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name matsandvects matrices and vector helper libary Helper functions function argumentsToArray args return concat apply Array prototype slice apply args function radians degrees return degrees Math PI 180 0 Vector Constructors function vec2 var result argumentsToArray arguments switch result length case 0 result push 0 0 case 1 result push 0 0 return result splice 0 2 function vec3 var result argumentsToArray arguments switch result length case 0 result push 0 0 case 1 result push 0 0 case 2 result push 0 0 return result splice 0 3 function vec4 var result argumentsToArray arguments switch result length case 0 result push 0 0 case 1 result push 0 0 case 2 result push 0 0 case 3 result push 1 0 return result splice 0 4 Matrix Constructors function mat2 var v argumentsToArray arguments var m switch v length case 0 v 0 1 case 1 m vec2 v 0 0 0 vec2 0 0 v 0 break default m push vec2 v v splice 0 2 m push vec2 v break m matrix true return m function mat3 var v argumentsToArray arguments var m switch v length case 0 v 0 1 case 1 m vec3 v 0 0 0 0 0 vec3 0 0 v 0 0 0 vec3 0 0 0 0 v 0 break default m push vec3 v v splice 0 3 m push vec3 v v splice 0 3 m push vec3 v break m matrix true return m function mat4 var v argumentsToArray arguments var m switch v length case 0 v 0 1 case 1 m vec4 v 0 0 0 0 0 0 0 vec4 0 0 v 0 0 0 0 0 vec4 0 0 0 0 v 0 0 0 vec4 0 0 0 0 0 0 v 0 break default m push vec4 v v splice 0 4 m push vec4 v v splice 0 4 m push vec4 v v splice 0 4 m push vec4 v break m matrix true return m Generic Mathematical Operations for Vectors and Matrices function equal u v if u length v length return false if u matrix v matrix for var i 0 i u length i if u i length v i length return false for var j 0 j u i length j if u i j v i j return false else if u matrix v matrix u matrix v matrix return false else for var i 0 i u length i if u i v i return false return true function add u v var result if u matrix v matrix if u length v length throw add trying to add matrices of different dimensions for var i 0 i u length i if u i length v i length throw add trying to add matrices of different dimensions result push for var j 0 j u i length j result i push u i j v i j result matrix true return result else if u matrix v matrix u matrix v matrix throw add trying to add matrix and non matrix variables else if u length v length throw add vectors are not the same dimension for var i 0 i u length i result push u i v i return result function subtract u v var result if u matrix v matrix if u length v length throw subtract trying to subtract matrices of different dimensions for var i 0 i u length i if u i length v i length throw subtract trying to subtact matrices of different dimensions result push for var j 0 j u i length j result i push u i j v i j result matrix true return result else if u matrix v matrix u matrix v matrix throw subtact trying to subtact matrix and non matrix variables else if u length v length throw subtract vectors are not the same length for var i 0 i u length i result push u i v i return result function mult u v var result if u matrix v matrix if u length v length throw mult trying to add matrices of different dimensions for var i 0 i u length i if u i length v i length throw mult trying to add matrices of different dimensions for var i 0 i u length i result push for var j 0 j v length j var sum 0 0 for var k 0 k u length k sum u i k v k j result i push sum result matrix true return result else if u length v length throw mult vectors are not the same dimension for var i 0 i u length i result push u i v i return result function distance a b return Math sqrt Math pow a 0 b 0 2 Math pow a 1 b 1 2 Math pow a 2 b 2 2 function midpoint a b return vec3 a 0 b 0 2 a 1 b 1 2 a 2 b 2 2 function hashcode v return v join function perturb a size factor var x var y var z if Math random 0 5 x a 0 Math random size factor else x a 0 Math random size factor if Math random 0 5 y a 1 Math random size factor else y a 1 Math random size factor if Math random 0 5 z a 2 Math random size factor else z a 2 Math random size factor return vec3 x y z do linear interpolation for n points from u to v function interpolate u v n var interpolatedPoints var difference subtract v u var delta scale 1 n 1 difference var point u for var i 0 i n i point add point delta interpolatedPoints push point return interpolatedPoints Basic Transformation Matrix Generators function translate x y z if Array isArray x x length 3 z x 2 y x 1 x x 0 var result mat4 result 0 3 x result 1 3 y result 2 3 z return result function rotate angle axis if Array isArray axis axis arguments 1 arguments 2 arguments 3 var v normalize axis var x v 0 var y v 1 var z v 2 var c Math cos radians angle var omc 1 0 c var s Math sin radians angle var result mat4 vec4 x x omc c x y omc z s x z omc y s 0 0 vec4 x y omc z s y y omc c y z omc x s 0 0 vec4 x z omc y s y z omc x s z z omc c 0 0 vec4 return result function scalem x y z if Array isArray x x length 3 z x 2 y x 1 x x 0 var result mat4 result 0 0 x result 1 1 y result 2 2 z return result ModelView Matrix Generators function lookAt eye at up if Array isArray eye eye length 3 throw lookAt first parameter eye must be an a vec3 if Array isArray at at length 3 throw lookAt first parameter at must be an a vec3 if Array isArray up up length 3 throw lookAt first parameter up must be an a vec3 if equal eye at return mat4 var v normalize subtract at eye view direction vector var n normalize cross v up perpendicular vector var u normalize cross n v new up vector v negate v var result mat4 vec4 n dot n eye vec4 u dot u eye vec4 v dot v eye vec4 return result Projection Matrix Generators function ortho left right bottom top near far if left right throw ortho left and right are equal if bottom top throw ortho bottom and top are equal if near far throw ortho near and far are equal var w right left var h top bottom var d far near var result mat4 result 0 0 2 0 w result 1 1 2 0 h result 2 2 2 0 d result 0 3 left right w result 1 3 top bottom h result 2 3 near far d return result function perspective fovy aspect near far var f 1 0 Math tan radians fovy 2 var d far near var result mat4 result 0 0 f aspect result 1 1 f result 2 2 near far d result 2 3 2 near far d result 3 2 1 result 3 3 0 0 return result Matrix Functions function transpose m if m matrix return transpose trying to transpose a non matrix var result for var i 0 i m length i result push for var j 0 j m i length j result i push m j i result matrix true return result Vector Functions function dot u v if u length v length throw dot vectors are not the same dimension var sum 0 0 for var i 0 i u length i sum u i v i return sum function negate u var result for var i 0 i u length i result push u i return result function cross u v if Array isArray u u length 3 throw cross first argument is not a vector of at least 3 if Array isArray v v length 3 throw cross second argument is not a vector of at least 3 var result u 1 v 2 u 2 v 1 u 2 v 0 u 0 v 2 u 0 v 1 u 1 v 0 return result function length u return Math sqrt dot u u function calculateNormalVectorFromPoints a b c var vecV subtract b a var vecW subtract c a return cross vecV vecW function normalize u excludeLastComponent if excludeLastComponent var last u pop var len length u if isFinite len throw normalize vector u has zero length for var i 0 i u length i u i len if excludeLastComponent u push last return u function mix u v s if typeof s number throw mix the last paramter s must be a number if u length v length throw vector dimension mismatch var result for var i 0 i u length i result push 1 0 s u i s v i return result Vector and Matrix functions function scale s u if Array isArray u throw scale second parameter u is not a vector var result for var i 0 i u length i result push s u i return result function flatten v if v matrix true v transpose v var n v length var elemsAreArrays false if Array isArray v 0 elemsAreArrays true n v 0 length var floats new Float32Array n if elemsAreArrays var idx 0 for var i 0 i v length i for var j 0 j v i length j floats idx v i j else for var i 0 i v length i floats i v i return floats var sizeof vec2 new Float32Array flatten vec2 byteLength vec3 new Float32Array flatten vec3 byteLength vec4 new Float32Array flatten vec4 byteLength mat2 new Float32Array flatten mat2 byteLength mat3 new Float32Array flatten mat3 byteLength mat4 new Float32Array flatten mat4 byteLength new functions 5 2 2015 printing function printm m if m length 2 for var i 0 i m length i console log m i 0 m i 1 else if m length 3 for var i 0 i m length i console log m i 0 m i 1 m i 2 else if m length 4 for var i 0 i m length i console log m i 0 m i 1 m i 2 m i 3 determinants function det2 m return m 0 0 m 1 1 m 0 1 m 1 0 function det3 m var d m 0 0 m 1 1 m 2 2 m 0 1 m 1 2 m 2 0 m 0 2 m 2 1 m 1 0 m 2 0 m 1 1 m 0 2 m 1 0 m 0 1 m 2 2 m 0 0 m 1 2 m 2 1 return d function det4 m var m0 vec3 m 1 1 m 1 2 m 1 3 vec3 m 2 1 m 2 2 m 2 3 vec3 m 3 1 m 3 2 m 3 3 var m1 vec3 m 1 0 m 1 2 m 1 3 vec3 m 2 0 m 2 2 m 2 3 vec3 m 3 0 m 3 2 m 3 3 var m2 vec3 m 1 0 m 1 1 m 1 3 vec3 m 2 0 m 2 1 m 2 3 vec3 m 3 0 m 3 1 m 3 3 var m3 vec3 m 1 0 m 1 1 m 1 2 vec3 m 2 0 m 2 1 m 2 2 vec3 m 3 0 m 3 1 m 3 2 return m 0 0 det3 m0 m 0 1 det3 m1 m 0 2 det3 m2 m 0 3 det3 m3 function det m if m matrix true console log not a matrix if m length 2 return det2 m if m length 3 return det3 m if m length 4 return det4 m inverses function inverse2 m var a mat2 var d det2 m a 0 0 m 1 1 d a 0 1 m 0 1 d a 1 0 m 1 0 d a 1 1 m 0 0 d a matrix true return a function inverse3 m var a mat3 var d det3 m var a00 vec2 m 1 1 m 1 2 vec2 m 2 1 m 2 2 var a01 vec2 m 1 0 m 1 2 vec2 m 2 0 m 2 2 var a02 vec2 m 1 0 m 1 1 vec2 m 2 0 m 2 1 var a10 vec2 m 0 1 m 0 2 vec2 m 2 1 m 2 2 var a11 vec2 m 0 0 m 0 2 vec2 m 2 0 m 2 2 var a12 vec2 m 0 0 m 0 1 vec2 m 2 0 m 2 1 var a20 vec2 m 0 1 m 0 2 vec2 m 1 1 m 1 2 var a21 vec2 m 0 0 m 0 2 vec2 m 1 0 m 1 2 var a22 vec2 m 0 0 m 0 1 vec2 m 1 0 m 1 1 a 0 0 det2 a00 d a 0 1 det2 a10 d a 0 2 det2 a20 d a 1 0 det2 a01 d a 1 1 det2 a11 d a 1 2 det2 a21 d a 2 0 det2 a02 d a 2 1 det2 a12 d a 2 2 det2 a22 d return a function inverse4 m var a mat4 var d det4 m var a00 vec3 m 1 1 m 1 2 m 1 3 vec3 m 2 1 m 2 2 m 2 3 vec3 m 3 1 m 3 2 m 3 3 var a01 vec3 m 1 0 m 1 2 m 1 3 vec3 m 2 0 m 2 2 m 2 3 vec3 m 3 0 m 3 2 m 3 3 var a02 vec3 m 1 0 m 1 1 m 1 3 vec3 m 2 0 m 2 1 m 2 3 vec3 m 3 0 m 3 1 m 3 3 var a03 vec3 m 1 0 m 1 1 m 1 2 vec3 m 2 0 m 2 1 m 2 2 vec3 m 3 0 m 3 1 m 3 2 var a10 vec3 m 0 1 m 0 2 m 0 3 vec3 m 2 1 m 2 2 m 2 3 vec3 m 3 1 m 3 2 m 3 3 var a11 vec3 m 0 0 m 0 2 m 0 3 vec3 m 2 0 m 2 2 m 2 3 vec3 m 3 0 m 3 2 m 3 3 var a12 vec3 m 0 0 m 0 1 m 0 3 vec3 m 2 0 m 2 1 m 2 3 vec3 m 3 0 m 3 1 m 3 3 var a13 vec3 m 0 0 m 0 1 m 0 2 vec3 m 2 0 m 2 1 m 2 2 vec3 m 3 0 m 3 1 m 3 2 var a20 vec3 m 0 1 m 0 2 m 0 3 vec3 m 1 1 m 1 2 m 1 3 vec3 m 3 1 m 3 2 m 3 3 var a21 vec3 m 0 0 m 0 2 m 0 3 vec3 m 1 0 m 1 2 m 1 3 vec3 m 3 0 m 3 2 m 3 3 var a22 vec3 m 0 0 m 0 1 m 0 3 vec3 m 1 0 m 1 1 m 1 3 vec3 m 3 0 m 3 1 m 3 3 var a23 vec3 m 0 0 m 0 1 m 0 2 vec3 m 1 0 m 1 1 m 1 2 vec3 m 3 0 m 3 1 m 3 2 var a30 vec3 m 0 1 m 0 2 m 0 3 vec3 m 1 1 m 1 2 m 1 3 vec3 m 2 1 m 2 2 m 2 3 var a31 vec3 m 0 0 m 0 2 m 0 3 vec3 m 1 0 m 1 2 m 1 3 vec3 m 2 0 m 2 2 m 2 3 var a32 vec3 m 0 0 m 0 1 m 0 3 vec3 m 1 0 m 1 1 m 1 3 vec3 m 2 0 m 2 1 m 2 3 var a33 vec3 m 0 0 m 0 1 m 0 2 vec3 m 1 0 m 1 1 m 1 2 vec3 m 2 0 m 2 1 m 2 2 a 0 0 det3 a00 d a 0 1 det3 a10 d a 0 2 det3 a20 d a 0 3 det3 a30 d a 1 0 det3 a01 d a 1 1 det3 a11 d a 1 2 det3 a21 d a 1 3 det3 a31 d a 2 0 det3 a02 d a 2 1 det3 a12 d a 2 2 det3 a22 d a 2 3 det3 a32 d a 3 0 det3 a03 d a 3 1 det3 a13 d a 3 2 det3 a23 d a 3 3 det3 a33 d return a function inverse m if m matrix true console log not a matrix if m length 2 return inverse2 m if m length 3 return inverse3 m if m length 4 return inverse4 m function normalMatrix m flag var a mat4 a inverse transpose m if flag true return a else var b mat3 for var i 0 i 3 i for var j 0 j 3 j b i j a i j return b console log read tests var v vec2 console log v var v new vec2 1 console log v

top bottom h result 2 3 near far d return result function perspective fovy aspect near far var f 1 0 Math tan radians fovy 2 var d far near var result mat4 result 0 0 f aspect result 1 1 f result 2 2 near far d result 2 3 2 near far d result 3 2 1 result 3 3 0 0 return result Matrix Functions function transpose m if m matrix return transpose trying to transpose a non matrix var result for var i 0 i m length i result push for var j 0 j m i length j result i push m j i result matrix true return result Vector Functions function dot u v if u length v length throw dot vectors are not the same dimension var sum 0 0 for var i 0 i u length i sum u i v i return sum function negate u var result for var i 0 i u length i result push u i return result function cross u v if Array isArray u u length 3 throw cross first argument is not a vector of at least 3 if Array isArray v v length 3 throw cross second argument is not a vector of at least 3 var result u 1 v 2 u 2 v 1 u 2 v 0 u 0 v 2 u 0 v 1 u 1 v 0 return result function length u return Math sqrt dot u u function calculateNormalVectorFromPoints a b c var vecV subtract b a var vecW subtract c a return cross vecV vecW function normalize u excludeLastComponent if excludeLastComponent var last u pop var len length u if isFinite len throw normalize vector u has zero length for var i 0 i u length i u i len if excludeLastComponent u push last return u function mix u v s if typeof s number throw mix the last paramter s must be a number if u length v length throw vector dimension mismatch var result for var i 0 i u length i result push 1 0 s u i s v i return result Vector and Matrix functions function scale s u if Array isArray u throw scale second parameter u is not a vector var result for var i 0 i u length i result push s u i return result function flatten v if v matrix true v transpose v var n v length var elemsAreArrays false if Array isArray v 0 elemsAreArrays true n v 0 length var floats new Float32Array n if elemsAreArrays var idx 0 for var i 0 i v length i for var j 0 j v i length j floats idx v i j else for var i 0 i v length i floats i v i return floats var sizeof vec2 new Float32Array flatten vec2 byteLength vec3 new Float32Array flatten vec3 byteLength vec4 new Float32Array flatten vec4 byteLength mat2 new Float32Array flatten mat2 byteLength mat3 new Float32Array flatten mat3 byteLength mat4 new Float32Array flatten mat4 byteLength new functions 5 2 2015 printing function printm m if m length 2 for var i 0 i m length i console log m i 0 m i 1 else if m length 3 for var i 0 i m length i console log m i 0 m i 1 m i 2 else if m length 4 for var i 0 i m length i console log m i 0 m i 1 m i 2 m i 3 determinants function det2 m return m 0 0 m 1 1 m 0 1 m 1 0 function det3 m var d m 0 0 m 1 1 m 2 2 m 0 1 m 1 2 m 2 0 m 0 2 m 2 1 m 1 0 m 2 0 m 1 1 m 0 2 m 1 0 m 0 1 m 2 2 m 0 0 m 1 2 m 2 1 return d function det4 m var m0 vec3 m 1 1 m 1 2 m 1 3 vec3 m 2 1 m 2 2 m 2 3 vec3 m 3 1 m 3 2 m 3 3 var m1 vec3 m 1 0 m 1 2 m 1 3 vec3 m 2 0 m 2 2 m 2 3 vec3 m 3 0 m 3 2 m 3 3 var m2 vec3 m 1 0 m 1 1 m 1 3 vec3 m 2 0 m 2 1 m 2 3 vec3 m 3 0 m 3 1 m 3 3 var m3 vec3 m 1 0 m 1 1 m 1 2 vec3 m 2 0 m 2 1 m 2 2 vec3 m 3 0 m 3 1 m 3 2 return m 0 0 det3 m0 m 0 1 det3 m1 m 0 2 det3 m2 m 0 3 det3 m3 function det m if m matrix true console log not a matrix if m length 2 return det2 m if m length 3 return det3 m if m length 4 return det4 m inverses function inverse2 m var a mat2 var d det2 m a 0 0 m 1 1 d a 0 1 m 0 1 d a 1 0 m 1 0 d a 1 1 m 0 0 d a matrix true return a function inverse3 m var a mat3 var d det3 m var a00 vec2 m 1 1 m 1 2 vec2 m 2 1 m 2 2 var a01 vec2 m 1 0 m 1 2 vec2 m 2 0 m 2 2 var a02 vec2 m 1 0 m 1 1 vec2 m 2 0 m 2 1 var a10 vec2 m 0 1 m 0 2 vec2 m 2 1 m 2 2 var a11 vec2 m 0 0 m 0 2 vec2 m 2 0 m 2 2 var a12 vec2 m 0 0 m 0 1 vec2 m 2 0 m 2 1 var a20 vec2 m 0 1 m 0 2 vec2 m 1 1 m 1 2 var a21 vec2 m 0 0 m 0 2 vec2 m 1 0 m 1 2 var a22 vec2 m 0 0 m 0 1 vec2 m 1 0 m 1 1 a 0 0 det2 a00 d a 0 1 det2 a10 d a 0 2 det2 a20 d a 1 0 det2 a01 d a 1 1 det2 a11 d a 1 2 det2 a21 d a 2 0 det2 a02 d a 2 1 det2 a12 d a 2 2 det2 a22 d return a function inverse4 m var a mat4 var d det4 m var a00 vec3 m 1 1 m 1 2 m 1 3 vec3 m 2 1 m 2 2 m 2 3 vec3 m 3 1 m 3 2 m 3 3 var a01 vec3 m 1 0 m 1 2 m 1 3 vec3 m 2 0 m 2 2 m 2 3 vec3 m 3 0 m 3 2 m 3 3 var a02 vec3 m 1 0 m 1 1 m 1 3 vec3 m 2 0 m 2 1 m 2 3 vec3 m 3 0 m 3 1 m 3 3 var a03 vec3 m 1 0 m 1 1 m 1 2 vec3 m 2 0 m 2 1 m 2 2 vec3 m 3 0 m 3 1 m 3 2 var a10 vec3 m 0 1 m 0 2 m 0 3 vec3 m 2 1 m 2 2 m 2 3 vec3 m 3 1 m 3 2 m 3 3 var a11 vec3 m 0 0 m 0 2 m 0 3 vec3 m 2 0 m 2 2 m 2 3 vec3 m 3 0 m 3 2 m 3 3 var a12 vec3 m 0 0 m 0 1 m 0 3 vec3 m 2 0 m 2 1 m 2 3 vec3 m 3 0 m 3 1 m 3 3 var a13 vec3 m 0 0 m 0 1 m 0 2 vec3 m 2 0 m 2 1 m 2 2 vec3 m 3 0 m 3 1 m 3 2 var a20 vec3 m 0 1 m 0 2 m 0 3 vec3 m 1 1 m 1 2 m 1 3 vec3 m 3 1 m 3 2 m 3 3 var a21 vec3 m 0 0 m 0 2 m 0 3 vec3 m 1 0 m 1 2 m 1 3 vec3 m 3 0 m 3 2 m 3 3 var a22 vec3 m 0 0 m 0 1 m 0 3 vec3 m 1 0 m 1 1 m 1 3 vec3 m 3 0 m 3 1 m 3 3 var a23 vec3 m 0 0 m 0 1 m 0 2 vec3 m 1 0 m 1 1 m 1 2 vec3 m 3 0 m 3 1 m 3 2 var a30 vec3 m 0 1 m 0 2 m 0 3 vec3 m 1 1 m 1 2 m 1 3 vec3 m 2 1 m 2 2 m 2 3 var a31 vec3 m 0 0 m 0 2 m 0 3 vec3 m 1 0 m 1 2 m 1 3 vec3 m 2 0 m 2 2 m 2 3 var a32 vec3 m 0 0 m 0 1 m 0 3 vec3 m 1 0 m 1 1 m 1 3 vec3 m 2 0 m 2 1 m 2 3 var a33 vec3 m 0 0 m 0 1 m 0 2 vec3 m 1 0 m 1 1 m 1 2 vec3 m 2 0 m 2 1 m 2 2 a 0 0 det3 a00 d a 0 1 det3 a10 d a 0 2 det3 a20 d a 0 3 det3 a30 d a 1 0 det3 a01 d a 1 1 det3 a11 d a 1 2 det3 a21 d a 1 3 det3 a31 d a 2 0 det3 a02 d a 2 1 det3 a12 d a 2 2 det3 a22 d a 2 3 det3 a32 d a 3 0 det3 a03 d a 3 1 det3 a13 d a 3 2 det3 a23 d a 3 3 det3 a33 d return a function inverse m if m matrix true console log not a matrix if m length 2 return inverse2 m if m length 3 return inverse3 m if m length 4 return inverse4 m function normalMatrix m flag var a mat4 a inverse transpose m if flag true return a else var b mat3 for var i 0 i 3 i for var j 0 j 3 j b i j a i j return b console log read tests var v vec2 console log v var v new vec2 1 console log v

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