) { this._w = - qb._w; this._x = - qb._x; this._y = - qb._y; this._z = - qb._z; cosHalfTheta = - cosHalfTheta; } else { this.copy( qb ); } if ( cosHalfTheta >= 1.0 ) { this._w = w; this._x = x; this._y = y; this._z = z; return this; } var halfTheta = Math.acos( cosHalfTheta ); var sinHalfTheta = Math.sqrt( 1.0 - cosHalfTheta * cosHalfTheta ); if ( Math.abs( sinHalfTheta ) < 0.001 ) { this._w = 0.5 * ( w + this._w ); this._x = 0.5 * ( x + this._x ); this._y = 0.5 * ( y + this._y ); this._z = 0.5 * ( z + this._z ); return this; } var ratioA = Math.sin( ( 1 - t ) * halfTheta ) / sinHalfTheta, ratioB = Math.sin( t * halfTheta ) / sinHalfTheta; this._w = ( w * ratioA + this._w * ratioB ); this._x = ( x * ratioA + this._x * ratioB ); this._y = ( y * ratioA + this._y * ratioB ); this._z = ( z * ratioA + this._z * ratioB ); this.onChangeCallback(); return this; }, equals: function ( quaternion ) { return ( quaternion._x === this._x ) && ( quaternion._y === this._y ) && ( quaternion._z === this._z ) && ( quaternion._w === this._w ); }, fromArray: function ( array ) { this._x = array[ 0 ]; this._y = array[ 1 ]; this._z = array[ 2 ]; this._w = array[ 3 ]; this.onChangeCallback(); return this; }, toArray: function () { return [ this._x, this._y, this._z, this._w ]; }, onChange: function ( callback ) { this.onChangeCallback = callback; return this; }, onChangeCallback: function () {}, clone: function () { return new THREE.Quaternion( this._x, this._y, this._z, this._w ); } }; THREE.Quaternion.slerp = function ( qa, qb, qm, t ) { return qm.copy( qa ).slerp( qb, t ); } // File:src/math/Vector2.js /** * @author mrdoob / http://mrdoob.com/ * @author philogb / http://blog.thejit.org/ * @author egraether / http://egraether.com/ * @author zz85 / http://www.lab4games.net/zz85/blog */ THREE.Vector2 = function ( x, y ) { this.x = x || 0; this.y = y || 0; }; THREE.Vector2.prototype = { constructor: THREE.Vector2, set: function ( x, y ) { this.x = x; this.y = y; return this; }, setX: function ( x ) { this.x = x; return this; }, setY: function ( y ) { this.y = y; return this; }, setComponent: function ( index, value ) { switch ( index ) { case 0: this.x = value; break; case 1: this.y = value; break; default: throw new Error( 'index is out of range: ' + index ); } }, getComponent: function ( index ) { switch ( index ) { case 0: return this.x; case 1: return this.y; default: throw new Error( 'index is out of range: ' + index ); } }, copy: function ( v ) { this.x = v.x; this.y = v.y; return this; }, add: function ( v, w ) { if ( w !== undefined ) { console.warn( 'THREE.Vector2: .add() now only accepts one argument. Use .addVectors( a, b ) instead.' ); return this.addVectors( v, w ); } this.x += v.x; this.y += v.y; return this; }, addVectors: function ( a, b ) { this.x = a.x + b.x; this.y = a.y + b.y; return this; }, addScalar: function ( s ) { this.x += s; this.y += s; return this; }, sub: function ( v, w ) { if ( w !== undefined ) { console.warn( 'THREE.Vector2: .sub() now only accepts one argument. Use .subVectors( a, b ) instead.' ); return this.subVectors( v, w ); } this.x -= v.x; this.y -= v.y; return this; }, subVectors: function ( a, b ) { this.x = a.x - b.x; this.y = a.y - b.y; return this; }, multiply: function ( v ) { this.x *= v.x; this.y *= v.y; return this; }, multiplyScalar: function ( s ) { this.x *= s; this.y *= s; return this; }, divide: function ( v ) { this.x /= v.x; this.y /= v.y; return this; }, divideScalar: function ( scalar ) { if ( scalar !== 0 ) { var invScalar = 1 / scalar; this.x *= invScalar; this.y *= invScalar; } else { this.x = 0; this.y = 0; } return this; }, min: function ( v ) { if ( this.x > v.x ) { this.x = v.x; } if ( this.y > v.y ) { this.y = v.y; } return this; }, max: function ( v ) { if ( this.x < v.x ) { this.x = v.x; } if ( this.y < v.y ) { this.y = v.y; } return this; }, clamp: 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; } return this; }, clampScalar: ( function () { var min, max; return function ( minVal, maxVal ) { if ( min === undefined ) { min = new THREE.Vector2(); max = new THREE.Vector2(); } min.set( minVal, minVal ); max.set( maxVal, maxVal ); return this.clamp( min, max ); }; } )(), floor: function () { this.x = Math.floor( this.x ); this.y = Math.floor( this.y ); return this; }, ceil: function () { this.x = Math.ceil( this.x ); this.y = Math.ceil( this.y ); return this; }, round: function () { this.x = Math.round( this.x ); this.y = Math.round( this.y ); return this; }, roundToZero: function () { this.x = ( this.x < 0 ) ? Math.ceil( this.x ) : Math.floor( this.x ); this.y = ( this.y < 0 ) ? Math.ceil( this.y ) : Math.floor( this.y ); return this; }, negate: function () { this.x = - this.x; this.y = - this.y; return this; }, dot: function ( v ) { return this.x * v.x + this.y * v.y; }, lengthSq: function () { return this.x * this.x + this.y * this.y; }, length: function () { return Math.sqrt( this.x * this.x + this.y * this.y ); }, normalize: function () { return this.divideScalar( this.length() ); }, distanceTo: function ( v ) { return Math.sqrt( this.distanceToSquared( v ) ); }, distanceToSquared: function ( v ) { var dx = this.x - v.x, dy = this.y - v.y; return dx * dx + dy * dy; }, setLength: function ( l ) { var oldLength = this.length(); if ( oldLength !== 0 && l !== oldLength ) { this.multiplyScalar( l / oldLength ); } return this; }, lerp: function ( v, alpha ) { this.x += ( v.x - this.x ) * alpha; this.y += ( v.y - this.y ) * alpha; return this; }, equals: function ( v ) { return ( ( v.x === this.x ) && ( v.y === this.y ) ); }, fromArray: function ( array ) { this.x = array[ 0 ]; this.y = array[ 1 ]; return this; }, toArray: function () { return [ this.x, this.y ]; }, clone: function () { return new THREE.Vector2( this.x, this.y ); } }; // File:src/math/Vector3.js /** * @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; }, setComponent: function ( index, value ) { switch ( index ) { case 0: this.x = value; break; case 1: this.y = value; break; case 2: this.z = value; break; default: throw new Error( 'index is out of range: ' + index ); } }, getComponent: function ( index ) { switch ( index ) { case 0: return this.x; case 1: return this.y; case 2: return this.z; default: throw new Error( 'index is out of range: ' + index ); } }, copy: function ( v ) { this.x = v.x; this.y = v.y; this.z = v.z; return this; }, add: function ( v, w ) { if ( w !== undefined ) { console.warn( 'THREE.Vector3: .add() now only accepts one argument. Use .addVectors( a, b ) instead.' ); return this.addVectors( v, w ); } 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; }, addVectors: function ( a, b ) { this.x = a.x + b.x; this.y = a.y + b.y; this.z = a.z + b.z; return this; }, sub: function ( v, w ) { if ( w !== undefined ) { console.warn( 'THREE.Vector3: .sub() now only accepts one argument. Use .subVectors( a, b ) instead.' ); return this.subVectors( v, w ); } this.x -= v.x; this.y -= v.y; this.z -= v.z; return this; }, subVectors: function ( a, b ) { this.x = a.x - b.x; this.y = a.y - b.y; this.z = a.z - b.z; return this; }, multiply: function ( v, w ) { if ( w !== undefined ) { console.warn( 'THREE.Vector3: .multiply() now only accepts one argument. Use .multiplyVectors( a, b ) instead.' ); return this.multiplyVectors( v, w ); } this.x *= v.x; this.y *= v.y; this.z *= v.z; return this; }, multiplyScalar: function ( scalar ) { this.x *= scalar; this.y *= scalar; this.z *= scalar; return this; }, multiplyVectors: function ( a, b ) { this.x = a.x * b.x; this.y = a.y * b.y; this.z = a.z * b.z; return this; }, applyEuler: function () { var quaternion; return function ( euler ) { if ( euler instanceof THREE.Euler === false ) { console.error( 'THREE.Vector3: .applyEuler() now expects a Euler rotation rather than a Vector3 and order.' ); } if ( quaternion === undefined ) quaternion = new THREE.Quaternion(); this.applyQuaternion( quaternion.setFromEuler( euler ) ); return this; }; }(), applyAxisAngle: function () { var quaternion; return function ( axis, angle ) { if ( quaternion === undefined ) quaternion = new THREE.Quaternion(); this.applyQuaternion( quaternion.setFromAxisAngle( axis, angle ) ); return this; }; }(), applyMatrix3: function ( m ) { var x = this.x; var y = this.y; var z = this.z; var e = m.elements; this.x = e[ 0 ] * x + e[ 3 ] * y + e[ 6 ] * z; this.y = e[ 1 ] * x + e[ 4 ] * y + e[ 7 ] * z; this.z = e[ 2 ] * x + e[ 5 ] * y + e[ 8 ] * z; return this; }, 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; }, applyProjection: function ( m ) { // input: THREE.Matrix4 projection matrix var x = this.x, y = this.y, z = this.z; var e = m.elements; var d = 1 / ( e[ 3 ] * x + e[ 7 ] * y + e[ 11 ] * z + e[ 15 ] ); // perspective divide this.x = ( e[ 0 ] * x + e[ 4 ] * y + e[ 8 ] * z + e[ 12 ] ) * d; this.y = ( e[ 1 ] * x + e[ 5 ] * y + e[ 9 ] * z + e[ 13 ] ) * d; this.z = ( e[ 2 ] * x + e[ 6 ] * y + e[ 10 ] * z + e[ 14 ] ) * d; return this; }, applyQuaternion: function ( q ) { var x = this.x; var y = this.y; var z = this.z; var qx = q.x; var qy = q.y; var qz = q.z; var qw = q.w; // calculate quat * vector var ix = qw * x + qy * z - qz * y; var iy = qw * y + qz * x - qx * z; var iz = qw * z + qx * y - qy * x; var iw = - qx * x - qy * y - qz * z; // calculate result * inverse quat this.x = ix * qw + iw * - qx + iy * - qz - iz * - qy; this.y = iy * qw + iw * - qy + iz * - qx - ix * - qz; this.z = iz * qw + iw * - qz + ix * - qy - iy * - qx; return this; }, transformDirection: function ( m ) { // input: THREE.Matrix4 affine matrix // vector interpreted as a direction 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; this.y = e[ 1 ] * x + e[ 5 ] * y + e[ 9 ] * z; this.z = e[ 2 ] * x + e[ 6 ] * y + e[ 10 ] * z; this.normalize(); return this; }, divide: function ( v ) { this.x /= v.x; this.y /= v.y; this.z /= v.z; return this; }, divideScalar: function ( scalar ) { if ( scalar !== 0 ) { var invScalar = 1 / scalar; this.x *= invScalar; this.y *= invScalar; this.z *= invScalar; } else { this.x = 0; this.y = 0; this.z = 0; } return this; }, min: 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; }, max: 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; }, clamp: 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; }, clampScalar: ( function () { var min, max; return function ( minVal, maxVal ) { if ( min === undefined ) { min = new THREE.Vector3(); max = new THREE.Vector3(); } min.set( minVal, minVal, minVal ); max.set( maxVal, maxVal, maxVal ); return this.clamp( min, max ); }; } )(), floor: function () { this.x = Math.floor( this.x ); this.y = Math.floor( this.y ); this.z = Math.floor( this.z ); return this; }, ceil: function () { this.x = Math.ceil( this.x ); this.y = Math.ceil( this.y ); this.z = Math.ceil( this.z ); return this; }, round: function () { this.x = Math.round( this.x ); this.y = Math.round( this.y ); this.z = Math.round( this.z ); return this; }, roundToZero: function () { this.x = ( this.x < 0 ) ? Math.ceil( this.x ) : Math.floor( this.x ); this.y = ( this.y < 0 ) ? Math.ceil( this.y ) : Math.floor( this.y ); this.z = ( this.z < 0 ) ? Math.ceil( this.z ) : Math.floor( this.z ); return this; }, negate: function () { this.x = - this.x; this.y = - this.y; this.z = - this.z; return this; }, 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.x * this.x + this.y * this.y + this.z * this.z ); }, 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 ) { var oldLength = this.length(); if ( oldLength !== 0 && l !== oldLength ) { this.multiplyScalar( l / oldLength ); } return this; }, lerp: 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 ( v, w ) { if ( w !== undefined ) { console.warn( 'THREE.Vector3: .cross() now only accepts one argument. Use .crossVectors( a, b ) instead.' ); return this.crossVectors( v, w ); } 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; }, crossVectors: function ( a, b ) { var ax = a.x, ay = a.y, az = a.z; var bx = b.x, by = b.y, bz = b.z; this.x = ay * bz - az * by; this.y = az * bx - ax * bz; this.z = ax * by - ay * bx; return this; }, projectOnVector: function () { var v1, dot; return function ( vector ) { if ( v1 === undefined ) v1 = new THREE.Vector3(); v1.copy( vector ).normalize(); dot = this.dot( v1 ); return this.copy( v1 ).multiplyScalar( dot ); }; }(), projectOnPlane: function () { var v1; return function ( planeNormal ) { if ( v1 === undefined ) v1 = new THREE.Vector3(); v1.copy( this ).projectOnVector( planeNormal ); return this.sub( v1 ); } }(), reflect: function () { // reflect incident vector off plane orthogonal to normal // normal is assumed to have unit length var v1; return function ( normal ) { if ( v1 === undefined ) v1 = new THREE.Vector3(); return this.sub( v1.copy( normal ).multiplyScalar( 2 * this.dot( normal ) ) ); } }(), angleTo: function ( v ) { var theta = this.dot( v ) / ( this.length() * v.length() ); // clamp, to handle numerical problems return Math.acos( THREE.Math.clamp( theta, - 1, 1 ) ); }, 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; }, setEulerFromRotationMatrix: function ( m, order ) { console.error( 'THREE.Vector3: .setEulerFromRotationMatrix() has been removed. Use Euler.setFromRotationMatrix() instead.' ); }, setEulerFromQuaternion: function ( q, order ) { console.error( 'THREE.Vector3: .setEulerFromQuaternion() has been removed. Use Euler.setFromQuaternion() instead.' ); }, getPositionFromMatrix: function ( m ) { console.warn( 'THREE.Vector3: .getPositionFromMatrix() has been renamed to .setFromMatrixPosition().' ); return this.setFromMatrixPosition( m ); }, getScaleFromMatrix: function ( m ) { console.warn( 'THREE.Vector3: .getScaleFromMatrix() has been renamed to .setFromMatrixScale().' ); return this.setFromMatrixScale( m ); }, getColumnFromMatrix: function ( index, matrix ) { console.warn( 'THREE.Vector3: .getColumnFromMatrix() has been renamed to .setFromMatrixColumn().' ); return this.setFromMatrixColumn( index, matrix ); }, setFromMatrixPosition: function ( m ) { this.x = m.elements[ 12 ]; this.y = m.elements[ 13 ]; this.z = m.elements[ 14 ]; return this; }, setFromMatrixScale: 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; }, setFromMatrixColumn: function ( index, matrix ) { var offset = index * 4; var me = matrix.elements; this.x = me[ offset ]; this.y = me[ offset + 1 ]; this.z = me[ offset + 2 ]; return this; }, equals: function ( v ) { return ( ( v.x === this.x ) && ( v.y === this.y ) && ( v.z === this.z ) ); }, fromArray: function ( array ) { this.x = array[ 0 ]; this.y = array[ 1 ]; this.z = array[ 2 ]; return this; }, toArray: function () { return [ this.x, this.y, this.z ]; }, clone: function () { return new THREE.Vector3( this.x, this.y, this.z ); } }; // File:src/math/Vector4.js /** * @author supereggbert / http://www.paulbrunt.co.uk/ * @author philogb / http://blog.thejit.org/ * @author mikael emtinger / http://gomo.se/ * @author egraether / http://egraether.com/ * @author WestLangley / http://github.com/WestLangley */ THREE.Vector4 = function ( x, y, z, w ) { this.x = x || 0; this.y = y || 0; this.z = z || 0; this.w = ( w !== undefined ) ? w : 1; }; THREE.Vector4.prototype = { constructor: THREE.Vector4, set: function ( x, y, z, w ) { this.x = x; this.y = y; this.z = z; this.w = w; 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; }, setW: function ( w ) { this.w = w; return this; }, setComponent: function ( index, value ) { switch ( index ) { case 0: this.x = value; break; case 1: this.y = value; break; case 2: this.z = value; break; case 3: this.w = value; break; default: throw new Error( 'index is out of range: ' + index ); } }, getComponent: function ( index ) { switch ( index ) { case 0: return this.x; case 1: return this.y; case 2: return this.z; case 3: return this.w; default: throw new Error( 'index is out of range: ' + index ); } }, copy: function ( v ) { this.x = v.x; this.y = v.y; this.z = v.z; this.w = ( v.w !== undefined ) ? v.w : 1; return this; }, add: function ( v, w ) { if ( w !== undefined ) { console.warn( 'THREE.Vector4: .add() now only accepts one argument. Use .addVectors( a, b ) instead.' ); return this.addVectors( v, w ); } this.x += v.x; this.y += v.y; this.z += v.z; this.w += v.w; return this; }, addScalar: function ( s ) { this.x += s; this.y += s; this.z += s; this.w += s; return this; }, addVectors: function ( a, b ) { this.x = a.x + b.x; this.y = a.y + b.y; this.z = a.z + b.z; this.w = a.w + b.w; return this; }, sub: function ( v, w ) { if ( w !== undefined ) { console.warn( 'THREE.Vector4: .sub() now only accepts one argument. Use .subVectors( a, b ) instead.' ); return this.subVectors( v, w ); } this.x -= v.x; this.y -= v.y; this.z -= v.z; this.w -= v.w; return this; }, subVectors: function ( a, b ) { this.x = a.x - b.x; this.y = a.y - b.y; this.z = a.z - b.z; this.w = a.w - b.w; return this; }, multiplyScalar: function ( scalar ) { this.x *= scalar; this.y *= scalar; this.z *= scalar; this.w *= scalar; return this; }, applyMatrix4: function ( m ) { var x = this.x; var y = this.y; var z = this.z; var w = this.w; var e = m.elements; this.x = e[ 0 ] * x + e[ 4 ] * y + e[ 8 ] * z + e[ 12 ] * w; this.y = e[ 1 ] * x + e[ 5 ] * y + e[ 9 ] * z + e[ 13 ] * w; this.z = e[ 2 ] * x + e[ 6 ] * y + e[ 10 ] * z + e[ 14 ] * w; this.w = e[ 3 ] * x + e[ 7 ] * y + e[ 11 ] * z + e[ 15 ] * w; return this; }, divideScalar: function ( scalar ) { if ( scalar !== 0 ) { var invScalar = 1 / scalar; this.x *= invScalar; this.y *= invScalar; this.z *= invScalar; this.w *= invScalar; } else { this.x = 0; this.y = 0; this.z = 0; this.w = 1; } return this; }, setAxisAngleFromQuaternion: function ( q ) { // http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToAngle/index.htm // q is assumed to be normalized this.w = 2 * Math.acos( q.w ); var s = Math.sqrt( 1 - q.w * q.w ); if ( s < 0.0001 ) { this.x = 1; this.y = 0; this.z = 0; } else { this.x = q.x / s; this.y = q.y / s; this.z = q.z / s; } return this; }, setAxisAngleFromRotationMatrix: function ( m ) { // http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToAngle/index.htm // assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled) var angle, x, y, z, // variables for result epsilon = 0.01, // margin to allow for rounding errors epsilon2 = 0.1, // margin to distinguish between 0 and 180 degrees te = m.elements, m11 = te[ 0 ], m12 = te[ 4 ], m13 = te[ 8 ], m21 = te[ 1 ], m22 = te[ 5 ], m23 = te[ 9 ], m31 = te[ 2 ], m32 = te[ 6 ], m33 = te[ 10 ]; if ( ( Math.abs( m12 - m21 ) < epsilon ) && ( Math.abs( m13 - m31 ) < epsilon ) && ( Math.abs( m23 - m32 ) < epsilon ) ) { // singularity found // first check for identity matrix which must have +1 for all terms // in leading diagonal and zero in other terms if ( ( Math.abs( m12 + m21 ) < epsilon2 ) && ( Math.abs( m13 + m31 ) < epsilon2 ) && ( Math.abs( m23 + m32 ) < epsilon2 ) && ( Math.abs( m11 + m22 + m33 - 3 ) < epsilon2 ) ) { // this singularity is identity matrix so angle = 0 this.set( 1, 0, 0, 0 ); return this; // zero angle, arbitrary axis } // otherwise this singularity is angle = 180 angle = Math.PI; var xx = ( m11 + 1 ) / 2; var yy = ( m22 + 1 ) / 2; var zz = ( m33 + 1 ) / 2; var xy = ( m12 + m21 ) / 4; var xz = ( m13 + m31 ) / 4; var yz = ( m23 + m32 ) / 4; if ( ( xx > yy ) && ( xx > zz ) ) { // m11 is the largest diagonal term if ( xx < epsilon ) { x = 0; y = 0.707106781; z = 0.707106781; } else { x = Math.sqrt( xx ); y = xy / x; z = xz / x; } } else if ( yy > zz ) { // m22 is the largest diagonal term if ( yy < epsilon ) { x = 0.707106781; y = 0; z = 0.707106781; } else { y = Math.sqrt( yy ); x = xy / y; z = yz / y; } } else { // m33 is the largest diagonal term so base result on this if ( zz < epsilon ) { x = 0.707106781; y = 0.707106781; z = 0; } else { z = Math.sqrt( zz ); x = xz / z; y = yz / z; } } this.set( x, y, z, angle ); return this; // return 180 deg rotation } // as we have reached here there are no singularities so we can handle normally var s = Math.sqrt( ( m32 - m23 ) * ( m32 - m23 ) + ( m13 - m31 ) * ( m13 - m31 ) + ( m21 - m12 ) * ( m21 - m12 ) ); // used to normalize if ( Math.abs( s ) < 0.001 ) s = 1; // prevent divide by zero, should not happen if matrix is orthogonal and should be // caught by singularity test above, but I've left it in just in case this.x = ( m32 - m23 ) / s; this.y = ( m13 - m31 ) / s; this.z = ( m21 - m12 ) / s; this.w = Math.acos( ( m11 + m22 + m33 - 1 ) / 2 ); return this; }, min: 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; } if ( this.w > v.w ) { this.w = v.w; } return this; }, max: 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; } if ( this.w < v.w ) { this.w = v.w; } return this; }, clamp: 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; } if ( this.w < min.w ) { this.w = min.w; } else if ( this.w > max.w ) { this.w = max.w; } return this; }, clampScalar: ( function () { var min, max; return function ( minVal, maxVal ) { if ( min === undefined ) { min = new THREE.Vector4(); max = new THREE.Vector4(); } min.set( minVal, minVal, minVal, minVal ); max.set( maxVal, maxVal, maxVal, maxVal ); return this.clamp( min, max ); }; } )(), floor: function () { this.x = Math.floor( this.x ); this.y = Math.floor( this.y ); this.z = Math.floor( this.z ); this.w = Math.floor( this.w ); return this; }, ceil: function () { this.x = Math.ceil( this.x ); this.y = Math.ceil( this.y ); this.z = Math.ceil( this.z ); this.w = Math.ceil( this.w ); return this; }, round: function () { this.x = Math.round( this.x ); this.y = Math.round( this.y ); this.z = Math.round( this.z ); this.w = Math.round( this.w ); return this; }, roundToZero: function () { this.x = ( this.x < 0 ) ? Math.ceil( this.x ) : Math.floor( this.x ); this.y = ( this.y < 0 ) ? Math.ceil( this.y ) : Math.floor( this.y ); this.z = ( this.z < 0 ) ? Math.ceil( this.z ) : Math.floor( this.z ); this.w = ( this.w < 0 ) ? Math.ceil( this.w ) : Math.floor( this.w ); return this; }, negate: function () { this.x = - this.x; this.y = - this.y; this.z = - this.z; this.w = - this.w; return this; }, dot: function ( v ) { return this.x * v.x + this.y * v.y + this.z * v.z + this.w * v.w; }, lengthSq: function () { return this.x * this.x + this.y * this.y + this.z * this.z + this.w * this.w; }, length: function () { return Math.sqrt( this.x * this.x + this.y * this.y + this.z * this.z + this.w * this.w ); }, lengthManhattan: function () { return Math.abs( this.x ) + Math.abs( this.y ) + Math.abs( this.z ) + Math.abs( this.w ); }, normalize: function () { return this.divideScalar( this.length() ); }, setLength: function ( l ) { var oldLength = this.length(); if ( oldLength !== 0 && l !== oldLength ) { this.multiplyScalar( l / oldLength ); } return this; }, lerp: function ( v, alpha ) { this.x += ( v.x - this.x ) * alpha; this.y += ( v.y - this.y ) * alpha; this.z += ( v.z - this.z ) * alpha; this.w += ( v.w - this.w ) * alpha; return this; }, equals: function ( v ) { return ( ( v.x === this.x ) && ( v.y === this.y ) && ( v.z === this.z ) && ( v.w === this.w ) ); }, fromArray: function ( array ) { this.x = array[ 0 ]; this.y = array[ 1 ]; this.z = array[ 2 ]; this.w = array[ 3 ]; return this; }, toArray: function () { return [ this.x, this.y, this.z, this.w ]; }, clone: function () { return new THREE.Vector4( this.x, this.y, this.z, this.w ); } }; // File:src/math/Euler.js /** * @author mrdoob / http://mrdoob.com/ * @author WestLangley / http://github.com/WestLangley * @author bhouston / http://exocortex.com */ THREE.Euler = function ( x, y, z, order ) { this._x = x || 0; this._y = y || 0; this._z = z || 0; this._order = order || THREE.Euler.DefaultOrder; }; THREE.Euler.RotationOrders = [ 'XYZ', 'YZX', 'ZXY', 'XZY', 'YXZ', 'ZYX' ]; THREE.Euler.DefaultOrder = 'XYZ'; THREE.Euler.prototype = { constructor: THREE.Euler, _x: 0, _y: 0, _z: 0, _order: THREE.Euler.DefaultOrder, get x () { return this._x; }, set x ( value ) { this._x = value; this.onChangeCallback(); }, get y () { return this._y; }, set y ( value ) { this._y = value; this.onChangeCallback(); }, get z () { return this._z; }, set z ( value ) { this._z = value; this.onChangeCallback(); }, get order () { return this._order; }, set order ( value ) { this._order = value; this.onChangeCallback(); }, set: function ( x, y, z, order ) { this._x = x; this._y = y; this._z = z; this._order = order || this._order; this.onChangeCallback(); return this; }, copy: function ( euler ) { this._x = euler._x; this._y = euler._y; this._z = euler._z; this._order = euler._order; this.onChangeCallback(); return this; }, setFromRotationMatrix: function ( m, order ) { var clamp = THREE.Math.clamp; // assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled) 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 ]; order = order || this._order; if ( order === 'XYZ' ) { this._y = Math.asin( clamp( m13, - 1, 1 ) ); 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, - 1, 1 ) ); 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, - 1, 1 ) ); 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, - 1, 1 ) ); 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, - 1, 1 ) ); 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, - 1, 1 ) ); 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; } } else { console.warn( 'THREE.Euler: .setFromRotationMatrix() given unsupported order: ' + order ) } this._order = order; this.onChangeCallback(); return this; }, setFromQuaternion: function ( q, order, update ) { var clamp = THREE.Math.clamp; // q is assumed to be normalized // 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; order = order || this._order; if ( 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 ), - 1, 1 ) ); 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 ), - 1, 1 ) ); 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 ), - 1, 1 ) ); 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 ), - 1, 1 ) ); 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 ), - 1, 1 ) ); } 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 ), - 1, 1 ) ); } else { console.warn( 'THREE.Euler: .setFromQuaternion() given unsupported order: ' + order ) } this._order = order; if ( update !== false ) this.onChangeCallback(); return this; }, reorder: function () { // WARNING: this discards revolution information -bhouston var q = new THREE.Quaternion(); return function ( newOrder ) { q.setFromEuler( this ); this.setFromQuaternion( q, newOrder ); }; }(), equals: function ( euler ) { return ( euler._x === this._x ) && ( euler._y === this._y ) && ( euler._z === this._z ) && ( euler._order === this._order ); }, fromArray: function ( array ) { this._x = array[ 0 ]; this._y = array[ 1 ]; this._z = array[ 2 ]; if ( array[ 3 ] !== undefined ) this._order = array[ 3 ]; this.onChangeCallback(); return this; }, toArray: function () { return [ this._x, this._y, this._z, this._order ]; }, onChange: function ( callback ) { this.onChangeCallback = callback; return this; }, onChangeCallback: function () {}, clone: function () { return new THREE.Euler( this._x, this._y, this._z, this._order ); } }; // File:src/math/Line3.js /** * @author bhouston / http://exocortex.com */ THREE.Line3 = function ( start, end ) { this.start = ( start !== undefined ) ? start : new THREE.Vector3(); this.end = ( end !== undefined ) ? end : new THREE.Vector3(); }; THREE.Line3.prototype = { constructor: THREE.Line3, set: function ( start, end ) { this.start.copy( start ); this.end.copy( end ); return this; }, copy: function ( line ) { this.start.copy( line.start ); this.end.copy( line.end ); return this; }, center: function ( optionalTarget ) { var result = optionalTarget || new THREE.Vector3(); return result.addVectors( this.start, this.end ).multiplyScalar( 0.5 ); }, delta: function ( optionalTarget ) { var result = optionalTarget || new THREE.Vector3(); return result.subVectors( this.end, this.start ); }, distanceSq: function () { return this.start.distanceToSquared( this.end ); }, distance: function () { return this.start.distanceTo( this.end ); }, at: function ( t, optionalTarget ) { var result = optionalTarget || new THREE.Vector3(); return this.delta( result ).multiplyScalar( t ).add( this.start ); }, closestPointToPointParameter: function () { var startP = new THREE.Vector3(); var startEnd = new THREE.Vector3(); return function ( point, clampToLine ) { startP.subVectors( point, this.start ); startEnd.subVectors( this.end, this.start ); var startEnd2 = startEnd.dot( startEnd ); var startEnd_startP = startEnd.dot( startP ); var t = startEnd_startP / startEnd2; if ( clampToLine ) { t = THREE.Math.clamp( t, 0, 1 ); } return t; }; }(), closestPointToPoint: function ( point, clampToLine, optionalTarget ) { var t = this.closestPointToPointParameter( point, clampToLine ); var result = optionalTarget || new THREE.Vector3(); return this.delta( result ).multiplyScalar( t ).add( this.start ); }, applyMatrix4: function ( matrix ) { this.start.applyMatrix4( matrix ); this.end.applyMatrix4( matrix ); return this; }, equals: function ( line ) { return line.start.equals( this.start ) && line.end.equals( this.end ); }, clone: function () { return new THREE.Line3().copy( this ); } }; // File:src/math/Box2.js /** * @author bhouston / http://exocortex.com */ THREE.Box2 = function ( min, max ) { this.min = ( min !== undefined ) ? min : new THREE.Vector2( Infinity, Infinity ); this.max = ( max !== undefined ) ? max : new THREE.Vector2( - Infinity, - Infinity ); }; THREE.Box2.prototype = { constructor: THREE.Box2, set: function ( min, max ) { this.min.copy( min ); this.max.copy( max ); return this; }, setFromPoints: function ( points ) { this.makeEmpty(); for ( var i = 0, il = points.length; i < il; i ++ ) { this.expandByPoint( points[ i ] ) } return this; }, setFromCenterAndSize: function () { var v1 = new THREE.Vector2(); return function ( center, size ) { var halfSize = v1.copy( size ).multiplyScalar( 0.5 ); this.min.copy( center ).sub( halfSize ); this.max.copy( center ).add( halfSize ); return this; }; }(), copy: function ( box ) { this.min.copy( box.min ); this.max.copy( box.max ); return this; }, makeEmpty: function () { this.min.x = this.min.y = Infinity; this.max.x = this.max.y = - Infinity; return this; }, empty: function () { // this is a more robust check for empty than ( volume <= 0 ) because volume can get positive with two negative axes return ( this.max.x < this.min.x ) || ( this.max.y < this.min.y ); }, center: function ( optionalTarget ) { var result = optionalTarget || new THREE.Vector2(); return result.addVectors( this.min, this.max ).multiplyScalar( 0.5 ); }, size: function ( optionalTarget ) { var result = optionalTarget || new THREE.Vector2(); return result.subVectors( this.max, this.min ); }, expandByPoint: function ( point ) { this.min.min( point ); this.max.max( point ); return this; }, expandByVector: function ( vector ) { this.min.sub( vector ); this.max.add( vector ); return this; }, expandByScalar: function ( scalar ) { this.min.addScalar( - scalar ); this.max.addScalar( scalar ); return this; }, containsPoint: function ( point ) { if ( point.x < this.min.x || point.x > this.max.x || point.y < this.min.y || point.y > this.max.y ) { return false; } return true; }, containsBox: function ( box ) { if ( ( this.min.x <= box.min.x ) && ( box.max.x <= this.max.x ) && ( this.min.y <= box.min.y ) && ( box.max.y <= this.max.y ) ) { return true; } return false; }, getParameter: function ( point, optionalTarget ) { // This can potentially have a divide by zero if the box // has a size dimension of 0. var result = optionalTarget || new THREE.Vector2(); return result.set( ( point.x - this.min.x ) / ( this.max.x - this.min.x ), ( point.y - this.min.y ) / ( this.max.y - this.min.y ) ); }, isIntersectionBox: function ( box ) { // using 6 splitting planes to rule out intersections. if ( box.max.x < this.min.x || box.min.x > this.max.x || box.max.y < this.min.y || box.min.y > this.max.y ) { return false; } return true; }, clampPoint: function ( point, optionalTarget ) { var result = optionalTarget || new THREE.Vector2(); return result.copy( point ).clamp( this.min, this.max ); }, distanceToPoint: function () { var v1 = new THREE.Vector2(); return function ( point ) { var clampedPoint = v1.copy( point ).clamp( this.min, this.max ); return clampedPoint.sub( point ).length(); }; }(), intersect: function ( box ) { this.min.max( box.min ); this.max.min( box.max ); return this; }, union: function ( box ) { this.min.min( box.min ); this.max.max( box.max ); return this; }, translate: function ( offset ) { this.min.add( offset ); this.max.add( offset ); return this; }, equals: function ( box ) { return box.min.equals( this.min ) && box.max.equals( this.max ); }, clone: function () { return new THREE.Box2().copy( this ); } }; // File:src/math/Box3.js /** * @author bhouston / http://exocortex.com * @author WestLangley / http://github.com/WestLangley */ THREE.Box3 = function ( min, max ) { this.min = ( min !== undefined ) ? min : new THREE.Vector3( Infinity, Infinity, Infinity ); this.max = ( max !== undefined ) ? max : new THREE.Vector3( - Infinity, - Infinity, - Infinity ); }; THREE.Box3.prototype = { constructor: THREE.Box3, set: function ( min, max ) { this.min.copy( min ); this.max.copy( max ); return this; }, setFromPoints: function ( points ) { this.makeEmpty(); for ( var i = 0, il = points.length; i < il; i ++ ) { this.expandByPoint( points[ i ] ) } return this; }, setFromCenterAndSize: function () { var v1 = new THREE.Vector3(); return function ( center, size ) { var halfSize = v1.copy( size ).multiplyScalar( 0.5 ); this.min.copy( center ).sub( halfSize ); this.max.copy( center ).add( halfSize ); return this; }; }(), setFromObject: function () { // Computes the world-axis-aligned bounding box of an object (including its children), // accounting for both the object's, and childrens', world transforms var v1 = new THREE.Vector3(); return function ( object ) { var scope = this; object.updateMatrixWorld( true ); this.makeEmpty(); object.traverse( function ( node ) { var geometry = node.geometry; if ( geometry !== undefined ) { if ( geometry instanceof THREE.Geometry ) { var vertices = geometry.vertices; for ( var i = 0, il = vertices.length; i < il; i ++ ) { v1.copy( vertices[ i ] ); v1.applyMatrix4( node.matrixWorld ); scope.expandByPoint( v1 ); } } else if ( geometry instanceof THREE.BufferGeometry && geometry.attributes[ 'position' ] !== undefined ) { var positions = geometry.attributes[ 'position' ].array; for ( var i = 0, il = positions.length; i < il; i += 3 ) { v1.set( positions[ i ], positions[ i + 1 ], positions[ i + 2 ] ); v1.applyMatrix4( node.matrixWorld ); scope.expandByPoint( v1 ); } } } } ); return this; }; }(), copy: function ( box ) { this.min.copy( box.min ); this.max.copy( box.max ); return this; }, makeEmpty: function () { this.min.x = this.min.y = this.min.z = Infinity; this.max.x = this.max.y = this.max.z = - Infinity; return this; }, empty: function () { // this is a more robust check for empty than ( volume <= 0 ) because volume can get positive with two negative axes return ( this.max.x < this.min.x ) || ( this.max.y < this.min.y ) || ( this.max.z < this.min.z ); }, center: function ( optionalTarget ) { var result = optionalTarget || new THREE.Vector3(); return result.addVectors( this.min, this.max ).multiplyScalar( 0.5 ); }, size: function ( optionalTarget ) { var result = optionalTarget || new THREE.Vector3(); return result.subVectors( this.max, this.min ); }, expandByPoint: function ( point ) { this.min.min( point ); this.max.max( point ); return this; }, expandByVector: function ( vector ) { this.min.sub( vector ); this.max.add( vector ); return this; }, expandByScalar: function ( scalar ) { this.min.addScalar( - scalar ); this.max.addScalar( scalar ); return this; }, containsPoint: function ( point ) { if ( point.x < this.min.x || point.x > this.max.x || point.y < this.min.y || point.y > this.max.y || point.z < this.min.z || point.z > this.max.z ) { return false; } return true; }, containsBox: function ( box ) { if ( ( this.min.x <= box.min.x ) && ( box.max.x <= this.max.x ) && ( this.min.y <= box.min.y ) && ( box.max.y <= this.max.y ) && ( this.min.z <= box.min.z ) && ( box.max.z <= this.max.z ) ) { return true; } return false; }, getParameter: function ( point, optionalTarget ) { // This can potentially have a divide by zero if the box // has a size dimension of 0. var result = optionalTarget || new THREE.Vector3(); return result.set( ( point.x - this.min.x ) / ( this.max.x - this.min.x ), ( point.y - this.min.y ) / ( this.max.y - this.min.y ), ( point.z - this.min.z ) / ( this.max.z - this.min.z ) ); }, isIntersectionBox: function ( box ) { // using 6 splitting planes to rule out intersections. if ( box.max.x < this.min.x || box.min.x > this.max.x || box.max.y < this.min.y || box.min.y > this.max.y || box.max.z < this.min.z || box.min.z > this.max.z ) { return false; } return true; }, clampPoint: function ( point, optionalTarget ) { var result = optionalTarget || new THREE.Vector3(); return result.copy( point ).clamp( this.min, this.max ); }, distanceToPoint: function () { var v1 = new THREE.Vector3(); return function ( point ) { var clampedPoint = v1.copy( point ).clamp( this.min, this.max ); return clampedPoint.sub( point ).length(); }; }(), getBoundingSphere: function () { var v1 = new THREE.Vector3(); return function ( optionalTarget ) { var result = optionalTarget || new THREE.Sphere(); result.center = this.center(); result.radius = this.size( v1 ).length() * 0.5; return result; }; }(), intersect: function ( box ) { this.min.max( box.min ); this.max.min( box.max ); return this; }, union: function ( box ) { this.min.min( box.min ); this.max.max( box.max ); return this; }, applyMatrix4: function () { var points = [ new THREE.Vector3(), new THREE.Vector3(), new THREE.Vector3(), new THREE.Vector3(), new THREE.Vector3(), new THREE.Vector3(), new THREE.Vector3(), new THREE.Vector3() ]; return function ( matrix ) { // NOTE: I am using a binary pattern to specify all 2^3 combinations below points[ 0 ].set( this.min.x, this.min.y, this.min.z ).applyMatrix4( matrix ); // 000 points[ 1 ].set( this.min.x, this.min.y, this.max.z ).applyMatrix4( matrix ); // 001 points[ 2 ].set( this.min.x, this.max.y, this.min.z ).applyMatrix4( matrix ); // 010 points[ 3 ].set( this.min.x, this.max.y, this.max.z ).applyMatrix4( matrix ); // 011 points[ 4 ].set( this.max.x, this.min.y, this.min.z ).applyMatrix4( matrix ); // 100 points[ 5 ].set( this.max.x, this.min.y, this.max.z ).applyMatrix4( matrix ); // 101 points[ 6 ].set( this.max.x, this.max.y, this.min.z ).applyMatrix4( matrix ); // 110 points[ 7 ].set( this.max.x, this.max.y, this.max.z ).applyMatrix4( matrix ); // 111 this.makeEmpty(); this.setFromPoints( points ); return this; }; }(), translate: function ( offset ) { this.min.add( offset ); this.max.add( offset ); return this; }, equals: function ( box ) { return box.min.equals( this.min ) && box.max.equals( this.max ); }, clone: function () { return new THREE.Box3().copy( this ); } }; // File:src/math/Matrix3.js /** * @author alteredq / http://alteredqualia.com/ * @author WestLangley / http://github.com/WestLangley * @author bhouston / http://exocortex.com */ THREE.Matrix3 = function () { this.elements = new Float32Array( [ 1, 0, 0, 0, 1, 0, 0, 0, 1 ] ); if ( arguments.length > 0 ) { console.error( 'THREE.Matrix3: the constructor no longer reads arguments. use .set() instead.' ); } }; THREE.Matrix3.prototype = { constructor: THREE.Matrix3, set: function ( n11, n12, n13, n21, n22, n23, n31, n32, n33 ) { var te = this.elements; te[ 0 ] = n11; te[ 3 ] = n12; te[ 6 ] = n13; te[ 1 ] = n21; te[ 4 ] = n22; te[ 7 ] = n23; te[ 2 ] = n31; te[ 5 ] = n32; te[ 8 ] = n33; return this; }, identity: function () { this.set( 1, 0, 0, 0, 1, 0, 0, 0, 1 ); return this; }, copy: function ( m ) { var me = m.elements; this.set( me[ 0 ], me[ 3 ], me[ 6 ], me[ 1 ], me[ 4 ], me[ 7 ], me[ 2 ], me[ 5 ], me[ 8 ] ); return this; }, multiplyVector3: function ( vector ) { console.warn( 'THREE.Matrix3: .multiplyVector3() has been removed. Use vector.applyMatrix3( matrix ) instead.' ); return vector.applyMatrix3( this ); }, multiplyVector3Array: function ( a ) { console.warn( 'THREE.Matrix3: .multiplyVector3Array() has been renamed. Use matrix.applyToVector3Array( array ) instead.' ); return this.applyToVector3Array( a ); }, applyToVector3Array: function () { var v1 = new THREE.Vector3(); return function ( array, offset, length ) { if ( offset === undefined ) offset = 0; if ( length === undefined ) length = array.length; for ( var i = 0, j = offset, il; i < length; i += 3, j += 3 ) { v1.x = array[ j ]; v1.y = array[ j + 1 ]; v1.z = array[ j + 2 ]; v1.applyMatrix3( this ); array[ j ] = v1.x; array[ j + 1 ] = v1.y; array[ j + 2 ] = v1.z; } return array; }; }(), multiplyScalar: function ( s ) { var te = this.elements; te[ 0 ] *= s; te[ 3 ] *= s; te[ 6 ] *= s; te[ 1 ] *= s; te[ 4 ] *= s; te[ 7 ] *= s; te[ 2 ] *= s; te[ 5 ] *= s; te[ 8 ] *= s; return this; }, determinant: function () { var te = this.elements; var a = te[ 0 ], b = te[ 1 ], c = te[ 2 ], d = te[ 3 ], e = te[ 4 ], f = te[ 5 ], g = te[ 6 ], h = te[ 7 ], i = te[ 8 ]; return a * e * i - a * f * h - b * d * i + b * f * g + c * d * h - c * e * g; }, getInverse: function ( matrix, throwOnInvertible ) { // input: THREE.Matrix4 // ( based on http://code.google.com/p/webgl-mjs/ ) var me = matrix.elements; var te = this.elements; te[ 0 ] = me[ 10 ] * me[ 5 ] - me[ 6 ] * me[ 9 ]; te[ 1 ] = - me[ 10 ] * me[ 1 ] + me[ 2 ] * me[ 9 ]; te[ 2 ] = me[ 6 ] * me[ 1 ] - me[ 2 ] * me[ 5 ]; te[ 3 ] = - me[ 10 ] * me[ 4 ] + me[ 6 ] * me[ 8 ]; te[ 4 ] = me[ 10 ] * me[ 0 ] - me[ 2 ] * me[ 8 ]; te[ 5 ] = - me[ 6 ] * me[ 0 ] + me[ 2 ] * me[ 4 ]; te[ 6 ] = me[ 9 ] * me[ 4 ] - me[ 5 ] * me[ 8 ]; te[ 7 ] = - me[ 9 ] * me[ 0 ] + me[ 1 ] * me[ 8 ]; te[ 8 ] = me[ 5 ] * me[ 0 ] - me[ 1 ] * me[ 4 ]; var det = me[ 0 ] * te[ 0 ] + me[ 1 ] * te[ 3 ] + me[ 2 ] * te[ 6 ]; // no inverse if ( det === 0 ) { var msg = "Matrix3.getInverse(): can't invert matrix, determinant is 0"; if ( throwOnInvertible || false ) { throw new Error( msg ); } else { console.warn( msg ); } this.identity(); return this; } this.multiplyScalar( 1.0 / det ); return this; }, transpose: function () { var tmp, m = this.elements; tmp = m[ 1 ]; m[ 1 ] = m[ 3 ]; m[ 3 ] = tmp; tmp = m[ 2 ]; m[ 2 ] = m[ 6 ]; m[ 6 ] = tmp; tmp = m[ 5 ]; m[ 5 ] = m[ 7 ]; m[ 7 ] = tmp; return this; }, flattenToArrayOffset: function ( array, offset ) { var te = this.elements; array[ offset ] = te[ 0 ]; array[ offset + 1 ] = te[ 1 ]; array[ offset + 2 ] = te[ 2 ]; array[ offset + 3 ] = te[ 3 ]; array[ offset + 4 ] = te[ 4 ]; array[ offset + 5 ] = te[ 5 ]; array[ offset + 6 ] = te[ 6 ]; array[ offset + 7 ] = te[ 7 ]; array[ offset + 8 ] = te[ 8 ]; return array; }, getNormalMatrix: function ( m ) { // input: THREE.Matrix4 this.getInverse( m ).transpose(); return this; }, transposeIntoArray: function ( r ) { var m = this.elements; r[ 0 ] = m[ 0 ]; r[ 1 ] = m[ 3 ]; r[ 2 ] = m[ 6 ]; r[ 3 ] = m[ 1 ]; r[ 4 ] = m[ 4 ]; r[ 5 ] = m[ 7 ]; r[ 6 ] = m[ 2 ]; r[ 7 ] = m[ 5 ]; r[ 8 ] = m[ 8 ]; return this; }, fromArray: function ( array ) { this.elements.set( array ); return this; }, toArray: function () { var te = this.elements; return [ te[ 0 ], te[ 1 ], te[ 2 ], te[ 3 ], te[ 4 ], te[ 5 ], te[ 6 ], te[ 7 ], te[ 8 ] ]; }, clone: function () { return new THREE.Matrix3().fromArray( this.elements ); } }; // File:src/math/Matrix4.js /** * @author mrdoob / http://mrdoob.com/ * @author supereggbert / http://www.paulbrunt.co.uk/ * @author philogb / http://blog.thejit.org/ * @author jordi_ros / http://plattsoft.com * @author D1plo1d / http://github.com/D1plo1d * @author alteredq / http://alteredqualia.com/ * @author mikael emtinger / http://gomo.se/ * @author timknip / http://www.floorplanner.com/ * @author bhouston / http://exocortex.com * @author WestLangley / http://github.com/WestLangley */ THREE.Matrix4 = function () { this.elements = new Float32Array( [ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 ] ); if ( arguments.length > 0 ) { console.error( 'THREE.Matrix4: the constructor no longer reads arguments. use .set() instead.' ); } }; THREE.Matrix4.prototype = { constructor: THREE.Matrix4, set: function ( n11, n12, n13, n14, n21, n22, n23, n24, n31, n32, n33, n34, n41, n42, n43, n44 ) { var te = this.elements; te[ 0 ] = n11; te[ 4 ] = n12; te[ 8 ] = n13; te[ 12 ] = n14; te[ 1 ] = n21; te[ 5 ] = n22; te[ 9 ] = n23; te[ 13 ] = n24; te[ 2 ] = n31; te[ 6 ] = n32; te[ 10 ] = n33; te[ 14 ] = n34; te[ 3 ] = n41; te[ 7 ] = n42; te[ 11 ] = n43; te[ 15 ] = n44; return this; }, identity: function () { this.set( 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 ); return this; }, copy: function ( m ) { this.elements.set( m.elements ); return this; }, extractPosition: function ( m ) { console.warn( 'THREE.Matrix4: .extractPosition() has been renamed to .copyPosition().' ); return this.copyPosition( m ); }, copyPosition: function ( m ) { var te = this.elements; var me = m.elements; te[ 12 ] = me[ 12 ]; te[ 13 ] = me[ 13 ]; te[ 14 ] = me[ 14 ]; return this; }, extractRotation: function () { var v1 = new THREE.Vector3(); return function ( m ) { var te = this.elements; var me = m.elements; var scaleX = 1 / v1.set( me[ 0 ], me[ 1 ], me[ 2 ] ).length(); var scaleY = 1 / v1.set( me[ 4 ], me[ 5 ], me[ 6 ] ).length(); var scaleZ = 1 / v1.set( me[ 8 ], me[ 9 ], me[ 10 ] ).length(); te[ 0 ] = me[ 0 ] * scaleX; te[ 1 ] = me[ 1 ] * scaleX; te[ 2 ] = me[ 2 ] * scaleX; te[ 4 ] = me[ 4 ] * scaleY; te[ 5 ] = me[ 5 ] * scaleY; te[ 6 ] = me[ 6 ] * scaleY; te[ 8 ] = me[ 8 ] * scaleZ; te[ 9 ] = me[ 9 ] * scaleZ; te[ 10 ] = me[ 10 ] * scaleZ; return this; }; }(), makeRotationFromEuler: function ( euler ) { if ( euler instanceof THREE.Euler === false ) { console.error( 'THREE.Matrix: .makeRotationFromEuler() now expects a Euler rotation rather than a Vector3 and order.' ); } var te = this.elements; var x = euler.x, y = euler.y, z = euler.z; var a = Math.cos( x ), b = Math.sin( x ); var c = Math.cos( y ), d = Math.sin( y ); var e = Math.cos( z ), f = Math.sin( z ); if ( euler.order === 'XYZ' ) { var ae = a * e, af = a * f, be = b * e, bf = b * f; te[ 0 ] = c * e; te[ 4 ] = - c * f; te[ 8 ] = d; te[ 1 ] = af + be * d; te[ 5 ] = ae - bf * d; te[ 9 ] = - b * c; te[ 2 ] = bf - ae * d; te[ 6 ] = be + af * d; te[ 10 ] = a * c; } else if ( euler.order === 'YXZ' ) { var ce = c * e, cf = c * f, de = d * e, df = d * f; te[ 0 ] = ce + df * b; te[ 4 ] = de * b - cf; te[ 8 ] = a * d; te[ 1 ] = a * f; te[ 5 ] = a * e; te[ 9 ] = - b; te[ 2 ] = cf * b - de; te[ 6 ] = df + ce * b; te[ 10 ] = a * c; } else if ( euler.order === 'ZXY' ) { var ce = c * e, cf = c * f, de = d * e, df = d * f; te[ 0 ] = ce - df * b; te[ 4 ] = - a * f; te[ 8 ] = de + cf * b; te[ 1 ] = cf + de * b; te[ 5 ] = a * e; te[ 9 ] = df - ce * b; te[ 2 ] = - a * d; te[ 6 ] = b; te[ 10 ] = a * c; } else if ( euler.order === 'ZYX' ) { var ae = a * e, af = a * f, be = b * e, bf = b * f; te[ 0 ] = c * e; te[ 4 ] = be * d - af; te[ 8 ] = ae * d + bf; te[ 1 ] = c * f; te[ 5 ] = bf * d + ae; te[ 9 ] = af * d - be; te[ 2 ] = - d; te[ 6 ] = b * c; te[ 10 ] = a * c; } else if ( euler.order === 'YZX' ) { var ac = a * c, ad = a * d, bc = b * c, bd = b * d; te[ 0 ] = c * e; te[ 4 ] = bd - ac * f; te[ 8 ] = bc * f + ad; te[ 1 ] = f; te[ 5 ] = a * e; te[ 9 ] = - b * e; te[ 2 ] = - d * e; te[ 6 ] = ad * f + bc; te[ 10 ] = ac - bd * f; } else if ( euler.order === 'XZY' ) { var ac = a * c, ad = a * d, bc = b * c, bd = b * d; te[ 0 ] = c * e; te[ 4 ] = - f; te[ 8 ] = d * e; te[ 1 ] = ac * f + bd; te[ 5 ] = a * e; te[ 9 ] = ad * f - bc; te[ 2 ] = bc * f - ad; te[ 6 ] = b * e; te[ 10 ] = bd * f + ac; } // last column te[ 3 ] = 0; te[ 7 ] = 0; te[ 11 ] = 0; // bottom row te[ 12 ] = 0; te[ 13 ] = 0; te[ 14 ] = 0; te[ 15 ] = 1; return this; }, setRotationFromQuaternion: function ( q ) { console.warn( 'THREE.Matrix4: .setRotationFromQuaternion() has been renamed to .makeRotationFromQuaternion().' ); return this.makeRotationFromQuaternion( q ); }, makeRotationFromQuaternion: function ( q ) { var te = this.elements; var x = q.x, y = q.y, z = q.z, w = q.w; var x2 = x + x, y2 = y + y, z2 = z + z; var xx = x * x2, xy = x * y2, xz = x * z2; var yy = y * y2, yz = y * z2, zz = z * z2; var wx = w * x2, wy = w * y2, wz = w * z2; te[ 0 ] = 1 - ( yy + zz ); te[ 4 ] = xy - wz; te[ 8 ] = xz + wy; te[ 1 ] = xy + wz; te[ 5 ] = 1 - ( xx + zz ); te[ 9 ] = yz - wx; te[ 2 ] = xz - wy; te[ 6 ] = yz + wx; te[ 10 ] = 1 - ( xx + yy ); // last column te[ 3 ] = 0; te[ 7 ] = 0; te[ 11 ] = 0; // bottom row te[ 12 ] = 0; te[ 13 ] = 0; te[ 14 ] = 0; te[ 15 ] = 1; return this; }, lookAt: function () { var x = new THREE.Vector3(); var y = new THREE.Vector3(); var z = new THREE.Vector3(); return function ( eye, target, up ) { var te = this.elements; z.subVectors( eye, target ).normalize(); if ( z.length() === 0 ) { z.z = 1; } x.crossVectors( up, z ).normalize(); if ( x.length() === 0 ) { z.x += 0.0001; x.crossVectors( up, z ).normalize(); } y.crossVectors( z, x ); te[ 0 ] = x.x; te[ 4 ] = y.x; te[ 8 ] = z.x; te[ 1 ] = x.y; te[ 5 ] = y.y; te[ 9 ] = z.y; te[ 2 ] = x.z; te[ 6 ] = y.z; te[ 10 ] = z.z; return this; }; }(), multiply: function ( m, n ) { if ( n !== undefined ) { console.warn( 'THREE.Matrix4: .multiply() now only accepts one argument. Use .multiplyMatrices( a, b ) instead.' ); return this.multiplyMatrices( m, n ); } return this.multiplyMatrices( this, m ); }, multiplyMatrices: function ( a, b ) { var ae = a.elements; var be = b.elements; var te = this.elements; var a11 = ae[ 0 ], a12 = ae[ 4 ], a13 = ae[ 8 ], a14 = ae[ 12 ]; var a21 = ae[ 1 ], a22 = ae[ 5 ], a23 = ae[ 9 ], a24 = ae[ 13 ]; var a31 = ae[ 2 ], a32 = ae[ 6 ], a33 = ae[ 10 ], a34 = ae[ 14 ]; var a41 = ae[ 3 ], a42 = ae[ 7 ], a43 = ae[ 11 ], a44 = ae[ 15 ]; var b11 = be[ 0 ], b12 = be[ 4 ], b13 = be[ 8 ], b14 = be[ 12 ]; var b21 = be[ 1 ], b22 = be[ 5 ], b23 = be[ 9 ], b24 = be[ 13 ]; var b31 = be[ 2 ], b32 = be[ 6 ], b33 = be[ 10 ], b34 = be[ 14 ]; var b41 = be[ 3 ], b42 = be[ 7 ], b43 = be[ 11 ], b44 = be[ 15 ]; te[ 0 ] = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41; te[ 4 ] = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42; te[ 8 ] = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43; te[ 12 ] = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44; te[ 1 ] = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41; te[ 5 ] = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42; te[ 9 ] = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43; te[ 13 ] = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44; te[ 2 ] = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41; te[ 6 ] = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42; te[ 10 ] = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43; te[ 14 ] = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44; te[ 3 ] = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41; te[ 7 ] = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42; te[ 11 ] = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43; te[ 15 ] = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44; return this; }, multiplyToArray: function ( a, b, r ) { var te = this.elements; this.multiplyMatrices( a, b ); r[ 0 ] = te[ 0 ]; r[ 1 ] = te[ 1 ]; r[ 2 ] = te[ 2 ]; r[ 3 ] = te[ 3 ]; r[ 4 ] = te[ 4 ]; r[ 5 ] = te[ 5 ]; r[ 6 ] = te[ 6 ]; r[ 7 ] = te[ 7 ]; r[ 8 ] = te[ 8 ]; r[ 9 ] = te[ 9 ]; r[ 10 ] = te[ 10 ]; r[ 11 ] = te[ 11 ]; r[ 12 ] = te[ 12 ]; r[ 13 ] = te[ 13 ]; r[ 14 ] = te[ 14 ]; r[ 15 ] = te[ 15 ]; return this; }, multiplyScalar: function ( s ) { var te = this.elements; te[ 0 ] *= s; te[ 4 ] *= s; te[ 8 ] *= s; te[ 12 ] *= s; te[ 1 ] *= s; te[ 5 ] *= s; te[ 9 ] *= s; te[ 13 ] *= s; te[ 2 ] *= s; te[ 6 ] *= s; te[ 10 ] *= s; te[ 14 ] *= s; te[ 3 ] *= s; te[ 7 ] *= s; te[ 11 ] *= s; te[ 15 ] *= s; return this; }, multiplyVector3: function ( vector ) { console.warn( 'THREE.Matrix4: .multiplyVector3() has been removed. Use vector.applyMatrix4( matrix ) or vector.applyProjection( matrix ) instead.' ); return vector.applyProjection( this ); }, multiplyVector4: function ( vector ) { console.warn( 'THREE.Matrix4: .multiplyVector4() has been removed. Use vector.applyMatrix4( matrix ) instead.' ); return vector.applyMatrix4( this ); }, multiplyVector3Array: function ( a ) { console.warn( 'THREE.Matrix4: .multiplyVector3Array() has been renamed. Use matrix.applyToVector3Array( array ) instead.' ); return this.applyToVector3Array( a ); }, applyToVector3Array: function () { var v1 = new THREE.Vector3(); return function ( array, offset, length ) { if ( offset === undefined ) offset = 0; if ( length === undefined ) length = array.length; for ( var i = 0, j = offset, il; i < length; i += 3, j += 3 ) { v1.x = array[ j ]; v1.y = array[ j + 1 ]; v1.z = array[ j + 2 ]; v1.applyMatrix4( this ); array[ j ] = v1.x; array[ j + 1 ] = v1.y; array[ j + 2 ] = v1.z; } return array; }; }(), rotateAxis: function ( v ) { console.warn( 'THREE.Matrix4: .rotateAxis() has been removed. Use Vector3.transformDirection( matrix ) instead.' ); v.transformDirection( this ); }, crossVector: function ( vector ) { console.warn( 'THREE.Matrix4: .crossVector() has been removed. Use vector.applyMatrix4( matrix ) instead.' ); return vector.applyMatrix4( this ); }, determinant: function () { var te = this.elements; var n11 = te[ 0 ], n12 = te[ 4 ], n13 = te[ 8 ], n14 = te[ 12 ]; var n21 = te[ 1 ], n22 = te[ 5 ], n23 = te[ 9 ], n24 = te[ 13 ]; var n31 = te[ 2 ], n32 = te[ 6 ], n33 = te[ 10 ], n34 = te[ 14 ]; var n41 = te[ 3 ], n42 = te[ 7 ], n43 = te[ 11 ], n44 = te[ 15 ]; //TODO: make this more efficient //( based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm ) return ( n41 * ( + n14 * n23 * n32 - n13 * n24 * n32 - n14 * n22 * n33 + n12 * n24 * n33 + n13 * n22 * n34 - n12 * n23 * n34 ) + n42 * ( + n11 * n23 * n34 - n11 * n24 * n33 + n14 * n21 * n33 - n13 * n21 * n34 + n13 * n24 * n31 - n14 * n23 * n31 ) + n43 * ( + n11 * n24 * n32 - n11 * n22 * n34 - n14 * n21 * n32 + n12 * n21 * n34 + n14 * n22 * n31 - n12 * n24 * n31 ) + n44 * ( - n13 * n22 * n31 - n11 * n23 * n32 + n11 * n22 * n33 + n13 * n21 * n32 - n12 * n21 * n33 + n12 * n23 * n31 ) ); }, transpose: function () { var te = this.elements; var tmp; tmp = te[ 1 ]; te[ 1 ] = te[ 4 ]; te[ 4 ] = tmp; tmp = te[ 2 ]; te[ 2 ] = te[ 8 ]; te[ 8 ] = tmp; tmp = te[ 6 ]; te[ 6 ] = te[ 9 ]; te[ 9 ] = tmp; tmp = te[ 3 ]; te[ 3 ] = te[ 12 ]; te[ 12 ] = tmp; tmp = te[ 7 ]; te[ 7 ] = te[ 13 ]; te[ 13 ] = tmp; tmp = te[ 11 ]; te[ 11 ] = te[ 14 ]; te[ 14 ] = tmp; return this; }, flattenToArrayOffset: function ( array, offset ) { var te = this.elements; array[ offset ] = te[ 0 ]; array[ offset + 1 ] = te[ 1 ]; array[ offset + 2 ] = te[ 2 ]; array[ offset + 3 ] = te[ 3 ]; array[ offset + 4 ] = te[ 4 ]; array[ offset + 5 ] = te[ 5 ]; array[ offset + 6 ] = te[ 6 ]; array[ offset + 7 ] = te[ 7 ]; array[ offset + 8 ] = te[ 8 ]; array[ offset + 9 ] = te[ 9 ]; array[ offset + 10 ] = te[ 10 ]; array[ offset + 11 ] = te[ 11 ]; array[ offset + 12 ] = te[ 12 ]; array[ offset + 13 ] = te[ 13 ]; array[ offset + 14 ] = te[ 14 ]; array[ offset + 15 ] = te[ 15 ]; return array; }, getPosition: function () { var v1 = new THREE.Vector3(); return function () { console.warn( 'THREE.Matrix4: .getPosition() has been removed. Use Vector3.setFromMatrixPosition( matrix ) instead.' ); var te = this.elements; return v1.set( te[ 12 ], te[ 13 ], te[ 14 ] ); }; }(), setPosition: function ( v ) { var te = this.elements; te[ 12 ] = v.x; te[ 13 ] = v.y; te[ 14 ] = v.z; return this; }, getInverse: function ( m, throwOnInvertible ) { // based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm var te = this.elements; var me = m.elements; var n11 = me[ 0 ], n12 = me[ 4 ], n13 = me[ 8 ], n14 = me[ 12 ]; var n21 = me[ 1 ], n22 = me[ 5 ], n23 = me[ 9 ], n24 = me[ 13 ]; var n31 = me[ 2 ], n32 = me[ 6 ], n33 = me[ 10 ], n34 = me[ 14 ]; var n41 = me[ 3 ], n42 = me[ 7 ], n43 = me[ 11 ], n44 = me[ 15 ]; te[ 0 ] = n23 * n34 * n42 - n24 * n33 * n42 + n24 * n32 * n43 - n22 * n34 * n43 - n23 * n32 * n44 + n22 * n33 * n44; te[ 4 ] = n14 * n33 * n42 - n13 * n34 * n42 - n14 * n32 * n43 + n12 * n34 * n43 + n13 * n32 * n44 - n12 * n33 * n44; te[ 8 ] = n13 * n24 * n42 - n14 * n23 * n42 + n14 * n22 * n43 - n12 * n24 * n43 - n13 * n22 * n44 + n12 * n23 * n44; te[ 12 ] = n14 * n23 * n32 - n13 * n24 * n32 - n14 * n22 * n33 + n12 * n24 * n33 + n13 * n22 * n34 - n12 * n23 * n34; te[ 1 ] = n24 * n33 * n41 - n23 * n34 * n41 - n24 * n31 * n43 + n21 * n34 * n43 + n23 * n31 * n44 - n21 * n33 * n44; te[ 5 ] = n13 * n34 * n41 - n14 * n33 * n41 + n14 * n31 * n43 - n11 * n34 * n43 - n13 * n31 * n44 + n11 * n33 * n44; te[ 9 ] = n14 * n23 * n41 - n13 * n24 * n41 - n14 * n21 * n43 + n11 * n24 * n43 + n13 * n21 * n44 - n11 * n23 * n44; te[ 13 ] = n13 * n24 * n31 - n14 * n23 * n31 + n14 * n21 * n33 - n11 * n24 * n33 - n13 * n21 * n34 + n11 * n23 * n34; te[ 2 ] = n22 * n34 * n41 - n24 * n32 * n41 + n24 * n31 * n42 - n21 * n34 * n42 - n22 * n31 * n44 + n21 * n32 * n44; te[ 6 ] = n14 * n32 * n41 - n12 * n34 * n41 - n14 * n31 * n42 + n11 * n34 * n42 + n12 * n31 * n44 - n11 * n32 * n44; te[ 10 ] = n12 * n24 * n41 - n14 * n22 * n41 + n14 * n21 * n42 - n11 * n24 * n42 - n12 * n21 * n44 + n11 * n22 * n44; te[ 14 ] = n14 * n22 * n31 - n12 * n24 * n31 - n14 * n21 * n32 + n11 * n24 * n32 + n12 * n21 * n34 - n11 * n22 * n34; te[ 3 ] = n23 * n32 * n41 - n22 * n33 * n41 - n23 * n31 * n42 + n21 * n33 * n42 + n22 * n31 * n43 - n21 * n32 * n43; te[ 7 ] = n12 * n33 * n41 - n13 * n32 * n41 + n13 * n31 * n42 - n11 * n33 * n42 - n12 * n31 * n43 + n11 * n32 * n43; te[ 11 ] = n13 * n22 * n41 - n12 * n23 * n41 - n13 * n21 * n42 + n11 * n23 * n42 + n12 * n21 * n43 - n11 * n22 * n43; te[ 15 ] = n12 * n23 * n31 - n13 * n22 * n31 + n13 * n21 * n32 - n11 * n23 * n32 - n12 * n21 * n33 + n11 * n22 * n33; var det = n11 * te[ 0 ] + n21 * te[ 4 ] + n31 * te[ 8 ] + n41 * te[ 12 ]; if ( det == 0 ) { var msg = "Matrix4.getInverse(): can't invert matrix, determinant is 0"; if ( throwOnInvertible || false ) { throw new Error( msg ); } else { console.warn( msg ); } this.identity(); return this; } this.multiplyScalar( 1 / det ); return this; }, translate: function ( v ) { console.warn( 'THREE.Matrix4: .translate() has been removed.' ); }, rotateX: function ( angle ) { console.warn( 'THREE.Matrix4: .rotateX() has been removed.' ); }, rotateY: function ( angle ) { console.warn( 'THREE.Matrix4: .rotateY() has been removed.' ); }, rotateZ: function ( angle ) { console.warn( 'THREE.Matrix4: .rotateZ() has been removed.' ); }, rotateByAxis: function ( axis, angle ) { console.warn( 'THREE.Matrix4: .rotateByAxis() has been removed.' ); }, scale: function ( v ) { var te = this.elements; var x = v.x, y = v.y, z = v.z; te[ 0 ] *= x; te[ 4 ] *= y; te[ 8 ] *= z; te[ 1 ] *= x; te[ 5 ] *= y; te[ 9 ] *= z; te[ 2 ] *= x; te[ 6 ] *= y; te[ 10 ] *= z; te[ 3 ] *= x; te[ 7 ] *= y; te[ 11 ] *= z; return this; }, getMaxScaleOnAxis: function () { var te = this.elements; var scaleXSq = te[ 0 ] * te[ 0 ] + te[ 1 ] * te[ 1 ] + te[ 2 ] * te[ 2 ]; var scaleYSq = te[ 4 ] * te[ 4 ] + te[ 5 ] * te[ 5 ] + te[ 6 ] * te[ 6 ]; var scaleZSq = te[ 8 ] * te[ 8 ] + te[ 9 ] * te[ 9 ] + te[ 10 ] * te[ 10 ]; return Math.sqrt( Math.max( scaleXSq, Math.max( scaleYSq, scaleZSq ) ) ); }, makeTranslation: function ( x, y, z ) { this.set( 1, 0, 0, x, 0, 1, 0, y, 0, 0, 1, z, 0, 0, 0, 1 ); return this; }, makeRotationX: function ( theta ) { var c = Math.cos( theta ), s = Math.sin( theta ); this.set( 1, 0, 0, 0, 0, c, - s, 0, 0, s, c, 0, 0, 0, 0, 1 ); return this; }, makeRotationY: function ( theta ) { var c = Math.cos( theta ), s = Math.sin( theta ); this.set( c, 0, s, 0, 0, 1, 0, 0, - s, 0, c, 0, 0, 0, 0, 1 ); return this; }, makeRotationZ: function ( theta ) { var c = Math.cos( theta ), s = Math.sin( theta ); this.set( c, - s, 0, 0, s, c, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 ); return this; }, makeRotationAxis: function ( axis, angle ) { // Based on http://www.gamedev.net/reference/articles/article1199.asp var c = Math.cos( angle ); var s = Math.sin( angle ); var t = 1 - c; var x = axis.x, y = axis.y, z = axis.z; var tx = t * x, ty = t * y; this.set( tx * x + c, tx * y - s * z, tx * z + s * y, 0, tx * y + s * z, ty * y + c, ty * z - s * x, 0, tx * z - s * y, ty * z + s * x, t * z * z + c, 0, 0, 0, 0, 1 ); return this; }, makeScale: function ( x, y, z ) { this.set( x, 0, 0, 0, 0, y, 0, 0, 0, 0, z, 0, 0, 0, 0, 1 ); return this; }, compose: function ( position, quaternion, scale ) { this.makeRotationFromQuaternion( quaternion ); this.scale( scale ); this.setPosition( position ); return this; }, decompose: function () { var vector = new THREE.Vector3(); var matrix = new THREE.Matrix4(); return function ( position, quaternion, scale ) { var te = this.elements; var sx = vector.set( te[ 0 ], te[ 1 ], te[ 2 ] ).length(); var sy = vector.set( te[ 4 ], te[ 5 ], te[ 6 ] ).length(); var sz = vector.set( te[ 8 ], te[ 9 ], te[ 10 ] ).length(); // if determine is negative, we need to invert one scale var det = this.determinant(); if ( det < 0 ) { sx = - sx; } position.x = te[ 12 ]; position.y = te[ 13 ]; position.z = te[ 14 ]; // scale the rotation part matrix.elements.set( this.elements ); // at this point matrix is incomplete so we can't use .copy() var invSX = 1 / sx; var invSY = 1 / sy; var invSZ = 1 / sz; matrix.elements[ 0 ] *= invSX; matrix.elements[ 1 ] *= invSX; matrix.elements[ 2 ] *= invSX; matrix.elements[ 4 ] *= invSY; matrix.elements[ 5 ] *= invSY; matrix.elements[ 6 ] *= invSY; matrix.elements[ 8 ] *= invSZ; matrix.elements[ 9 ] *= invSZ; matrix.elements[ 10 ] *= invSZ; quaternion.setFromRotationMatrix( matrix ); scale.x = sx; scale.y = sy; scale.z = sz; return this; }; }(), makeFrustum: function ( left, right, bottom, top, near, far ) { var te = this.elements; var x = 2 * near / ( right - left ); var y = 2 * near / ( top - bottom ); var a = ( right + left ) / ( right - left ); var b = ( top + bottom ) / ( top - bottom ); var c = - ( far + near ) / ( far - near ); var d = - 2 * far * near / ( far - near ); te[ 0 ] = x; te[ 4 ] = 0; te[ 8 ] = a; te[ 12 ] = 0; te[ 1 ] = 0; te[ 5 ] = y; te[ 9 ] = b; te[ 13 ] = 0; te[ 2 ] = 0; te[ 6 ] = 0; te[ 10 ] = c; te[ 14 ] = d; te[ 3 ] = 0; te[ 7 ] = 0; te[ 11 ] = - 1; te[ 15 ] = 0; return this; }, makePerspective: function ( fov, aspect, near, far ) { var ymax = near * Math.tan( THREE.Math.degToRad( fov * 0.5 ) ); var ymin = - ymax; var xmin = ymin * aspect; var xmax = ymax * aspect; return this.makeFrustum( xmin, xmax, ymin, ymax, near, far ); }, makeOrthographic: function ( left, right, top, bottom, near, far ) { var te = this.elements; var w = right - left; var h = top - bottom; var p = far - near; var x = ( right + left ) / w; var y = ( top + bottom ) / h; var z = ( far + near ) / p; te[ 0 ] = 2 / w; te[ 4 ] = 0; te[ 8 ] = 0; te[ 12 ] = - x; te[ 1 ] = 0; te[ 5 ] = 2 / h; te[ 9 ] = 0; te[ 13 ] = - y; te[ 2 ] = 0; te[ 6 ] = 0; te[ 10 ] = - 2 / p; te[ 14 ] = - z; te[ 3 ] = 0; te[ 7 ] = 0; te[ 11 ] = 0; te[ 15 ] = 1; return this; }, fromArray: function ( array ) { this.elements.set( array ); return this; }, toArray: function () { var te = this.elements; return [ te[ 0 ], te[ 1 ], te[ 2 ], te[ 3 ], te[ 4 ], te[ 5 ], te[ 6 ], te[ 7 ], te[ 8 ], te[ 9 ], te[ 10 ], te[ 11 ], te[ 12 ], te[ 13 ], te[ 14 ], te[ 15 ] ]; }, clone: function () { return new THREE.Matrix4().fromArray( this.elements ); } }; // File:src/math/Ray.js /** * @author bhouston / http://exocortex.com */ THREE.Ray = function ( origin, direction ) { this.origin = ( origin !== undefined ) ? origin : new THREE.Vector3(); this.direction = ( direction !== undefined ) ? direction : new THREE.Vector3(); }; THREE.Ray.prototype = { constructor: THREE.Ray, set: function ( origin, direction ) { this.origin.copy( origin ); this.direction.copy( direction ); return this; }, copy: function ( ray ) { this.origin.copy( ray.origin ); this.direction.copy( ray.direction ); return this; }, at: function ( t, optionalTarget ) { var result = optionalTarget || new THREE.Vector3(); return result.copy( this.direction ).multiplyScalar( t ).add( this.origin ); }, recast: function () { var v1 = new THREE.Vector3(); return function ( t ) { this.origin.copy( this.at( t, v1 ) ); return this; }; }(), closestPointToPoint: function ( point, optionalTarget ) { var result = optionalTarget || new THREE.Vector3(); result.subVectors( point, this.origin ); var directionDistance = result.dot( this.direction ); if ( directionDistance < 0 ) { return result.copy( this.origin ); } return result.copy( this.direction ).multiplyScalar( directionDistance ).add( this.origin ); }, distanceToPoint: function () { var v1 = new THREE.Vector3(); return function ( point ) { var directionDistance = v1.subVectors( point, this.origin ).dot( this.direction ); // point behind the ray if ( directionDistance < 0 ) { return this.origin.distanceTo( point ); } v1.copy( this.direction ).multiplyScalar( directionDistance ).add( this.origin ); return v1.distanceTo( point ); }; }(), distanceSqToSegment: function ( v0, v1, optionalPointOnRay, optionalPointOnSegment ) { // from http://www.geometrictools.com/LibMathematics/Distance/Wm5DistRay3Segment3.cpp // It returns the min distance between the ray and the segment // defined by v0 and v1 // It can also set two optional targets : // - The closest point on the ray // - The closest point on the segment var segCenter = v0.clone().add( v1 ).multiplyScalar( 0.5 ); var segDir = v1.clone().sub( v0 ).normalize(); var segExtent = v0.distanceTo( v1 ) * 0.5; var diff = this.origin.clone().sub( segCenter ); var a01 = - this.direction.dot( segDir ); var b0 = diff.dot( this.direction ); var b1 = - diff.dot( segDir ); var c = diff.lengthSq(); var det = Math.abs( 1 - a01 * a01 ); var s0, s1, sqrDist, extDet; if ( det >= 0 ) { // The ray and segment are not parallel. s0 = a01 * b1 - b0; s1 = a01 * b0 - b1; extDet = segExtent * det; if ( s0 >= 0 ) { if ( s1 >= - extDet ) { if ( s1 <= extDet ) { // region 0 // Minimum at interior points of ray and segment. var invDet = 1 / det; s0 *= invDet; s1 *= invDet; sqrDist = s0 * ( s0 + a01 * s1 + 2 * b0 ) + s1 * ( a01 * s0 + s1 + 2 * b1 ) + c; } else { // region 1 s1 = segExtent; s0 = Math.max( 0, - ( a01 * s1 + b0 ) ); sqrDist = - s0 * s0 + s1 * ( s1 + 2 * b1 ) + c; } } else { // region 5 s1 = - segExtent; s0 = Math.max( 0, - ( a01 * s1 + b0 ) ); sqrDist = - s0 * s0 + s1 * ( s1 + 2 * b1 ) + c; } } else { if ( s1 <= - extDet ) { // region 4 s0 = Math.max( 0, - ( - a01 * segExtent + b0 ) ); s1 = ( s0 > 0 ) ? - segExtent : Math.min( Math.max( - segExtent, - b1 ), segExtent ); sqrDist = - s0 * s0 + s1 * ( s1 + 2 * b1 ) + c; } else if ( s1 <= extDet ) { // region 3 s0 = 0; s1 = Math.min( Math.max( - segExtent, - b1 ), segExtent ); sqrDist = s1 * ( s1 + 2 * b1 ) + c; } else { // region 2 s0 = Math.max( 0, - ( a01 * segExtent + b0 ) ); s1 = ( s0 > 0 ) ? segExtent : Math.min( Math.max( - segExtent, - b1 ), segExtent ); sqrDist = - s0 * s0 + s1 * ( s1 + 2 * b1 ) + c; } } } else { // Ray and segment are parallel. s1 = ( a01 > 0 ) ? - segExtent : segExtent; s0 = Math.max( 0, - ( a01 * s1 + b0 ) ); sqrDist = - s0 * s0 + s1 * ( s1 + 2 * b1 ) + c; } if ( optionalPointOnRay ) { optionalPointOnRay.copy( this.direction.clone().multiplyScalar( s0 ).add( this.origin ) ); } if ( optionalPointOnSegment ) { optionalPointOnSegment.copy( segDir.clone().multiplyScalar( s1 ).add( segCenter ) ); } return sqrDist; }, isIntersectionSphere: function ( sphere ) { return this.distanceToPoint( sphere.center ) <= sphere.radius; }, intersectSphere: function () { // from http://www.scratchapixel.com/lessons/3d-basic-lessons/lesson-7-intersecting-simple-shapes/ray-sphere-intersection/ var v1 = new THREE.Vector3(); return function ( sphere, optionalTarget ) { v1.subVectors( sphere.center, this.origin ); var tca = v1.dot( this.direction ); var d2 = v1.dot( v1 ) - tca * tca; var radius2 = sphere.radius * sphere.radius; if ( d2 > radius2 ) return null; var thc = Math.sqrt( radius2 - d2 ); // t0 = first intersect point - entrance on front of sphere var t0 = tca - thc; // t1 = second intersect point - exit point on back of sphere var t1 = tca + thc; // test to see if both t0 and t1 are behind the ray - if so, return null if ( t0 < 0 && t1 < 0 ) return null; // test to see if t0 is behind the ray: // if it is, the ray is inside the sphere, so return the second exit point scaled by t1, // in order to always return an intersect point that is in front of the ray. if ( t0 < 0 ) return this.at( t1, optionalTarget ); // else t0 is in front of the ray, so return the first collision point scaled by t0 return this.at( t0, optionalTarget ); } }(), isIntersectionPlane: function ( plane ) { // check if the ray lies on the plane first var distToPoint = plane.distanceToPoint( this.origin ); if ( distToPoint === 0 ) { return true; } var denominator = plane.normal.dot( this.direction ); if ( denominator * distToPoint < 0 ) { return true; } // ray origin is behind the plane (and is pointing behind it) return false; }, distanceToPlane: function ( plane ) { var denominator = plane.normal.dot( this.direction ); if ( denominator == 0 ) { // line is coplanar, return origin if ( plane.distanceToPoint( this.origin ) == 0 ) { return 0; } // Null is preferable to undefined since undefined means.... it is undefined return null; } var t = - ( this.origin.dot( plane.normal ) + plane.constant ) / denominator; // Return if the ray never intersects the plane return t >= 0 ? t : null; }, intersectPlane: function ( plane, optionalTarget ) { var t = this.distanceToPlane( plane ); if ( t === null ) { return null; } return this.at( t, optionalTarget ); }, isIntersectionBox: function () { var v = new THREE.Vector3(); return function ( box ) { return this.intersectBox( box, v ) !== null; }; }(), intersectBox: function ( box , optionalTarget ) { // http://www.scratchapixel.com/lessons/3d-basic-lessons/lesson-7-intersecting-simple-shapes/ray-box-intersection/ var tmin,tmax,tymin,tymax,tzmin,tzmax; var invdirx = 1 / this.direction.x, invdiry = 1 / this.direction.y, invdirz = 1 / this.direction.z; var origin = this.origin; if ( invdirx >= 0 ) { tmin = ( box.min.x - origin.x ) * invdirx; tmax = ( box.max.x - origin.x ) * invdirx; } else { tmin = ( box.max.x - origin.x ) * invdirx; tmax = ( box.min.x - origin.x ) * invdirx; } if ( invdiry >= 0 ) { tymin = ( box.min.y - origin.y ) * invdiry; tymax = ( box.max.y - origin.y ) * invdiry; } else { tymin = ( box.max.y - origin.y ) * invdiry; tymax = ( box.min.y - origin.y ) * invdiry; } if ( ( tmin > tymax ) || ( tymin > tmax ) ) return null; // These lines also handle the case where tmin or tmax is NaN // (result of 0 * Infinity). x !== x returns true if x is NaN if ( tymin > tmin || tmin !== tmin ) tmin = tymin; if ( tymax < tmax || tmax !== tmax ) tmax = tymax; if ( invdirz >= 0 ) { tzmin = ( box.min.z - origin.z ) * invdirz; tzmax = ( box.max.z - origin.z ) * invdirz; } else { tzmin = ( box.max.z - origin.z ) * invdirz; tzmax = ( box.min.z - origin.z ) * invdirz; } if ( ( tmin > tzmax ) || ( tzmin > tmax ) ) return null; if ( tzmin > tmin || tmin !== tmin ) tmin = tzmin; if ( tzmax < tmax || tmax !== tmax ) tmax = tzmax; //return point closest to the ray (positive side) if ( tmax < 0 ) return null; return this.at( tmin >= 0 ? tmin : tmax, optionalTarget ); }, intersectTriangle: function () { // Compute the offset origin, edges, and normal. var diff = new THREE.Vector3(); var edge1 = new THREE.Vector3(); var edge2 = new THREE.Vector3(); var normal = new THREE.Vector3(); return function ( a, b, c, backfaceCulling, optionalTarget ) { // from http://www.geometrictools.com/LibMathematics/Intersection/Wm5IntrRay3Triangle3.cpp edge1.subVectors( b, a ); edge2.subVectors( c, a ); normal.crossVectors( edge1, edge2 ); // Solve Q + t*D = b1*E1 + b2*E2 (Q = kDiff, D = ray direction, // E1 = kEdge1, E2 = kEdge2, N = Cross(E1,E2)) by // |Dot(D,N)|*b1 = sign(Dot(D,N))*Dot(D,Cross(Q,E2)) // |Dot(D,N)|*b2 = sign(Dot(D,N))*Dot(D,Cross(E1,Q)) // |Dot(D,N)|*t = -sign(Dot(D,N))*Dot(Q,N) var DdN = this.direction.dot( normal ); var sign; if ( DdN > 0 ) { if ( backfaceCulling ) return null; sign = 1; } else if ( DdN < 0 ) { sign = - 1; DdN = - DdN; } else { return null; } diff.subVectors( this.origin, a ); var DdQxE2 = sign * this.direction.dot( edge2.crossVectors( diff, edge2 ) ); // b1 < 0, no intersection if ( DdQxE2 < 0 ) { return null; } var DdE1xQ = sign * this.direction.dot( edge1.cross( diff ) ); // b2 < 0, no intersection if ( DdE1xQ < 0 ) { return null; } // b1+b2 > 1, no intersection if ( DdQxE2 + DdE1xQ > DdN ) { return null; } // Line intersects triangle, check if ray does. var QdN = - sign * diff.dot( normal ); // t < 0, no intersection if ( QdN < 0 ) { return null; } // Ray intersects triangle. return this.at( QdN / DdN, optionalTarget ); }; }(), applyMatrix4: function ( matrix4 ) { this.direction.add( this.origin ).applyMatrix4( matrix4 ); this.origin.applyMatrix4( matrix4 ); this.direction.sub( this.origin ); this.direction.normalize(); return this; }, equals: function ( ray ) { return ray.origin.equals( this.origin ) && ray.direction.equals( this.direction ); }, clone: function () { return new THREE.Ray().copy( this ); } }; // File:src/math/Sphere.js /** * @author bhouston / http://exocortex.com * @author mrdoob / http://mrdoob.com/ */ THREE.Sphere = function ( center, radius ) { this.center = ( center !== undefined ) ? center : new THREE.Vector3(); this.radius = ( radius !== undefined ) ? radius : 0; }; THREE.Sphere.prototype = { constructor: THREE.Sphere, set: function ( center, radius ) { this.center.copy( center ); this.radius = radius; return this; }, setFromPoints: function () { var box = new THREE.Box3(); return function ( points, optionalCenter ) { var center = this.center; if ( optionalCenter !== undefined ) { center.copy( optionalCenter ); } else { box.setFromPoints( points ).center( center ); } var maxRadiusSq = 0; for ( var i = 0, il = points.length; i < il; i ++ ) { maxRadiusSq = Math.max( maxRadiusSq, center.distanceToSquared( points[ i ] ) ); } this.radius = Math.sqrt( maxRadiusSq ); return this; }; }(), copy: function ( sphere ) { this.center.copy( sphere.center ); this.radius = sphere.radius; return this; }, empty: function () { return ( this.radius <= 0 ); }, containsPoint: function ( point ) { return ( point.distanceToSquared( this.center ) <= ( this.radius * this.radius ) ); }, distanceToPoint: function ( point ) { return ( point.distanceTo( this.center ) - this.radius ); }, intersectsSphere: function ( sphere ) { var radiusSum = this.radius + sphere.radius; return sphere.center.distanceToSquared( this.center ) <= ( radiusSum * radiusSum ); }, clampPoint: function ( point, optionalTarget ) { var deltaLengthSq = this.center.distanceToSquared( point ); var result = optionalTarget || new THREE.Vector3(); result.copy( point ); if ( deltaLengthSq > ( this.radius * this.radius ) ) { result.sub( this.center ).normalize(); result.multiplyScalar( this.radius ).add( this.center ); } return result; }, getBoundingBox: function ( optionalTarget ) { var box = optionalTarget || new THREE.Box3(); box.set( this.center, this.center ); box.expandByScalar( this.radius ); return box; }, applyMatrix4: function ( matrix ) { this.center.applyMatrix4( matrix ); this.radius = this.radius * matrix.getMaxScaleOnAxis(); return this; }, translate: function ( offset ) { this.center.add( offset ); return this; }, equals: function ( sphere ) { return sphere.center.equals( this.center ) && ( sphere.radius === this.radius ); }, clone: function () { return new THREE.Sphere().copy( this ); } }; // File:src/math/Frustum.js /** * @author mrdoob / http://mrdoob.com/ * @author alteredq / http://alteredqualia.com/ * @author bhouston / http://exocortex.com */ THREE.Frustum = function ( p0, p1, p2, p3, p4, p5 ) { this.planes = [ ( p0 !== undefined ) ? p0 : new THREE.Plane(), ( p1 !== undefined ) ? p1 : new THREE.Plane(), ( p2 !== undefined ) ? p2 : new THREE.Plane(), ( p3 !== undefined ) ? p3 : new THREE.Plane(), ( p4 !== undefined ) ? p4 : new THREE.Plane(), ( p5 !== undefined ) ? p5 : new THREE.Plane() ]; }; THREE.Frustum.prototype = { constructor: THREE.Frustum, set: function ( p0, p1, p2, p3, p4, p5 ) { var planes = this.planes; planes[ 0 ].copy( p0 ); planes[ 1 ].copy( p1 ); planes[ 2 ].copy( p2 ); planes[ 3 ].copy( p3 ); planes[ 4 ].copy( p4 ); planes[ 5 ].copy( p5 ); return this; }, copy: function ( frustum ) { var planes = this.planes; for ( var i = 0; i < 6; i ++ ) { planes[ i ].copy( frustum.planes[ i ] ); } return this; }, setFromMatrix: function ( m ) { var planes = this.planes; var me = m.elements; var me0 = me[ 0 ], me1 = me[ 1 ], me2 = me[ 2 ], me3 = me[ 3 ]; var me4 = me[ 4 ], me5 = me[ 5 ], me6 = me[ 6 ], me7 = me[ 7 ]; var me8 = me[ 8 ], me9 = me[ 9 ], me10 = me[ 10 ], me11 = me[ 11 ]; var me12 = me[ 12 ], me13 = me[ 13 ], me14 = me[ 14 ], me15 = me[ 15 ]; planes[ 0 ].setComponents( me3 - me0, me7 - me4, me11 - me8, me15 - me12 ).normalize(); planes[ 1 ].setComponents( me3 + me0, me7 + me4, me11 + me8, me15 + me12 ).normalize(); planes[ 2 ].setComponents( me3 + me1, me7 + me5, me11 + me9, me15 + me13 ).normalize(); planes[ 3 ].setComponents( me3 - me1, me7 - me5, me11 - me9, me15 - me13 ).normalize(); planes[ 4 ].setComponents( me3 - me2, me7 - me6, me11 - me10, me15 - me14 ).normalize(); planes[ 5 ].setComponents( me3 + me2, me7 + me6, me11 + me10, me15 + me14 ).normalize(); return this; }, intersectsObject: function () { var sphere = new THREE.Sphere(); return function ( object ) { var geometry = object.geometry; if ( geometry.boundingSphere === null ) geometry.computeBoundingSphere(); sphere.copy( geometry.boundingSphere ); sphere.applyMatrix4( object.matrixWorld ); return this.intersectsSphere( sphere ); }; }(), intersectsSphere: function ( sphere ) { var planes = this.planes; var center = sphere.center; var negRadius = - sphere.radius; for ( var i = 0; i < 6; i ++ ) { var distance = planes[ i ].distanceToPoint( center ); if ( distance < negRadius ) { return false; } } return true; }, intersectsBox: function () { var p1 = new THREE.Vector3(), p2 = new THREE.Vector3(); return function ( box ) { var planes = this.planes; for ( var i = 0; i < 6 ; i ++ ) { var plane = planes[ i ]; p1.x = plane.normal.x > 0 ? box.min.x : box.max.x; p2.x = plane.normal.x > 0 ? box.max.x : box.min.x; p1.y = plane.normal.y > 0 ? box.min.y : box.max.y; p2.y = plane.normal.y > 0 ? box.max.y : box.min.y; p1.z = plane.normal.z > 0 ? box.min.z : box.max.z; p2.z = plane.normal.z > 0 ? box.max.z : box.min.z; var d1 = plane.distanceToPoint( p1 ); var d2 = plane.distanceToPoint( p2 ); // if both outside plane, no intersection if ( d1 < 0 && d2 < 0 ) { return false; } } return true; }; }(), containsPoint: function ( point ) { var planes = this.planes; for ( var i = 0; i < 6; i ++ ) { if ( planes[ i ].distanceToPoint( point ) < 0 ) { return false; } } return true; }, clone: function () { return new THREE.Frustum().copy( this ); } }; // File:src/math/Plane.js /** * @author bhouston / http://exocortex.com */ THREE.Plane = function ( normal, constant ) { this.normal = ( normal !== undefined ) ? normal : new THREE.Vector3( 1, 0, 0 ); this.constant = ( constant !== undefined ) ? constant : 0; }; THREE.Plane.prototype = { constructor: THREE.Plane, set: function ( normal, constant ) { this.normal.copy( normal ); this.constant = constant; return this; }, setComponents: function ( x, y, z, w ) { this.normal.set( x, y, z ); this.constant = w; return this; }, setFromNormalAndCoplanarPoint: function ( normal, point ) { this.normal.copy( normal ); this.constant = - point.dot( this.normal ); // must be this.normal, not normal, as this.normal is normalized return this; }, setFromCoplanarPoints: function () { var v1 = new THREE.Vector3(); var v2 = new THREE.Vector3(); return function ( a, b, c ) { var normal = v1.subVectors( c, b ).cross( v2.subVectors( a, b ) ).normalize(); // Q: should an error be thrown if normal is zero (e.g. degenerate plane)? this.setFromNormalAndCoplanarPoint( normal, a ); return this; }; }(), copy: function ( plane ) { this.normal.copy( plane.normal ); this.constant = plane.constant; return this; }, normalize: function () { // Note: will lead to a divide by zero if the plane is invalid. var inverseNormalLength = 1.0 / this.normal.length(); this.normal.multiplyScalar( inverseNormalLength ); this.constant *= inverseNormalLength; return this; }, negate: function () { this.constant *= - 1; this.normal.negate(); return this; }, distanceToPoint: function ( point ) { return this.normal.dot( point ) + this.constant; }, distanceToSphere: function ( sphere ) { return this.distanceToPoint( sphere.center ) - sphere.radius; }, projectPoint: function ( point, optionalTarget ) { return this.orthoPoint( point, optionalTarget ).sub( point ).negate(); }, orthoPoint: function ( point, optionalTarget ) { var perpendicularMagnitude = this.distanceToPoint( point ); var result = optionalTarget || new THREE.Vector3(); return result.copy( this.normal ).multiplyScalar( perpendicularMagnitude ); }, isIntersectionLine: function ( line ) { // Note: this tests if a line intersects the plane, not whether it (or its end-points) are coplanar with it. var startSign = this.distanceToPoint( line.start ); var endSign = this.distanceToPoint( line.end ); return ( startSign < 0 && endSign > 0 ) || ( endSign < 0 && startSign > 0 ); }, intersectLine: function () { var v1 = new THREE.Vector3(); return function ( line, optionalTarget ) { var result = optionalTarget || new THREE.Vector3(); var direction = line.delta( v1 ); var denominator = this.normal.dot( direction ); if ( denominator == 0 ) { // line is coplanar, return origin if ( this.distanceToPoint( line.start ) == 0 ) { return result.copy( line.start ); } // Unsure if this is the correct method to handle this case. return undefined; } var t = - ( line.start.dot( this.normal ) + this.constant ) / denominator; if ( t < 0 || t > 1 ) { return undefined; } return result.copy( direction ).multiplyScalar( t ).add( line.start ); }; }(), coplanarPoint: function ( optionalTarget ) { var result = optionalTarget || new THREE.Vector3(); return result.copy( this.normal ).multiplyScalar( - this.constant ); }, applyMatrix4: function () { var v1 = new THREE.Vector3(); var v2 = new THREE.Vector3(); var m1 = new THREE.Matrix3(); return function ( matrix, optionalNormalMatrix ) { // compute new normal based on theory here: // http://www.songho.ca/opengl/gl_normaltransform.html var normalMatrix = optionalNormalMatrix || m1.getNormalMatrix( matrix ); var newNormal = v1.copy( this.normal ).applyMatrix3( normalMatrix ); var newCoplanarPoint = this.coplanarPoint( v2 ); newCoplanarPoint.applyMatrix4( matrix ); this.setFromNormalAndCoplanarPoint( newNormal, newCoplanarPoint ); return this; }; }(), translate: function ( offset ) { this.constant = this.constant - offset.dot( this.normal ); return this; }, equals: function ( plane ) { return plane.normal.equals( this.normal ) && ( plane.constant == this.constant ); }, clone: function () { return new THREE.Plane().copy( this ); } }; // File:src/math/Math.js /** * @author alteredq / http://alteredqualia.com/ * @author mrdoob / http://mrdoob.com/ */ THREE.Math = { generateUUID: function () { // http://www.broofa.com/Tools/Math.uuid.htm var chars = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'.split( '' ); var uuid = new Array( 36 ); var rnd = 0, r; return function () { for ( var i = 0; i < 36; i ++ ) { if ( i == 8 || i == 13 || i == 18 || i == 23 ) { uuid[ i ] = '-'; } else if ( i == 14 ) { uuid[ i ] = '4'; } else { if ( rnd <= 0x02 ) rnd = 0x2000000 + ( Math.random() * 0x1000000 ) | 0; r = rnd & 0xf; rnd = rnd >> 4; uuid[ i ] = chars[ ( i == 19 ) ? ( r & 0x3 ) | 0x8 : r ]; } } return uuid.join( '' ); }; }(), // Clamp value to range clamp: function ( x, a, b ) { return ( x < a ) ? a : ( ( x > b ) ? b : x ); }, // Clamp value to range to range mapLinear: function ( x, a1, a2, b1, b2 ) { return b1 + ( x - a1 ) * ( b2 - b1 ) / ( a2 - a1 ); }, // http://en.wikipedia.org/wiki/Smoothstep smoothstep: function ( x, min, max ) { if ( x <= min ) return 0; if ( x >= max ) return 1; x = ( x - min ) / ( max - min ); return x * x * ( 3 - 2 * x ); }, smootherstep: function ( x, min, max ) { if ( x <= min ) return 0; if ( x >= max ) return 1; x = ( x - min ) / ( max - min ); return x * x * x * ( x * ( x * 6 - 15 ) + 10 ); }, // Random float from <0, 1> with 16 bits of randomness // (standard Math.random() creates repetitive patterns when applied over larger space) random16: function () { return ( 65280 * Math.random() + 255 * Math.random() ) / 65535; }, // Random integer from interval randInt: function ( low, high ) { return low + Math.floor( Math.random() * ( high - low + 1 ) ); }, // Random float from interval randFloat: function ( low, high ) { return low + Math.random() * ( high - low ); }, // Random float from <-range/2, range/2> interval randFloatSpread: function ( range ) { return range * ( 0.5 - Math.random() ); }, sign: function ( x ) { return ( x < 0 ) ? - 1 : ( x > 0 ) ? 1 : 0; }, degToRad: function () { var degreeToRadiansFactor = Math.PI / 180; return function ( degrees ) { return degrees * degreeToRadiansFactor; }; }(), radToDeg: function () { var radianToDegreesFactor = 180 / Math.PI; return function ( radians ) { return radians * radianToDegreesFactor; }; }(), isPowerOfTwo: function ( value ) { return ( value & ( value - 1 ) ) === 0 && value !== 0; } }; // File:src/math/Spline.js /** * Spline from Tween.js, slightly optimized (and trashed) * http://sole.github.com/tween.js/examples/05_spline.html * * @author mrdoob / http://mrdoob.com/ * @author alteredq / http://alteredqualia.com/ */ THREE.Spline = function ( points ) { this.points = points; var c = [], v3 = { x: 0, y: 0, z: 0 }, point, intPoint, weight, w2, w3, pa, pb, pc, pd; this.initFromArray = function ( a ) { this.points = []; for ( var i = 0; i < a.length; i ++ ) { this.points[ i ] = { x: a[ i ][ 0 ], y: a[ i ][ 1 ], z: a[ i ][ 2 ] }; } }; this.getPoint = function ( k ) { point = ( this.points.length - 1 ) * k; intPoint = Math.floor( point ); weight = point - intPoint; c[ 0 ] = intPoint === 0 ? intPoint : intPoint - 1; c[ 1 ] = intPoint; c[ 2 ] = intPoint > this.points.length - 2 ? this.points.length - 1 : intPoint + 1; c[ 3 ] = intPoint > this.points.length - 3 ? this.points.length - 1 : intPoint + 2; pa = this.points[ c[ 0 ] ]; pb = this.points[ c[ 1 ] ]; pc = this.points[ c[ 2 ] ]; pd = this.points[ c[ 3 ] ]; w2 = weight * weight; w3 = weight * w2; v3.x = interpolate( pa.x, pb.x, pc.x, pd.x, weight, w2, w3 ); v3.y = interpolate( pa.y, pb.y, pc.y, pd.y, weight, w2, w3 ); v3.z = interpolate( pa.z, pb.z, pc.z, pd.z, weight, w2, w3 ); return v3; }; this.getControlPointsArray = function () { var i, p, l = this.points.length, coords = []; for ( i = 0; i < l; i ++ ) { p = this.points[ i ]; coords[ i ] = [ p.x, p.y, p.z ]; } return coords; }; // approximate length by summing linear segments this.getLength = function ( nSubDivisions ) { var i, index, nSamples, position, point = 0, intPoint = 0, oldIntPoint = 0, oldPosition = new THREE.Vector3(), tmpVec = new THREE.Vector3(), chunkLengths = [], totalLength = 0; // first point has 0 length chunkLengths[ 0 ] = 0; if ( ! nSubDivisions ) nSubDivisions = 100; nSamples = this.points.length * nSubDivisions; oldPosition.copy( this.points[ 0 ] ); for ( i = 1; i < nSamples; i ++ ) { index = i / nSamples; position = this.getPoint( index ); tmpVec.copy( position ); totalLength += tmpVec.distanceTo( oldPosition ); oldPosition.copy( position ); point = ( this.points.length - 1 ) * index; intPoint = Math.floor( point ); if ( intPoint != oldIntPoint ) { chunkLengths[ intPoint ] = totalLength; oldIntPoint = intPoint; } } // last point ends with total length chunkLengths[ chunkLengths.length ] = totalLength; return { chunks: chunkLengths, total: totalLength }; }; this.reparametrizeByArcLength = function ( samplingCoef ) { var i, j, index, indexCurrent, indexNext, linearDistance, realDistance, sampling, position, newpoints = [], tmpVec = new THREE.Vector3(), sl = this.getLength(); newpoints.push( tmpVec.copy( this.points[ 0 ] ).clone() ); for ( i = 1; i < this.points.length; i ++ ) { //tmpVec.copy( this.points[ i - 1 ] ); //linearDistance = tmpVec.distanceTo( this.points[ i ] ); realDistance = sl.chunks[ i ] - sl.chunks[ i - 1 ]; sampling = Math.ceil( samplingCoef * realDistance / sl.total ); indexCurrent = ( i - 1 ) / ( this.points.length - 1 ); indexNext = i / ( this.points.length - 1 ); for ( j = 1; j < sampling - 1; j ++ ) { index = indexCurrent + j * ( 1 / sampling ) * ( indexNext - indexCurrent ); position = this.getPoint( index ); newpoints.push( tmpVec.copy( position ).clone() ); } newpoints.push( tmpVec.copy( this.points[ i ] ).clone() ); } this.points = newpoints; }; // Catmull-Rom function interpolate( p0, p1, p2, p3, t, t2, t3 ) { var v0 = ( p2 - p0 ) * 0.5, v1 = ( p3 - p1 ) * 0.5; return ( 2 * ( p1 - p2 ) + v0 + v1 ) * t3 + ( - 3 * ( p1 - p2 ) - 2 * v0 - v1 ) * t2 + v0 * t + p1; }; }; // File:src/math/Triangle.js /** * @author bhouston / http://exocortex.com * @author mrdoob / http://mrdoob.com/ */ THREE.Triangle = function ( a, b, c ) { this.a = ( a !== undefined ) ? a : new THREE.Vector3(); this.b = ( b !== undefined ) ? b : new THREE.Vector3(); this.c = ( c !== undefined ) ? c : new THREE.Vector3(); }; THREE.Triangle.normal = function () { var v0 = new THREE.Vector3(); return function ( a, b, c, optionalTarget ) { var result = optionalTarget || new THREE.Vector3(); result.subVectors( c, b ); v0.subVectors( a, b ); result.cross( v0 ); var resultLengthSq = result.lengthSq(); if ( resultLengthSq > 0 ) { return result.multiplyScalar( 1 / Math.sqrt( resultLengthSq ) ); } return result.set( 0, 0, 0 ); }; }(); // static/instance method to calculate barycoordinates // based on: http://www.blackpawn.com/texts/pointinpoly/default.html THREE.Triangle.barycoordFromPoint = function () { var v0 = new THREE.Vector3(); var v1 = new THREE.Vector3(); var v2 = new THREE.Vector3(); return function ( point, a, b, c, optionalTarget ) { v0.subVectors( c, a ); v1.subVectors( b, a ); v2.subVectors( point, a ); var dot00 = v0.dot( v0 ); var dot01 = v0.dot( v1 ); var dot02 = v0.dot( v2 ); var dot11 = v1.dot( v1 ); var dot12 = v1.dot( v2 ); var denom = ( dot00 * dot11 - dot01 * dot01 ); var result = optionalTarget || new THREE.Vector3(); // colinear or singular triangle if ( denom == 0 ) { // arbitrary location outside of triangle? // not sure if this is the best idea, maybe should be returning undefined return result.set( - 2, - 1, - 1 ); } var invDenom = 1 / denom; var u = ( dot11 * dot02 - dot01 * dot12 ) * invDenom; var v = ( dot00 * dot12 - dot01 * dot02 ) * invDenom; // barycoordinates must always sum to 1 return result.set( 1 - u - v, v, u ); }; }(); THREE.Triangle.containsPoint = function () { var v1 = new THREE.Vector3(); return function ( point, a, b, c ) { var result = THREE.Triangle.barycoordFromPoint( point, a, b, c, v1 ); return ( result.x >= 0 ) && ( result.y >= 0 ) && ( ( result.x + result.y ) <= 1 ); }; }(); THREE.Triangle.prototype = { constructor: THREE.Triangle, set: function ( a, b, c ) { this.a.copy( a ); this.b.copy( b ); this.c.copy( c ); return this; }, setFromPointsAndIndices: function ( points, i0, i1, i2 ) { this.a.copy( points[ i0 ] ); this.b.copy( points[ i1 ] ); this.c.copy( points[ i2 ] ); return this; }, copy: function ( triangle ) { this.a.copy( triangle.a ); this.b.copy( triangle.b ); this.c.copy( triangle.c ); return this; }, area: function () { var v0 = new THREE.Vector3(); var v1 = new THREE.Vector3(); return function () { v0.subVectors( this.c, this.b ); v1.subVectors( this.a, this.b ); return v0.cross( v1 ).length() * 0.5; }; }(), midpoint: function ( optionalTarget ) { var result = optionalTarget || new THREE.Vector3(); return result.addVectors( this.a, this.b ).add( this.c ).multiplyScalar( 1 / 3 ); }, normal: function ( optionalTarget ) { return THREE.Triangle.normal( this.a, this.b, this.c, optionalTarget ); }, plane: function ( optionalTarget ) { var result = optionalTarget || new THREE.Plane(); return result.setFromCoplanarPoints( this.a, this.b, this.c ); }, barycoordFromPoint: function ( point, optionalTarget ) { return THREE.Triangle.barycoordFromPoint( point, this.a, this.b, this.c, optionalTarget ); }, containsPoint: function ( point ) { return THREE.Triangle.containsPoint( point, this.a, this.b, this.c ); }, equals: function ( triangle ) { return triangle.a.equals( this.a ) && triangle.b.equals( this.b ) && triangle.c.equals( this.c ); }, clone: function () { return new THREE.Triangle().copy( this ); } };